def thermalblock_demo(args): args = parse_arguments(args) pool = new_parallel_pool(ipython_num_engines=args['--ipython-engines'], ipython_profile=args['--ipython-profile']) if args['--fenics']: d, d_summary = discretize_fenics(args['XBLOCKS'], args['YBLOCKS'], args['--grid'], args['--order']) else: d, d_summary = discretize_pymor(args['XBLOCKS'], args['YBLOCKS'], args['--grid'], args['--list-vector-array']) if args['--cache-region'] != 'none': d.enable_caching(args['--cache-region']) if args['--plot-solutions']: print('Showing some solutions') Us = tuple() legend = tuple() for mu in d.parameter_space.sample_randomly(2): print('Solving for diffusion = \n{} ... '.format(mu['diffusion'])) sys.stdout.flush() Us = Us + (d.solve(mu),) legend = legend + (str(mu['diffusion']),) d.visualize(Us, legend=legend, title='Detailed Solutions for different parameters', separate_colorbars=False, block=True) print('RB generation ...') # define estimator for coercivity constant from pymor.parameters.functionals import ExpressionParameterFunctional coercivity_estimator = ExpressionParameterFunctional('min(diffusion)', d.parameter_type) # inner product for computation of Riesz representatives error_product = d.h1_0_semi_product if args['--estimator-norm'] == 'h1' else None if args['--reductor'] == 'residual_basis': from pymor.reductors.stationary import reduce_stationary_coercive reductor = partial(reduce_stationary_coercive, error_product=error_product, coercivity_estimator=coercivity_estimator) elif args['--reductor'] == 'traditional': from pymor.reductors.linear import reduce_stationary_affine_linear reductor = partial(reduce_stationary_affine_linear, error_product=error_product, coercivity_estimator=coercivity_estimator) else: assert False # this should never happen if args['--pod']: rd, rc, red_summary = reduce_pod(d=d, reductor=reductor, snapshots_per_block=args['SNAPSHOTS'], basis_size=args['RBSIZE'], product_name=args['--pod-product']) else: rd, rc, red_summary = reduce_greedy(d=d, reductor=reductor, snapshots_per_block=args['SNAPSHOTS'], extension_alg_name=args['--extension-alg'], max_extensions=args['RBSIZE'], use_estimator=not args['--without-estimator'], pool=pool) if args['--pickle']: print('\nWriting reduced discretization to file {} ...'.format(args['--pickle'] + '_reduced')) with open(args['--pickle'] + '_reduced', 'w') as f: dump(rd, f) if not args['--fenics']: # FEniCS data structures do not support serialization print('Writing detailed discretization and reconstructor to file {} ...' .format(args['--pickle'] + '_detailed')) with open(args['--pickle'] + '_detailed', 'w') as f: dump((d, rc), f) print('\nSearching for maximum error on random snapshots ...') results = reduction_error_analysis(rd, discretization=d, reconstructor=rc, estimator=True, error_norms=(d.h1_0_semi_norm, d.l2_norm), condition=True, test_mus=args['--test'], basis_sizes=0 if args['--plot-error-sequence'] else 1, plot=args['--plot-error-sequence'], pool=pool) print('\n*** RESULTS ***\n') print(d_summary) print(red_summary) print(results['summary']) sys.stdout.flush() if args['--plot-error-sequence']: from matplotlib import pyplot as plt plt.show(results['figure']) if args['--plot-err']: mumax = results['max_error_mus'][0, -1] U = d.solve(mumax) URB = rc.reconstruct(rd.solve(mumax)) d.visualize((U, URB, U - URB), legend=('Detailed Solution', 'Reduced Solution', 'Error'), title='Maximum Error Solution', separate_colorbars=True, block=True)
def main( exp_min: float = Argument(..., help='Minimal exponent'), exp_max: float = Argument(..., help='Maximal exponent'), ei_snapshots: int = Argument( ..., help='Number of snapshots for empirical interpolation.'), ei_size: int = Argument(..., help='Number of interpolation DOFs.'), snapshots: int = Argument( ..., help='Number of snapshots for basis generation.'), rb_size: int = Argument(..., help='Size of the reduced basis.'), cache_region: Choices('none memory disk persistent') = Option( 'disk', help='Name of cache region to use for caching solution snapshots.' ), ei_alg: Choices('ei_greedy deim') = Option( 'ei_greedy', help='Interpolation algorithm to use.'), grid: int = Option(60, help='Use grid with (2*NI)*NI elements.'), grid_type: Choices('rect tria') = Option('rect', help='Type of grid to use.'), initial_data: Choices('sin bump') = Option( 'sin', help='Select the initial data (sin, bump).'), ipython_engines: int = Option( 0, help= 'If positive, the number of IPython cluster engines to use for parallel greedy search. ' 'If zero, no parallelization is performed.'), ipython_profile: str = Option( None, help='IPython profile to use for parallelization.'), lxf_lambda: float = Option( 1., help='Parameter lambda in Lax-Friedrichs flux.'), periodic: bool = Option( True, help ='If not, solve with dirichlet boundary conditions on left and bottom boundary.' ), nt: int = Option(100, help='Number of time steps.'), num_flux: Choices('lax_friedrichs engquist_osher') = Option( 'engquist_osher', help='Numerical flux to use.'), plot_err: bool = Option(False, help='Plot error.'), plot_ei_err: bool = Option(False, help='Plot empirical interpolation error.'), plot_error_landscape: bool = Option( False, help='Calculate and show plot of reduction error vs. basis sizes.' ), plot_error_landscape_M: int = Option( 10, help='Number of collateral basis sizes to test.'), plot_error_landscape_N: int = Option( 10, help='Number of basis sizes to test.'), plot_solutions: bool = Option(False, help='Plot some example solutions.'), test: int = Option( 10, help='Number of snapshots to use for stochastic error estimation.' ), vx: float = Option(1., help='Speed in x-direction.'), vy: float = Option(1., help='Speed in y-direction.'), ): """Model order reduction of a two-dimensional Burgers-type equation (see pymor.analyticalproblems.burgers) using the reduced basis method with empirical operator interpolation. """ print('Setup Problem ...') problem = burgers_problem_2d(vx=vx, vy=vy, initial_data_type=initial_data.value, parameter_range=(exp_min, exp_max), torus=periodic) print('Discretize ...') if grid_type == 'rect': grid *= 1. / math.sqrt(2) fom, _ = discretize_instationary_fv( problem, diameter=1. / grid, grid_type=RectGrid if grid_type == 'rect' else TriaGrid, num_flux=num_flux.value, lxf_lambda=lxf_lambda, nt=nt) if cache_region != 'none': # building a cache_id is only needed for persistent CacheRegions cache_id = ( f"pymordemos.burgers_ei {vx} {vy} {initial_data}" f"{periodic} {grid} {grid_type} {num_flux} {lxf_lambda} {nt}") fom.enable_caching(cache_region.value, cache_id) print(fom.operator.grid) print(f'The parameters are {fom.parameters}') if plot_solutions: print('Showing some solutions') Us = () legend = () for mu in problem.parameter_space.sample_uniformly(4): print(f"Solving for exponent = {mu['exponent']} ... ") sys.stdout.flush() Us = Us + (fom.solve(mu), ) legend = legend + (f"exponent: {mu['exponent']}", ) fom.visualize(Us, legend=legend, title='Detailed Solutions', block=True) pool = new_parallel_pool(ipython_num_engines=ipython_engines, ipython_profile=ipython_profile) eim, ei_data = interpolate_operators( fom, ['operator'], problem.parameter_space.sample_uniformly(ei_snapshots), error_norm=fom.l2_norm, product=fom.l2_product, max_interpolation_dofs=ei_size, alg=ei_alg.value, pool=pool) if plot_ei_err: print('Showing some EI errors') ERRs = () legend = () for mu in problem.parameter_space.sample_randomly(2): print(f"Solving for exponent = \n{mu['exponent']} ... ") sys.stdout.flush() U = fom.solve(mu) U_EI = eim.solve(mu) ERR = U - U_EI ERRs = ERRs + (ERR, ) legend = legend + (f"exponent: {mu['exponent']}", ) print(f'Error: {np.max(fom.l2_norm(ERR))}') fom.visualize(ERRs, legend=legend, title='EI Errors', separate_colorbars=True) print('Showing interpolation DOFs ...') U = np.zeros(U.dim) dofs = eim.operator.interpolation_dofs U[dofs] = np.arange(1, len(dofs) + 1) U[eim.operator.source_dofs] += int(len(dofs) / 2) fom.visualize(fom.solution_space.make_array(U), title='Interpolation DOFs') print('RB generation ...') reductor = InstationaryRBReductor(eim) greedy_data = rb_greedy( fom, reductor, problem.parameter_space.sample_uniformly(snapshots), use_error_estimator=False, error_norm=lambda U: np.max(fom.l2_norm(U)), extension_params={'method': 'pod'}, max_extensions=rb_size, pool=pool) rom = greedy_data['rom'] print('\nSearching for maximum error on random snapshots ...') tic = time.perf_counter() mus = problem.parameter_space.sample_randomly(test) def error_analysis(N, M): print(f'N = {N}, M = {M}: ', end='') rom = reductor.reduce(N) rom = rom.with_(operator=rom.operator.with_cb_dim(M)) l2_err_max = -1 mumax = None for mu in mus: print('.', end='') sys.stdout.flush() u = rom.solve(mu) URB = reductor.reconstruct(u) U = fom.solve(mu) l2_err = np.max(fom.l2_norm(U - URB)) l2_err = np.inf if not np.isfinite(l2_err) else l2_err if l2_err > l2_err_max: l2_err_max = l2_err mumax = mu print() return l2_err_max, mumax error_analysis = np.frompyfunc(error_analysis, 2, 2) real_rb_size = len(reductor.bases['RB']) real_cb_size = len(ei_data['basis']) if plot_error_landscape: N_count = min(real_rb_size - 1, plot_error_landscape_N) M_count = min(real_cb_size - 1, plot_error_landscape_M) Ns = np.linspace(1, real_rb_size, N_count).astype(np.int) Ms = np.linspace(1, real_cb_size, M_count).astype(np.int) else: Ns = np.array([real_rb_size]) Ms = np.array([real_cb_size]) N_grid, M_grid = np.meshgrid(Ns, Ms) errs, err_mus = error_analysis(N_grid, M_grid) errs = errs.astype(np.float) l2_err_max = errs[-1, -1] mumax = err_mus[-1, -1] toc = time.perf_counter() t_est = toc - tic print(''' *** RESULTS *** Problem: parameter range: ({exp_min}, {exp_max}) h: sqrt(2)/{grid} grid-type: {grid_type} initial-data: {initial_data} lxf-lambda: {lxf_lambda} nt: {nt} not-periodic: {periodic} num-flux: {num_flux} (vx, vy): ({vx}, {vy}) Greedy basis generation: number of ei-snapshots: {ei_snapshots} prescribed collateral basis size: {ei_size} actual collateral basis size: {real_cb_size} number of snapshots: {snapshots} prescribed basis size: {rb_size} actual basis size: {real_rb_size} elapsed time: {greedy_data[time]} Stochastic error estimation: number of samples: {test} maximal L2-error: {l2_err_max} (mu = {mumax}) elapsed time: {t_est} '''.format(**locals())) sys.stdout.flush() if plot_error_landscape: import matplotlib.pyplot as plt import mpl_toolkits.mplot3d # NOQA fig = plt.figure() ax = fig.add_subplot(111, projection='3d') # rescale the errors since matplotlib does not support logarithmic scales on 3d plots # https://github.com/matplotlib/matplotlib/issues/209 surf = ax.plot_surface(M_grid, N_grid, np.log(np.minimum(errs, 1)) / np.log(10), rstride=1, cstride=1, cmap='jet') plt.show() if plot_err: U = fom.solve(mumax) URB = reductor.reconstruct(rom.solve(mumax)) fom.visualize( (U, URB, U - URB), legend=('Detailed Solution', 'Reduced Solution', 'Error'), title='Maximum Error Solution', separate_colorbars=True) global test_results test_results = (ei_data, greedy_data)
def main(args): args = parse_arguments(args) pool = new_parallel_pool(ipython_num_engines=args["--ipython-engines"], ipython_profile=args["--ipython-profile"]) if args["--fenics"]: d, d_summary = discretize_fenics(args["XBLOCKS"], args["YBLOCKS"], args["--grid"], args["--order"]) else: d, d_summary = discretize_pymor(args["XBLOCKS"], args["YBLOCKS"], args["--grid"], args["--list-vector-array"]) if args["--cache-region"] != "none": d.enable_caching(args["--cache-region"]) if args["--plot-solutions"]: print("Showing some solutions") Us = () legend = () for mu in d.parameter_space.sample_randomly(2): print("Solving for diffusion = \n{} ... ".format(mu["diffusion"])) sys.stdout.flush() Us = Us + (d.solve(mu),) legend = legend + (str(mu["diffusion"]),) d.visualize( Us, legend=legend, title="Detailed Solutions for different parameters", separate_colorbars=False, block=True ) print("RB generation ...") # define estimator for coercivity constant from pymor.parameters.functionals import ExpressionParameterFunctional coercivity_estimator = ExpressionParameterFunctional("min(diffusion)", d.parameter_type) # inner product for computation of Riesz representatives product = d.h1_0_semi_product if args["--estimator-norm"] == "h1" else None if args["--reductor"] == "residual_basis": from pymor.reductors.coercive import reduce_coercive reductor = partial(reduce_coercive, product=product, coercivity_estimator=coercivity_estimator) elif args["--reductor"] == "traditional": from pymor.reductors.coercive import reduce_coercive_simple reductor = partial(reduce_coercive_simple, product=product, coercivity_estimator=coercivity_estimator) else: assert False # this should never happen if args["--alg"] == "naive": rd, rc, red_summary = reduce_naive(d=d, reductor=reductor, basis_size=args["RBSIZE"]) elif args["--alg"] == "greedy": parallel = not (args["--fenics"] and args["--greedy-without-estimator"]) # cannot pickle FEniCS discretization rd, rc, red_summary = reduce_greedy( d=d, reductor=reductor, snapshots_per_block=args["SNAPSHOTS"], extension_alg_name=args["--extension-alg"], max_extensions=args["RBSIZE"], use_estimator=not args["--greedy-without-estimator"], pool=pool if parallel else None, ) elif args["--alg"] == "adaptive_greedy": parallel = not (args["--fenics"] and args["--greedy-without-estimator"]) # cannot pickle FEniCS discretization rd, rc, red_summary = reduce_adaptive_greedy( d=d, reductor=reductor, validation_mus=args["SNAPSHOTS"], extension_alg_name=args["--extension-alg"], max_extensions=args["RBSIZE"], use_estimator=not args["--greedy-without-estimator"], rho=args["--adaptive-greedy-rho"], gamma=args["--adaptive-greedy-gamma"], theta=args["--adaptive-greedy-theta"], pool=pool if parallel else None, ) elif args["--alg"] == "pod": rd, rc, red_summary = reduce_pod( d=d, reductor=reductor, snapshots_per_block=args["SNAPSHOTS"], basis_size=args["RBSIZE"], product_name=args["--pod-product"], ) else: assert False # this should never happen if args["--pickle"]: print("\nWriting reduced discretization to file {} ...".format(args["--pickle"] + "_reduced")) with open(args["--pickle"] + "_reduced", "wb") as f: dump(rd, f) if not args["--fenics"]: # FEniCS data structures do not support serialization print( "Writing detailed discretization and reconstructor to file {} ...".format( args["--pickle"] + "_detailed" ) ) with open(args["--pickle"] + "_detailed", "wb") as f: dump((d, rc), f) print("\nSearching for maximum error on random snapshots ...") results = reduction_error_analysis( rd, discretization=d, reconstructor=rc, estimator=True, error_norms=(d.h1_0_semi_norm, d.l2_norm), condition=True, test_mus=args["--test"], basis_sizes=0 if args["--plot-error-sequence"] else 1, plot=args["--plot-error-sequence"], pool=None if args["--fenics"] else pool, # cannot pickle FEniCS discretization random_seed=999, ) print("\n*** RESULTS ***\n") print(d_summary) print(red_summary) print(results["summary"]) sys.stdout.flush() if args["--plot-error-sequence"]: import matplotlib.pyplot matplotlib.pyplot.show(results["figure"]) if args["--plot-err"]: mumax = results["max_error_mus"][0, -1] U = d.solve(mumax) URB = rc.reconstruct(rd.solve(mumax)) d.visualize( (U, URB, U - URB), legend=("Detailed Solution", "Reduced Solution", "Error"), title="Maximum Error Solution", separate_colorbars=True, block=True, ) return results
def main(args): args = docopt(__doc__, args) args['--cache-region'] = args['--cache-region'].lower() args['--grid'] = int(args['--grid']) args['--grid-type'] = args['--grid-type'].lower() assert args['--grid-type'] in ('rect', 'tria') args['--initial-data'] = args['--initial-data'].lower() assert args['--initial-data'] in ('sin', 'bump') args['--lxf-lambda'] = float(args['--lxf-lambda']) args['--nt'] = int(args['--nt']) args['--not-periodic'] = bool(args['--not-periodic']) args['--num-flux'] = args['--num-flux'].lower() assert args['--num-flux'] in ('lax_friedrichs', 'engquist_osher') args['--plot-error-landscape-N'] = int(args['--plot-error-landscape-N']) args['--plot-error-landscape-M'] = int(args['--plot-error-landscape-M']) args['--test'] = int(args['--test']) args['--vx'] = float(args['--vx']) args['--vy'] = float(args['--vy']) args['--ipython-engines'] = int(args['--ipython-engines']) args['EXP_MIN'] = int(args['EXP_MIN']) args['EXP_MAX'] = int(args['EXP_MAX']) args['EI_SNAPSHOTS'] = int(args['EI_SNAPSHOTS']) args['EISIZE'] = int(args['EISIZE']) args['SNAPSHOTS'] = int(args['SNAPSHOTS']) args['RBSIZE'] = int(args['RBSIZE']) print('Setup Problem ...') problem = burgers_problem_2d(vx=args['--vx'], vy=args['--vy'], initial_data_type=args['--initial-data'], parameter_range=(args['EXP_MIN'], args['EXP_MAX']), torus=not args['--not-periodic']) print('Discretize ...') if args['--grid-type'] == 'rect': args['--grid'] *= 1. / m.sqrt(2) d, _ = discretize_instationary_fv( problem, diameter=1. / args['--grid'], grid_type=RectGrid if args['--grid-type'] == 'rect' else TriaGrid, num_flux=args['--num-flux'], lxf_lambda=args['--lxf-lambda'], nt=args['--nt'] ) if args['--cache-region'] != 'none': d.enable_caching(args['--cache-region']) print(d.operator.grid) print('The parameter type is {}'.format(d.parameter_type)) if args['--plot-solutions']: print('Showing some solutions') Us = () legend = () for mu in d.parameter_space.sample_uniformly(4): print('Solving for exponent = {} ... '.format(mu['exponent'])) sys.stdout.flush() Us = Us + (d.solve(mu),) legend = legend + ('exponent: {}'.format(mu['exponent']),) d.visualize(Us, legend=legend, title='Detailed Solutions', block=True) pool = new_parallel_pool(ipython_num_engines=args['--ipython-engines'], ipython_profile=args['--ipython-profile']) ei_d, ei_data = interpolate_operators(d, ['operator'], d.parameter_space.sample_uniformly(args['EI_SNAPSHOTS']), # NOQA error_norm=d.l2_norm, max_interpolation_dofs=args['EISIZE'], pool=pool) if args['--plot-ei-err']: print('Showing some EI errors') ERRs = () legend = () for mu in d.parameter_space.sample_randomly(2): print('Solving for exponent = \n{} ... '.format(mu['exponent'])) sys.stdout.flush() U = d.solve(mu) U_EI = ei_d.solve(mu) ERR = U - U_EI ERRs = ERRs + (ERR,) legend = legend + ('exponent: {}'.format(mu['exponent']),) print('Error: {}'.format(np.max(d.l2_norm(ERR)))) d.visualize(ERRs, legend=legend, title='EI Errors', separate_colorbars=True) print('Showing interpolation DOFs ...') U = np.zeros(U.dim) dofs = ei_d.operator.interpolation_dofs U[dofs] = np.arange(1, len(dofs) + 1) U[ei_d.operator.source_dofs] += int(len(dofs)/2) d.visualize(d.solution_space.make_array(U), title='Interpolation DOFs') print('RB generation ...') reductor = GenericRBReductor(ei_d) greedy_data = greedy(d, reductor, d.parameter_space.sample_uniformly(args['SNAPSHOTS']), use_estimator=False, error_norm=lambda U: np.max(d.l2_norm(U)), extension_params={'method': 'pod'}, max_extensions=args['RBSIZE'], pool=pool) rd = greedy_data['rd'] print('\nSearching for maximum error on random snapshots ...') tic = time.time() mus = d.parameter_space.sample_randomly(args['--test']) def error_analysis(N, M): print('N = {}, M = {}: '.format(N, M), end='') rd = reductor.reduce(N) rd = rd.with_(operator=rd.operator.with_cb_dim(M)) l2_err_max = -1 mumax = None for mu in mus: print('.', end='') sys.stdout.flush() u = rd.solve(mu) URB = reductor.reconstruct(u) U = d.solve(mu) l2_err = np.max(d.l2_norm(U - URB)) l2_err = np.inf if not np.isfinite(l2_err) else l2_err if l2_err > l2_err_max: l2_err_max = l2_err mumax = mu print() return l2_err_max, mumax error_analysis = np.frompyfunc(error_analysis, 2, 2) real_rb_size = len(reductor.RB) real_cb_size = len(ei_data['basis']) if args['--plot-error-landscape']: N_count = min(real_rb_size - 1, args['--plot-error-landscape-N']) M_count = min(real_cb_size - 1, args['--plot-error-landscape-M']) Ns = np.linspace(1, real_rb_size, N_count).astype(np.int) Ms = np.linspace(1, real_cb_size, M_count).astype(np.int) else: Ns = np.array([real_rb_size]) Ms = np.array([real_cb_size]) N_grid, M_grid = np.meshgrid(Ns, Ms) errs, err_mus = error_analysis(N_grid, M_grid) errs = errs.astype(np.float) l2_err_max = errs[-1, -1] mumax = err_mus[-1, -1] toc = time.time() t_est = toc - tic print(''' *** RESULTS *** Problem: parameter range: ({args[EXP_MIN]}, {args[EXP_MAX]}) h: sqrt(2)/{args[--grid]} grid-type: {args[--grid-type]} initial-data: {args[--initial-data]} lxf-lambda: {args[--lxf-lambda]} nt: {args[--nt]} not-periodic: {args[--not-periodic]} num-flux: {args[--num-flux]} (vx, vy): ({args[--vx]}, {args[--vy]}) Greedy basis generation: number of ei-snapshots: {args[EI_SNAPSHOTS]} prescribed collateral basis size: {args[EISIZE]} actual collateral basis size: {real_cb_size} number of snapshots: {args[SNAPSHOTS]} prescribed basis size: {args[RBSIZE]} actual basis size: {real_rb_size} elapsed time: {greedy_data[time]} Stochastic error estimation: number of samples: {args[--test]} maximal L2-error: {l2_err_max} (mu = {mumax}) elapsed time: {t_est} '''.format(**locals())) sys.stdout.flush() if args['--plot-error-landscape']: import matplotlib.pyplot as plt import mpl_toolkits.mplot3d # NOQA fig = plt.figure() ax = fig.add_subplot(111, projection='3d') # we have to rescale the errors since matplotlib does not support logarithmic scales on 3d plots # https://github.com/matplotlib/matplotlib/issues/209 surf = ax.plot_surface(M_grid, N_grid, np.log(np.minimum(errs, 1)) / np.log(10), rstride=1, cstride=1, cmap='jet') plt.show() if args['--plot-err']: U = d.solve(mumax) URB = reductor.reconstruct(rd.solve(mumax)) d.visualize((U, URB, U - URB), legend=('Detailed Solution', 'Reduced Solution', 'Error'), title='Maximum Error Solution', separate_colorbars=True) return ei_data, greedy_data
def main(args): args = parse_arguments(args) pool = new_parallel_pool(ipython_num_engines=args['--ipython-engines'], ipython_profile=args['--ipython-profile']) if args['--fenics']: fom, fom_summary = discretize_fenics(args['XBLOCKS'], args['YBLOCKS'], args['--grid'], args['--order']) else: fom, fom_summary = discretize_pymor(args['XBLOCKS'], args['YBLOCKS'], args['--grid'], args['--list-vector-array']) if args['--cache-region'] != 'none': # building a cache_id is only needed for persistent CacheRegions cache_id = (f"pymordemos.thermalblock {args['--fenics']} {args['XBLOCKS']} {args['YBLOCKS']}" f"{args['--grid']} {args['--order']}") fom.enable_caching(args['--cache-region'], cache_id) if args['--plot-solutions']: print('Showing some solutions') Us = () legend = () for mu in fom.parameter_space.sample_randomly(2): print(f"Solving for diffusion = \n{mu['diffusion']} ... ") sys.stdout.flush() Us = Us + (fom.solve(mu),) legend = legend + (str(mu['diffusion']),) fom.visualize(Us, legend=legend, title='Detailed Solutions for different parameters', separate_colorbars=False, block=True) print('RB generation ...') # define estimator for coercivity constant from pymor.parameters.functionals import ExpressionParameterFunctional coercivity_estimator = ExpressionParameterFunctional('min(diffusion)', fom.parameter_type) # inner product for computation of Riesz representatives product = fom.h1_0_semi_product if args['--product'] == 'h1' else None if args['--reductor'] == 'residual_basis': from pymor.reductors.coercive import CoerciveRBReductor reductor = CoerciveRBReductor(fom, product=product, coercivity_estimator=coercivity_estimator, check_orthonormality=False) elif args['--reductor'] == 'traditional': from pymor.reductors.coercive import SimpleCoerciveRBReductor reductor = SimpleCoerciveRBReductor(fom, product=product, coercivity_estimator=coercivity_estimator, check_orthonormality=False) else: assert False # this should never happen if args['--alg'] == 'naive': rom, red_summary = reduce_naive(fom=fom, reductor=reductor, basis_size=args['RBSIZE']) elif args['--alg'] == 'greedy': parallel = not (args['--fenics'] and args['--greedy-without-estimator']) # cannot pickle FEniCS model rom, red_summary = reduce_greedy(fom=fom, reductor=reductor, snapshots_per_block=args['SNAPSHOTS'], extension_alg_name=args['--extension-alg'], max_extensions=args['RBSIZE'], use_estimator=not args['--greedy-without-estimator'], pool=pool if parallel else None) elif args['--alg'] == 'adaptive_greedy': parallel = not (args['--fenics'] and args['--greedy-without-estimator']) # cannot pickle FEniCS model rom, red_summary = reduce_adaptive_greedy(fom=fom, reductor=reductor, validation_mus=args['SNAPSHOTS'], extension_alg_name=args['--extension-alg'], max_extensions=args['RBSIZE'], use_estimator=not args['--greedy-without-estimator'], rho=args['--adaptive-greedy-rho'], gamma=args['--adaptive-greedy-gamma'], theta=args['--adaptive-greedy-theta'], pool=pool if parallel else None) elif args['--alg'] == 'pod': rom, red_summary = reduce_pod(fom=fom, reductor=reductor, snapshots_per_block=args['SNAPSHOTS'], basis_size=args['RBSIZE']) else: assert False # this should never happen if args['--pickle']: print(f"\nWriting reduced model to file {args['--pickle']}_reduced ...") with open(args['--pickle'] + '_reduced', 'wb') as f: dump(rom, f) if not args['--fenics']: # FEniCS data structures do not support serialization print(f"Writing detailed model and reductor to file {args['--pickle']}_detailed ...") with open(args['--pickle'] + '_detailed', 'wb') as f: dump((fom, reductor), f) print('\nSearching for maximum error on random snapshots ...') results = reduction_error_analysis(rom, fom=fom, reductor=reductor, estimator=True, error_norms=(fom.h1_0_semi_norm, fom.l2_norm), condition=True, test_mus=args['--test'], basis_sizes=0 if args['--plot-error-sequence'] else 1, plot=args['--plot-error-sequence'], pool=None if args['--fenics'] else pool, # cannot pickle FEniCS model random_seed=999) print('\n*** RESULTS ***\n') print(fom_summary) print(red_summary) print(results['summary']) sys.stdout.flush() if args['--plot-error-sequence']: import matplotlib.pyplot matplotlib.pyplot.show(results['figure']) if args['--plot-err']: mumax = results['max_error_mus'][0, -1] U = fom.solve(mumax) URB = reductor.reconstruct(rom.solve(mumax)) fom.visualize((U, URB, U - URB), legend=('Detailed Solution', 'Reduced Solution', 'Error'), title='Maximum Error Solution', separate_colorbars=True, block=True) return results
def thermalblock_demo(args): args['--grid'] = int(args['--grid']) args['RBSIZE'] = int(args['RBSIZE']) args['--test'] = int(args['--test']) args['--ipython-engines'] = int(args['--ipython-engines']) args['--extension-alg'] = args['--extension-alg'].lower() assert args['--extension-alg'] in {'trivial', 'gram_schmidt'} args['--product'] = args['--product'].lower() assert args['--product'] in {'trivial', 'h1'} args['--reductor'] = args['--reductor'].lower() assert args['--reductor'] in {'traditional', 'residual_basis'} args['--cache-region'] = args['--cache-region'].lower() args['--validation-mus'] = int(args['--validation-mus']) args['--rho'] = float(args['--rho']) args['--gamma'] = float(args['--gamma']) args['--theta'] = float(args['--theta']) problem = thermal_block_problem(num_blocks=(2, 2)) functionals = [ ExpressionParameterFunctional('diffusion[0]', {'diffusion': 2}), ExpressionParameterFunctional('diffusion[1]**2', {'diffusion': 2}), ExpressionParameterFunctional('diffusion[0]', {'diffusion': 2}), ExpressionParameterFunctional('diffusion[1]', {'diffusion': 2}) ] problem = problem.with_( diffusion=problem.diffusion.with_(coefficients=functionals), ) print('Discretize ...') fom, _ = discretize_stationary_cg(problem, diameter=1. / args['--grid']) if args['--list-vector-array']: from pymor.discretizers.builtin.list import convert_to_numpy_list_vector_array fom = convert_to_numpy_list_vector_array(fom) if args['--cache-region'] != 'none': # building a cache_id is only needed for persistent CacheRegions cache_id = f"pymordemos.thermalblock_adaptive {args['--grid']}" fom.enable_caching(args['--cache-region'], cache_id) if args['--plot-solutions']: print('Showing some solutions') Us = () legend = () for mu in problem.parameter_space.sample_randomly(2): print(f"Solving for diffusion = \n{mu['diffusion']} ... ") sys.stdout.flush() Us = Us + (fom.solve(mu), ) legend = legend + (str(mu['diffusion']), ) fom.visualize(Us, legend=legend, title='Detailed Solutions for different parameters', block=True) print('RB generation ...') product = fom.h1_0_semi_product if args['--product'] == 'h1' else None coercivity_estimator = ExpressionParameterFunctional( 'min([diffusion[0], diffusion[1]**2])', fom.parameters) reductors = { 'residual_basis': CoerciveRBReductor(fom, product=product, coercivity_estimator=coercivity_estimator), 'traditional': SimpleCoerciveRBReductor(fom, product=product, coercivity_estimator=coercivity_estimator) } reductor = reductors[args['--reductor']] pool = new_parallel_pool(ipython_num_engines=args['--ipython-engines'], ipython_profile=args['--ipython-profile']) greedy_data = rb_adaptive_greedy( fom, reductor, problem.parameter_space, validation_mus=args['--validation-mus'], rho=args['--rho'], gamma=args['--gamma'], theta=args['--theta'], use_estimator=not args['--without-estimator'], error_norm=fom.h1_0_semi_norm, max_extensions=args['RBSIZE'], visualize=not args['--no-visualize-refinement']) rom = greedy_data['rom'] if args['--pickle']: print( f"\nWriting reduced model to file {args['--pickle']}_reduced ...") with open(args['--pickle'] + '_reduced', 'wb') as f: dump(rom, f) print( f"Writing detailed model and reductor to file {args['--pickle']}_detailed ..." ) with open(args['--pickle'] + '_detailed', 'wb') as f: dump((fom, reductor), f) print('\nSearching for maximum error on random snapshots ...') results = reduction_error_analysis( rom, fom=fom, reductor=reductor, estimator=True, error_norms=(fom.h1_0_semi_norm, ), condition=True, test_mus=problem.parameter_space.sample_randomly(args['--test']), basis_sizes=25 if args['--plot-error-sequence'] else 1, plot=True, pool=pool) real_rb_size = rom.solution_space.dim print(''' *** RESULTS *** Problem: number of blocks: 2x2 h: sqrt(2)/{args[--grid]} Greedy basis generation: estimator disabled: {args[--without-estimator]} extension method: {args[--extension-alg]} product: {args[--product]} prescribed basis size: {args[RBSIZE]} actual basis size: {real_rb_size} elapsed time: {greedy_data[time]} '''.format(**locals())) print(results['summary']) sys.stdout.flush() if args['--plot-error-sequence']: from matplotlib import pyplot as plt plt.show(results['figure']) if args['--plot-err']: mumax = results['max_error_mus'][0, -1] U = fom.solve(mumax) URB = reductor.reconstruct(rom.solve(mumax)) fom.visualize( (U, URB, U - URB), legend=('Detailed Solution', 'Reduced Solution', 'Error'), title='Maximum Error Solution', separate_colorbars=True, block=True)
def main(args): args = docopt(__doc__, args) args['--cache-region'] = args['--cache-region'].lower() args['--ei-alg'] = args['--ei-alg'].lower() assert args['--ei-alg'] in ('ei_greedy', 'deim') args['--grid'] = int(args['--grid']) args['--grid-type'] = args['--grid-type'].lower() assert args['--grid-type'] in ('rect', 'tria') args['--initial-data'] = args['--initial-data'].lower() assert args['--initial-data'] in ('sin', 'bump') args['--lxf-lambda'] = float(args['--lxf-lambda']) args['--nt'] = int(args['--nt']) args['--not-periodic'] = bool(args['--not-periodic']) args['--num-flux'] = args['--num-flux'].lower() assert args['--num-flux'] in ('lax_friedrichs', 'engquist_osher') args['--plot-error-landscape-N'] = int(args['--plot-error-landscape-N']) args['--plot-error-landscape-M'] = int(args['--plot-error-landscape-M']) args['--test'] = int(args['--test']) args['--vx'] = float(args['--vx']) args['--vy'] = float(args['--vy']) args['--ipython-engines'] = int(args['--ipython-engines']) args['EXP_MIN'] = int(args['EXP_MIN']) args['EXP_MAX'] = int(args['EXP_MAX']) args['EI_SNAPSHOTS'] = int(args['EI_SNAPSHOTS']) args['EISIZE'] = int(args['EISIZE']) args['SNAPSHOTS'] = int(args['SNAPSHOTS']) args['RBSIZE'] = int(args['RBSIZE']) print('Setup Problem ...') problem = burgers_problem_2d(vx=args['--vx'], vy=args['--vy'], initial_data_type=args['--initial-data'], parameter_range=(args['EXP_MIN'], args['EXP_MAX']), torus=not args['--not-periodic']) print('Discretize ...') if args['--grid-type'] == 'rect': args['--grid'] *= 1. / math.sqrt(2) fom, _ = discretize_instationary_fv( problem, diameter=1. / args['--grid'], grid_type=RectGrid if args['--grid-type'] == 'rect' else TriaGrid, num_flux=args['--num-flux'], lxf_lambda=args['--lxf-lambda'], nt=args['--nt']) if args['--cache-region'] != 'none': fom.enable_caching(args['--cache-region']) print(fom.operator.grid) print(f'The parameter type is {fom.parameter_type}') if args['--plot-solutions']: print('Showing some solutions') Us = () legend = () for mu in fom.parameter_space.sample_uniformly(4): print(f"Solving for exponent = {mu['exponent']} ... ") sys.stdout.flush() Us = Us + (fom.solve(mu), ) legend = legend + (f"exponent: {mu['exponent']}", ) fom.visualize(Us, legend=legend, title='Detailed Solutions', block=True) pool = new_parallel_pool(ipython_num_engines=args['--ipython-engines'], ipython_profile=args['--ipython-profile']) eim, ei_data = interpolate_operators( fom, ['operator'], fom.parameter_space.sample_uniformly(args['EI_SNAPSHOTS']), # NOQA error_norm=fom.l2_norm, product=fom.l2_product, max_interpolation_dofs=args['EISIZE'], alg=args['--ei-alg'], pool=pool) if args['--plot-ei-err']: print('Showing some EI errors') ERRs = () legend = () for mu in fom.parameter_space.sample_randomly(2): print(f"Solving for exponent = \n{mu['exponent']} ... ") sys.stdout.flush() U = fom.solve(mu) U_EI = eim.solve(mu) ERR = U - U_EI ERRs = ERRs + (ERR, ) legend = legend + (f"exponent: {mu['exponent']}", ) print(f'Error: {np.max(fom.l2_norm(ERR))}') fom.visualize(ERRs, legend=legend, title='EI Errors', separate_colorbars=True) print('Showing interpolation DOFs ...') U = np.zeros(U.dim) dofs = eim.operator.interpolation_dofs U[dofs] = np.arange(1, len(dofs) + 1) U[eim.operator.source_dofs] += int(len(dofs) / 2) fom.visualize(fom.solution_space.make_array(U), title='Interpolation DOFs') print('RB generation ...') reductor = InstationaryRBReductor(eim) greedy_data = rb_greedy(fom, reductor, fom.parameter_space.sample_uniformly( args['SNAPSHOTS']), use_estimator=False, error_norm=lambda U: np.max(fom.l2_norm(U)), extension_params={'method': 'pod'}, max_extensions=args['RBSIZE'], pool=pool) rom = greedy_data['rom'] print('\nSearching for maximum error on random snapshots ...') tic = time.time() mus = fom.parameter_space.sample_randomly(args['--test']) def error_analysis(N, M): print(f'N = {N}, M = {M}: ', end='') rom = reductor.reduce(N) rom = rom.with_(operator=rom.operator.with_cb_dim(M)) l2_err_max = -1 mumax = None for mu in mus: print('.', end='') sys.stdout.flush() u = rom.solve(mu) URB = reductor.reconstruct(u) U = fom.solve(mu) l2_err = np.max(fom.l2_norm(U - URB)) l2_err = np.inf if not np.isfinite(l2_err) else l2_err if l2_err > l2_err_max: l2_err_max = l2_err mumax = mu print() return l2_err_max, mumax error_analysis = np.frompyfunc(error_analysis, 2, 2) real_rb_size = len(reductor.bases['RB']) real_cb_size = len(ei_data['basis']) if args['--plot-error-landscape']: N_count = min(real_rb_size - 1, args['--plot-error-landscape-N']) M_count = min(real_cb_size - 1, args['--plot-error-landscape-M']) Ns = np.linspace(1, real_rb_size, N_count).astype(np.int) Ms = np.linspace(1, real_cb_size, M_count).astype(np.int) else: Ns = np.array([real_rb_size]) Ms = np.array([real_cb_size]) N_grid, M_grid = np.meshgrid(Ns, Ms) errs, err_mus = error_analysis(N_grid, M_grid) errs = errs.astype(np.float) l2_err_max = errs[-1, -1] mumax = err_mus[-1, -1] toc = time.time() t_est = toc - tic print(''' *** RESULTS *** Problem: parameter range: ({args[EXP_MIN]}, {args[EXP_MAX]}) h: sqrt(2)/{args[--grid]} grid-type: {args[--grid-type]} initial-data: {args[--initial-data]} lxf-lambda: {args[--lxf-lambda]} nt: {args[--nt]} not-periodic: {args[--not-periodic]} num-flux: {args[--num-flux]} (vx, vy): ({args[--vx]}, {args[--vy]}) Greedy basis generation: number of ei-snapshots: {args[EI_SNAPSHOTS]} prescribed collateral basis size: {args[EISIZE]} actual collateral basis size: {real_cb_size} number of snapshots: {args[SNAPSHOTS]} prescribed basis size: {args[RBSIZE]} actual basis size: {real_rb_size} elapsed time: {greedy_data[time]} Stochastic error estimation: number of samples: {args[--test]} maximal L2-error: {l2_err_max} (mu = {mumax}) elapsed time: {t_est} '''.format(**locals())) sys.stdout.flush() if args['--plot-error-landscape']: import matplotlib.pyplot as plt import mpl_toolkits.mplot3d # NOQA fig = plt.figure() ax = fig.add_subplot(111, projection='3d') # we have to rescale the errors since matplotlib does not support logarithmic scales on 3d plots # https://github.com/matplotlib/matplotlib/issues/209 surf = ax.plot_surface(M_grid, N_grid, np.log(np.minimum(errs, 1)) / np.log(10), rstride=1, cstride=1, cmap='jet') plt.show() if args['--plot-err']: U = fom.solve(mumax) URB = reductor.reconstruct(rom.solve(mumax)) fom.visualize( (U, URB, U - URB), legend=('Detailed Solution', 'Reduced Solution', 'Error'), title='Maximum Error Solution', separate_colorbars=True) return ei_data, greedy_data
def thermalblock_demo(args): args['--grid'] = int(args['--grid']) args['RBSIZE'] = int(args['RBSIZE']) args['--test'] = int(args['--test']) args['--ipython-engines'] = int(args['--ipython-engines']) args['--estimator-norm'] = args['--estimator-norm'].lower() assert args['--estimator-norm'] in {'trivial', 'h1'} args['--extension-alg'] = args['--extension-alg'].lower() assert args['--extension-alg'] in {'trivial', 'gram_schmidt', 'h1_gram_schmidt'} args['--reductor'] = args['--reductor'].lower() assert args['--reductor'] in {'traditional', 'residual_basis'} args['--cache-region'] = args['--cache-region'].lower() args['--validation-mus'] = int(args['--validation-mus']) args['--rho'] = float(args['--rho']) args['--gamma'] = float(args['--gamma']) args['--theta'] = float(args['--theta']) print('Solving on TriaGrid(({0},{0}))'.format(args['--grid'])) print('Setup Problem ...') problem = ThermalBlockProblem(num_blocks=(2, 2)) functionals = [ExpressionParameterFunctional('diffusion[0]', {'diffusion': (2,)}), ExpressionParameterFunctional('diffusion[1]**2', {'diffusion': (2,)}), ExpressionParameterFunctional('diffusion[0]', {'diffusion': (2,)}), ExpressionParameterFunctional('diffusion[1]', {'diffusion': (2,)})] problem = EllipticProblem(domain=problem.domain, diffusion_functions=problem.diffusion_functions, diffusion_functionals=functionals, rhs=problem.rhs, parameter_space=CubicParameterSpace({'diffusion': (2,)}, 0.1, 1.)) print('Discretize ...') discretization, _ = discretize_elliptic_cg(problem, diameter=1. / args['--grid']) if args['--list-vector-array']: from pymor.playground.discretizers.numpylistvectorarray import convert_to_numpy_list_vector_array discretization = convert_to_numpy_list_vector_array(discretization) if args['--cache-region'] != 'none': discretization.enable_caching(args['--cache-region']) print('The parameter type is {}'.format(discretization.parameter_type)) if args['--plot-solutions']: print('Showing some solutions') Us = () legend = () for mu in discretization.parameter_space.sample_randomly(2): print('Solving for diffusion = \n{} ... '.format(mu['diffusion'])) sys.stdout.flush() Us = Us + (discretization.solve(mu),) legend = legend + (str(mu['diffusion']),) discretization.visualize(Us, legend=legend, title='Detailed Solutions for different parameters', block=True) print('RB generation ...') product = discretization.h1_0_semi_product if args['--estimator-norm'] == 'h1' else None coercivity_estimator=ExpressionParameterFunctional('min([diffusion[0], diffusion[1]**2])', discretization.parameter_type) reductors = {'residual_basis': partial(reduce_coercive, product=product, coercivity_estimator=coercivity_estimator), 'traditional': partial(reduce_coercive_simple, product=product, coercivity_estimator=coercivity_estimator)} reductor = reductors[args['--reductor']] extension_algorithms = {'trivial': trivial_basis_extension, 'gram_schmidt': gram_schmidt_basis_extension, 'h1_gram_schmidt': partial(gram_schmidt_basis_extension, product=discretization.h1_0_semi_product)} extension_algorithm = extension_algorithms[args['--extension-alg']] pool = new_parallel_pool(ipython_num_engines=args['--ipython-engines'], ipython_profile=args['--ipython-profile']) greedy_data = adaptive_greedy(discretization, reductor, validation_mus=args['--validation-mus'], rho=args['--rho'], gamma=args['--gamma'], theta=args['--theta'], use_estimator=not args['--without-estimator'], error_norm=discretization.h1_0_semi_norm, extension_algorithm=extension_algorithm, max_extensions=args['RBSIZE'], visualize=args['--visualize-refinement']) rb_discretization, reconstructor = greedy_data['reduced_discretization'], greedy_data['reconstructor'] if args['--pickle']: print('\nWriting reduced discretization to file {} ...'.format(args['--pickle'] + '_reduced')) with open(args['--pickle'] + '_reduced', 'wb') as f: dump(rb_discretization, f) print('Writing detailed discretization and reconstructor to file {} ...'.format(args['--pickle'] + '_detailed')) with open(args['--pickle'] + '_detailed', 'wb') as f: dump((discretization, reconstructor), f) print('\nSearching for maximum error on random snapshots ...') results = reduction_error_analysis(rb_discretization, discretization=discretization, reconstructor=reconstructor, estimator=True, error_norms=(discretization.h1_0_semi_norm,), condition=True, test_mus=args['--test'], basis_sizes=25 if args['--plot-error-sequence'] else 1, plot=True, pool=pool) real_rb_size = rb_discretization.solution_space.dim print(''' *** RESULTS *** Problem: number of blocks: 2x2 h: sqrt(2)/{args[--grid]} Greedy basis generation: estimator disabled: {args[--without-estimator]} estimator norm: {args[--estimator-norm]} extension method: {args[--extension-alg]} prescribed basis size: {args[RBSIZE]} actual basis size: {real_rb_size} elapsed time: {greedy_data[time]} '''.format(**locals())) print(results['summary']) sys.stdout.flush() if args['--plot-error-sequence']: from matplotlib import pyplot as plt plt.show(results['figure']) if args['--plot-err']: mumax = results['max_error_mus'][0, -1] U = discretization.solve(mumax) URB = reconstructor.reconstruct(rb_discretization.solve(mumax)) discretization.visualize((U, URB, U - URB), legend=('Detailed Solution', 'Reduced Solution', 'Error'), title='Maximum Error Solution', separate_colorbars=True, block=True)
def main( xblocks: int = Argument(..., help='Number of blocks in x direction.'), yblocks: int = Argument(..., help='Number of blocks in y direction.'), snapshots: int = Argument( ..., help='naive: ignored\n\n' 'greedy/pod: Number of training_set parameters per block ' '(in total SNAPSHOTS^(XBLOCKS * YBLOCKS) parameters).\n\n' 'adaptive_greedy: size of validation set.\n\n'), rbsize: int = Argument(..., help='Size of the reduced basis.'), adaptive_greedy_gamma: float = Option( 0.2, help='See pymor.algorithms.adaptivegreedy.'), adaptive_greedy_rho: float = Option( 1.1, help='See pymor.algorithms.adaptivegreedy.'), adaptive_greedy_theta: float = Option( 0., help='See pymor.algorithms.adaptivegreedy.'), alg: Choices('naive greedy adaptive_greedy pod') = Option( 'greedy', help='The model reduction algorithm to use.'), cache_region: Choices('none memory disk persistent') = Option( 'none', help='Name of cache region to use for caching solution snapshots.'), extension_alg: Choices('trivial gram_schmidt') = Option( 'gram_schmidt', help='Basis extension algorithm to be used.'), fenics: bool = Option(False, help='Use FEniCS model.'), greedy_with_error_estimator: bool = Option( True, help='Use error estimator for basis generation.'), grid: int = Option(100, help='Use grid with 4*NI*NI elements'), ipython_engines: int = Option( None, help='If positive, the number of IPython cluster engines to use for ' 'parallel greedy search. If zero, no parallelization is performed.'), ipython_profile: str = Option( None, help='IPython profile to use for parallelization.'), list_vector_array: bool = Option( False, help= 'Solve using ListVectorArray[NumpyVector] instead of NumpyVectorArray.' ), order: int = Option( 1, help= 'Polynomial order of the Lagrange finite elements to use in FEniCS.'), pickle: str = Option( None, help= 'Pickle reduced model, as well as reductor and high-dimensional model ' 'to files with this prefix.'), product: Choices('euclidean h1') = Option( 'h1', help= 'Product w.r.t. which to orthonormalize and calculate Riesz representatives.' ), plot_err: bool = Option(False, help='Plot error'), plot_error_sequence: bool = Option( False, help='Plot reduction error vs. basis size.'), plot_solutions: bool = Option(False, help='Plot some example solutions.'), reductor: Choices('traditional residual_basis') = Option( 'residual_basis', help='Reductor (error estimator) to choose.'), test: int = Option( 10, help='Use COUNT snapshots for stochastic error estimation.'), ): """Thermalblock demo.""" if fenics and cache_region != 'none': raise ValueError( 'Caching of high-dimensional solutions is not supported for FEniCS model.' ) if not fenics and order != 1: raise ValueError( 'Higher-order finite elements only supported for FEniCS model.') pool = new_parallel_pool(ipython_num_engines=ipython_engines, ipython_profile=ipython_profile) if fenics: fom, fom_summary = discretize_fenics(xblocks, yblocks, grid, order) else: fom, fom_summary = discretize_pymor(xblocks, yblocks, grid, list_vector_array) parameter_space = fom.parameters.space(0.1, 1.) if cache_region != 'none': # building a cache_id is only needed for persistent CacheRegions cache_id = (f"pymordemos.thermalblock {fenics} {xblocks} {yblocks}" f"{grid} {order}") fom.enable_caching(cache_region.value, cache_id) if plot_solutions: print('Showing some solutions') Us = () legend = () for mu in parameter_space.sample_randomly(2): print(f"Solving for diffusion = \n{mu['diffusion']} ... ") sys.stdout.flush() Us = Us + (fom.solve(mu), ) legend = legend + (str(mu['diffusion']), ) fom.visualize(Us, legend=legend, title='Detailed Solutions for different parameters', separate_colorbars=False, block=True) print('RB generation ...') # define estimator for coercivity constant from pymor.parameters.functionals import ExpressionParameterFunctional coercivity_estimator = ExpressionParameterFunctional( 'min(diffusion)', fom.parameters) # inner product for computation of Riesz representatives product = fom.h1_0_semi_product if product == 'h1' else None if reductor == 'residual_basis': from pymor.reductors.coercive import CoerciveRBReductor reductor = CoerciveRBReductor( fom, product=product, coercivity_estimator=coercivity_estimator, check_orthonormality=False) elif reductor == 'traditional': from pymor.reductors.coercive import SimpleCoerciveRBReductor reductor = SimpleCoerciveRBReductor( fom, product=product, coercivity_estimator=coercivity_estimator, check_orthonormality=False) else: assert False # this should never happen if alg == 'naive': rom, red_summary = reduce_naive(fom=fom, reductor=reductor, parameter_space=parameter_space, basis_size=rbsize) elif alg == 'greedy': parallel = greedy_with_error_estimator or not fenics # cannot pickle FEniCS model rom, red_summary = reduce_greedy( fom=fom, reductor=reductor, parameter_space=parameter_space, snapshots_per_block=snapshots, extension_alg_name=extension_alg.value, max_extensions=rbsize, use_error_estimator=greedy_with_error_estimator, pool=pool if parallel else None) elif alg == 'adaptive_greedy': parallel = greedy_with_error_estimator or not fenics # cannot pickle FEniCS model rom, red_summary = reduce_adaptive_greedy( fom=fom, reductor=reductor, parameter_space=parameter_space, validation_mus=snapshots, extension_alg_name=extension_alg.value, max_extensions=rbsize, use_error_estimator=greedy_with_error_estimator, rho=adaptive_greedy_rho, gamma=adaptive_greedy_gamma, theta=adaptive_greedy_theta, pool=pool if parallel else None) elif alg == 'pod': rom, red_summary = reduce_pod(fom=fom, reductor=reductor, parameter_space=parameter_space, snapshots_per_block=snapshots, basis_size=rbsize) else: assert False # this should never happen if pickle: print(f"\nWriting reduced model to file {pickle}_reduced ...") with open(pickle + '_reduced', 'wb') as f: dump((rom, parameter_space), f) if not fenics: # FEniCS data structures do not support serialization print( f"Writing detailed model and reductor to file {pickle}_detailed ..." ) with open(pickle + '_detailed', 'wb') as f: dump((fom, reductor), f) print('\nSearching for maximum error on random snapshots ...') results = reduction_error_analysis( rom, fom=fom, reductor=reductor, error_estimator=True, error_norms=(fom.h1_0_semi_norm, fom.l2_norm), condition=True, test_mus=parameter_space.sample_randomly(test, seed=999), basis_sizes=0 if plot_error_sequence else 1, plot=plot_error_sequence, pool=None if fenics else pool # cannot pickle FEniCS model ) print('\n*** RESULTS ***\n') print(fom_summary) print(red_summary) print(results['summary']) sys.stdout.flush() if plot_error_sequence: import matplotlib.pyplot matplotlib.pyplot.show() if plot_err: mumax = results['max_error_mus'][0, -1] U = fom.solve(mumax) URB = reductor.reconstruct(rom.solve(mumax)) fom.visualize( (U, URB, U - URB), legend=('Detailed Solution', 'Reduced Solution', 'Error'), title='Maximum Error Solution', separate_colorbars=True, block=True) global test_results test_results = results
def main(args): args = parse_arguments(args) pool = new_parallel_pool(ipython_num_engines=args['--ipython-engines'], ipython_profile=args['--ipython-profile']) if args['--fenics']: fom, fom_summary = discretize_fenics(args['XBLOCKS'], args['YBLOCKS'], args['--grid'], args['--order']) else: fom, fom_summary = discretize_pymor(args['XBLOCKS'], args['YBLOCKS'], args['--grid'], args['--list-vector-array']) if args['--cache-region'] != 'none': fom.enable_caching(args['--cache-region']) if args['--plot-solutions']: print('Showing some solutions') Us = () legend = () for mu in fom.parameter_space.sample_randomly(2): print(f"Solving for diffusion = \n{mu['diffusion']} ... ") sys.stdout.flush() Us = Us + (fom.solve(mu),) legend = legend + (str(mu['diffusion']),) fom.visualize(Us, legend=legend, title='Detailed Solutions for different parameters', separate_colorbars=False, block=True) print('RB generation ...') # define estimator for coercivity constant from pymor.parameters.functionals import ExpressionParameterFunctional coercivity_estimator = ExpressionParameterFunctional('min(diffusion)', fom.parameter_type) # inner product for computation of Riesz representatives product = fom.h1_0_semi_product if args['--product'] == 'h1' else None if args['--reductor'] == 'residual_basis': from pymor.reductors.coercive import CoerciveRBReductor reductor = CoerciveRBReductor(fom, product=product, coercivity_estimator=coercivity_estimator, check_orthonormality=False) elif args['--reductor'] == 'traditional': from pymor.reductors.coercive import SimpleCoerciveRBReductor reductor = SimpleCoerciveRBReductor(fom, product=product, coercivity_estimator=coercivity_estimator, check_orthonormality=False) else: assert False # this should never happen if args['--alg'] == 'naive': rom, red_summary = reduce_naive(fom=fom, reductor=reductor, basis_size=args['RBSIZE']) elif args['--alg'] == 'greedy': parallel = not (args['--fenics'] and args['--greedy-without-estimator']) # cannot pickle FEniCS model rom, red_summary = reduce_greedy(fom=fom, reductor=reductor, snapshots_per_block=args['SNAPSHOTS'], extension_alg_name=args['--extension-alg'], max_extensions=args['RBSIZE'], use_estimator=not args['--greedy-without-estimator'], pool=pool if parallel else None) elif args['--alg'] == 'adaptive_greedy': parallel = not (args['--fenics'] and args['--greedy-without-estimator']) # cannot pickle FEniCS model rom, red_summary = reduce_adaptive_greedy(fom=fom, reductor=reductor, validation_mus=args['SNAPSHOTS'], extension_alg_name=args['--extension-alg'], max_extensions=args['RBSIZE'], use_estimator=not args['--greedy-without-estimator'], rho=args['--adaptive-greedy-rho'], gamma=args['--adaptive-greedy-gamma'], theta=args['--adaptive-greedy-theta'], pool=pool if parallel else None) elif args['--alg'] == 'pod': rom, red_summary = reduce_pod(fom=fom, reductor=reductor, snapshots_per_block=args['SNAPSHOTS'], basis_size=args['RBSIZE']) else: assert False # this should never happen if args['--pickle']: print(f"\nWriting reduced model to file {args['--pickle']}_reduced ...") with open(args['--pickle'] + '_reduced', 'wb') as f: dump(rom, f) if not args['--fenics']: # FEniCS data structures do not support serialization print(f"Writing detailed model and reductor to file {args['--pickle']}_detailed ...") with open(args['--pickle'] + '_detailed', 'wb') as f: dump((fom, reductor), f) print('\nSearching for maximum error on random snapshots ...') results = reduction_error_analysis(rom, fom=fom, reductor=reductor, estimator=True, error_norms=(fom.h1_0_semi_norm, fom.l2_norm), condition=True, test_mus=args['--test'], basis_sizes=0 if args['--plot-error-sequence'] else 1, plot=args['--plot-error-sequence'], pool=None if args['--fenics'] else pool, # cannot pickle FEniCS model random_seed=999) print('\n*** RESULTS ***\n') print(fom_summary) print(red_summary) print(results['summary']) sys.stdout.flush() if args['--plot-error-sequence']: import matplotlib.pyplot matplotlib.pyplot.show(results['figure']) if args['--plot-err']: mumax = results['max_error_mus'][0, -1] U = fom.solve(mumax) URB = reductor.reconstruct(rom.solve(mumax)) fom.visualize((U, URB, U - URB), legend=('Detailed Solution', 'Reduced Solution', 'Error'), title='Maximum Error Solution', separate_colorbars=True, block=True) return results
def main( rbsize: int = Argument(..., help='Size of the reduced basis.'), cache_region: Choices('none memory disk persistent') = Option( 'none', help='Name of cache region to use for caching solution snapshots.' ), error_estimator: bool = Option(True, help='Use error estimator for basis generation.'), gamma: float = Option(0.2, help='Weight factor for age penalty term in refinement indicators.'), grid: int = Option(100, help='Use grid with 2*NI*NI elements.'), ipython_engines: int = Option( 0, help='If positive, the number of IPython cluster engines to use for parallel greedy search. ' 'If zero, no parallelization is performed.' ), ipython_profile: str = Option(None, help='IPython profile to use for parallelization.'), list_vector_array: bool = Option( False, help='Solve using ListVectorArray[NumpyVector] instead of NumpyVectorArray.' ), pickle: str = Option( None, help='Pickle reduced discretization, as well as reductor and high-dimensional model to files with this prefix.' ), plot_err: bool = Option(False, help='Plot error.'), plot_solutions: bool = Option(False, help='Plot some example solutions.'), plot_error_sequence: bool = Option(False, help='Plot reduction error vs. basis size.'), product: Choices('euclidean h1') = Option( 'h1', help='Product w.r.t. which to orthonormalize and calculate Riesz representatives.' ), reductor: Choices('traditional residual_basis') = Option( 'residual_basis', help='Reductor (error estimator) to choose (traditional, residual_basis).' ), rho: float = Option(1.1, help='Maximum allowed ratio between error on validation set and on training set.'), test: int = Option(10, help='Use COUNT snapshots for stochastic error estimation.'), theta: float = Option(0., help='Ratio of elements to refine.'), validation_mus: int = Option(0, help='Size of validation set.'), visualize_refinement: bool = Option(True, help='Visualize the training set refinement indicators.'), ): """Modified thermalblock demo using adaptive greedy basis generation algorithm.""" problem = thermal_block_problem(num_blocks=(2, 2)) functionals = [ExpressionParameterFunctional('diffusion[0]', {'diffusion': 2}), ExpressionParameterFunctional('diffusion[1]**2', {'diffusion': 2}), ExpressionParameterFunctional('diffusion[0]', {'diffusion': 2}), ExpressionParameterFunctional('diffusion[1]', {'diffusion': 2})] problem = problem.with_( diffusion=problem.diffusion.with_(coefficients=functionals), ) print('Discretize ...') fom, _ = discretize_stationary_cg(problem, diameter=1. / grid) if list_vector_array: from pymor.discretizers.builtin.list import convert_to_numpy_list_vector_array fom = convert_to_numpy_list_vector_array(fom) if cache_region != 'none': # building a cache_id is only needed for persistent CacheRegions cache_id = f"pymordemos.thermalblock_adaptive {grid}" fom.enable_caching(cache_region.value, cache_id) if plot_solutions: print('Showing some solutions') Us = () legend = () for mu in problem.parameter_space.sample_randomly(2): print(f"Solving for diffusion = \n{mu['diffusion']} ... ") sys.stdout.flush() Us = Us + (fom.solve(mu),) legend = legend + (str(mu['diffusion']),) fom.visualize(Us, legend=legend, title='Detailed Solutions for different parameters', block=True) print('RB generation ...') product_op = fom.h1_0_semi_product if product == 'h1' else None coercivity_estimator = ExpressionParameterFunctional('min([diffusion[0], diffusion[1]**2])', fom.parameters) reductors = {'residual_basis': CoerciveRBReductor(fom, product=product_op, coercivity_estimator=coercivity_estimator), 'traditional': SimpleCoerciveRBReductor(fom, product=product_op, coercivity_estimator=coercivity_estimator)} reductor = reductors[reductor] pool = new_parallel_pool(ipython_num_engines=ipython_engines, ipython_profile=ipython_profile) greedy_data = rb_adaptive_greedy( fom, reductor, problem.parameter_space, validation_mus=validation_mus, rho=rho, gamma=gamma, theta=theta, use_error_estimator=error_estimator, error_norm=fom.h1_0_semi_norm, max_extensions=rbsize, visualize=visualize_refinement ) rom = greedy_data['rom'] if pickle: print(f"\nWriting reduced model to file {pickle}_reduced ...") with open(pickle + '_reduced', 'wb') as f: dump(rom, f) print(f"Writing detailed model and reductor to file {pickle}_detailed ...") with open(pickle + '_detailed', 'wb') as f: dump((fom, reductor), f) print('\nSearching for maximum error on random snapshots ...') results = reduction_error_analysis(rom, fom=fom, reductor=reductor, error_estimator=True, error_norms=(fom.h1_0_semi_norm,), condition=True, test_mus=problem.parameter_space.sample_randomly(test), basis_sizes=25 if plot_error_sequence else 1, plot=True, pool=pool) real_rb_size = rom.solution_space.dim print(''' *** RESULTS *** Problem: number of blocks: 2x2 h: sqrt(2)/{grid} Greedy basis generation: error estimator enalbed: {error_estimator} product: {product} prescribed basis size: {rbsize} actual basis size: {real_rb_size} elapsed time: {greedy_data[time]} '''.format(**locals())) print(results['summary']) sys.stdout.flush() if plot_error_sequence: from matplotlib import pyplot as plt plt.show() if plot_err: mumax = results['max_error_mus'][0, -1] U = fom.solve(mumax) URB = reductor.reconstruct(rom.solve(mumax)) fom.visualize((U, URB, U - URB), legend=('Detailed Solution', 'Reduced Solution', 'Error'), title='Maximum Error Solution', separate_colorbars=True, block=True)