# Add noise for ii in range(len(DD)): if PRINT: print 'source {}'.format(ii) dd = DD[ii] rndnoise = RAND[ii] mu = np.abs(dd).mean(axis=1) sigmas = mu / (10**(SNRdB / 10.)) #sigmas = np.sqrt((dd**2).sum(axis=1)/nbt)*0.1 #rndnoise = np.random.randn(nbobspt*nbt).reshape((nbobspt, nbt)) print 'mpiglobalrank={}, sigmas={}, |rndnoise|={}'.format(\ mpiglobalrank, sigmas.sum()/len(sigmas), (rndnoise**2).sum().sum()) DD[ii] = dd + sigmas.reshape((nbobspt, 1)) * rndnoise MPI.barrier(mpicommbarrier) waveobj.dd = DD if PLOTTS: if PRINT: src = int(len(Pt.src_loc) * 0.5) print 'Plotting source #{}'.format(src) fig = plotobservations(waveobj.PDE.times, waveobj.Bp[src], waveobj.dd[src], 9) plt.show() MPI.barrier(mpicommbarrier) # check: waveobj.solvefwd_cost() costmisfit = waveobj.cost_misfit #assert costmisfit < 1e-14, costmisfit # Compute gradient at initial parameters waveobj.update_PDE({'a': a0, 'b': b0})
wavepde.timestepper = "backward" wavepde.lump = True wavepde.set_abc(mesh, ABC(), True) wavepde.update( {"lambda": TargetMed, "rho": 1.0, "t0": t0, "tf": tf, "Dt": Dt, "u0init": dl.Function(V), "utinit": dl.Function(V)} ) wavepde.ftime = mysrc # define objective function: waveobj = ObjectiveAcoustic(wavepde) waveobj.obsop = obsop # data print "generate data" waveobj.solvefwd() myplot.plot_timeseries(waveobj.solfwd, "pd", 0, 40, fctV) dd = waveobj.Bp.copy() waveobj.dd = dd # Plot observations # fig = plt.figure() # for ii in range(len(obspts)): # ax = fig.add_subplot(3,3,ii+1) # ax.plot(waveobj.times, waveobj.dd[ii,:], 'k--') # ax.plot(waveobj.times, waveobj.Bp[ii,:], 'r--') # ax.set_title('recv '+str(ii+1)) # fig.savefig(filename + '/observations.eps') # perturbate medium V = np.linspace(1.0, 3.0, 20) MISFIT = [] for ii, eps in enumerate(V): print "run case ", ii PerturbationMedExpr = dl.Expression(medformula, A=eps)
def run_test(fpeak, lambdamin, lambdamax, Nxy, tfilterpts, r, Dt, skip): h = 1. / Nxy checkdt(Dt, h, r, np.sqrt(lambdamax), True) mesh = dl.UnitSquareMesh(Nxy, Nxy) Vl = dl.FunctionSpace(mesh, 'Lagrange', 1) V = dl.FunctionSpace(mesh, 'Lagrange', r) fctV = dl.Function(V) # set up plots: filename, ext = splitext(sys.argv[0]) if isdir(filename + '/'): rmtree(filename + '/') myplot = PlotFenics(filename) # source: Ricker = RickerWavelet(fpeak, 1e-10) Pt = PointSources(V, [[0.5, 0.5]]) mydelta = Pt[0].array() def mysrc(tt): return Ricker(tt) * mydelta # target medium: lambda_target = dl.Expression('lmin + x[0]*(lmax-lmin)', \ lmin=lambdamin, lmax=lambdamax) lambda_target_fn = dl.interpolate(lambda_target, Vl) myplot.set_varname('lambda_target') myplot.plot_vtk(lambda_target_fn) # initial medium: lambda_init = dl.Constant(lambdamin) lambda_init_fn = dl.interpolate(lambda_init, Vl) myplot.set_varname('lambda_init') myplot.plot_vtk(lambda_init_fn) # observation operator: #obspts = [[0.2, 0.5], [0.5, 0.2], [0.5, 0.8], [0.8, 0.5]] obspts = [[0.2, ii/10.] for ii in range(2,9)] + \ [[0.8, ii/10.] for ii in range(2,9)] + \ [[ii/10., 0.2] for ii in range(3,8)] + \ [[ii/10., 0.8] for ii in range(3,8)] obsop = TimeObsPtwise({'V': V, 'Points': obspts}, tfilterpts) # define pde operator: wavepde = AcousticWave({'V': V, 'Vl': Vl, 'Vr': Vl}) wavepde.timestepper = 'backward' wavepde.lump = True wavepde.set_abc(mesh, LeftRight(), True) wavepde.update({'lambda':lambda_target_fn, 'rho':1.0, \ 't0':t0, 'tf':tf, 'Dt':Dt, 'u0init':dl.Function(V), 'utinit':dl.Function(V)}) wavepde.ftime = mysrc # define objective function: waveobj = ObjectiveAcoustic(wavepde) waveobj.obsop = obsop # data print 'generate data' waveobj.solvefwd() myplot.plot_timeseries(waveobj.solfwd, 'pd', 0, skip, fctV) dd = waveobj.Bp.copy() # gradient print 'generate observations' waveobj.dd = dd waveobj.update_m(lambda_init_fn) waveobj.solvefwd_cost() cost1 = waveobj.misfit print 'misfit = {}'.format(waveobj.misfit) myplot.plot_timeseries(waveobj.solfwd, 'p', 0, skip, fctV) # Plot data and observations fig = plt.figure() if len(obspts) > 9: fig.set_size_inches(20., 15.) for ii in range(len(obspts)): if len(obspts) == 4: ax = fig.add_subplot(2, 2, ii + 1) else: ax = fig.add_subplot(4, 6, ii + 1) ax.plot(waveobj.PDE.times, waveobj.dd[ii, :], 'k--') ax.plot(waveobj.PDE.times, waveobj.Bp[ii, :], 'b') ax.set_title('Plot' + str(ii)) fig.savefig(filename + '/observations.eps') print 'compute gradient' waveobj.solveadj_constructgrad() myplot.plot_timeseries(waveobj.soladj, 'v', 0, skip, fctV) MG = waveobj.MGv.array().copy() myplot.set_varname('grad') myplot.plot_vtk(waveobj.Grad) """
SNRdB = 20.0 # [dB], i.e, log10(mu/sigma) = SNRdB/10 np.random.seed(11) for ii, dd in enumerate(DD): if mpirank == 0: print 'source {}'.format(ii) nbobspt, dimsol = dd.shape #mu = np.abs(dd).mean(axis=1) #sigmas = mu/(10**(SNRdB/10.)) sigmas = np.sqrt((dd**2).sum(axis=1)/dimsol)*0.01 rndnoise = np.random.randn(nbobspt*dimsol).reshape((nbobspt, dimsol)) print 'mpirank={}, sigmas={}, |rndnoise|={}'.format(\ mpirank, sigmas.sum()/len(sigmas), (rndnoise**2).sum().sum()) DD[ii] = dd + sigmas.reshape((nbobspt,1))*rndnoise MPI.barrier(mpicomm) waveobjab.dd = DD waveobjabnoregul.dd = DD # check: waveobjab.solvefwd_cost() costmisfit = waveobjab.cost_misfit waveobjabnoregul.solvefwd_cost() costmisfitnoregul = waveobjabnoregul.cost_misfit # Compare cost functionals from both objective functions waveobjab.update_PDE({'a':a0, 'b':b0}) waveobjab.solvefwd_cost() waveobjabnoregul.update_PDE({'a':a0, 'b':b0}) waveobjabnoregul.solvefwd_cost() if mpirank == 0: print 'misfit at target={:.6e}; at initial state={:.6e}'.format(\ costmisfit, waveobjab.cost_misfit)
def run_test(fpeak, lambdamin, lambdamax, Nxy, tfilterpts, r, Dt, skip): h = 1./Nxy checkdt(Dt, h, r, np.sqrt(lambdamax), True) mesh = dl.UnitSquareMesh(Nxy, Nxy) Vl = dl.FunctionSpace(mesh, 'Lagrange', 1) V = dl.FunctionSpace(mesh, 'Lagrange', r) fctV = dl.Function(V) # set up plots: filename, ext = splitext(sys.argv[0]) if isdir(filename + '/'): rmtree(filename + '/') myplot = PlotFenics(filename) # source: Ricker = RickerWavelet(fpeak, 1e-10) Pt = PointSources(V, [[0.5,0.5]]) mydelta = Pt[0].array() def mysrc(tt): return Ricker(tt)*mydelta # target medium: lambda_target = dl.Expression('lmin + x[0]*(lmax-lmin)', \ lmin=lambdamin, lmax=lambdamax) lambda_target_fn = dl.interpolate(lambda_target, Vl) myplot.set_varname('lambda_target') myplot.plot_vtk(lambda_target_fn) # initial medium: lambda_init = dl.Constant(lambdamin) lambda_init_fn = dl.interpolate(lambda_init, Vl) myplot.set_varname('lambda_init') myplot.plot_vtk(lambda_init_fn) # observation operator: #obspts = [[0.2, 0.5], [0.5, 0.2], [0.5, 0.8], [0.8, 0.5]] obspts = [[0.2, ii/10.] for ii in range(2,9)] + \ [[0.8, ii/10.] for ii in range(2,9)] + \ [[ii/10., 0.2] for ii in range(3,8)] + \ [[ii/10., 0.8] for ii in range(3,8)] obsop = TimeObsPtwise({'V':V, 'Points':obspts}, tfilterpts) # define pde operator: wavepde = AcousticWave({'V':V, 'Vl':Vl, 'Vr':Vl}) wavepde.timestepper = 'centered' wavepde.lump = True wavepde.set_abc(mesh, LeftRight(), True) wavepde.update({'lambda':lambda_target_fn, 'rho':1.0, \ 't0':t0, 'tf':tf, 'Dt':Dt, 'u0init':dl.Function(V), 'utinit':dl.Function(V)}) wavepde.ftime = mysrc # define objective function: waveobj = ObjectiveAcoustic(wavepde) waveobj.obsop = obsop # data print 'generate noisy data' waveobj.solvefwd() myplot.plot_timeseries(waveobj.solfwd, 'pd', 0, skip, fctV) dd = waveobj.Bp.copy() nbobspt, dimsol = dd.shape noiselevel = 0.1 # = 10% sigmas = np.sqrt((dd**2).sum(axis=1)/dimsol)*noiselevel rndnoise = np.random.randn(nbobspt*dimsol).reshape((nbobspt, dimsol)) waveobj.dd = dd + sigmas.reshape((len(sigmas),1))*rndnoise # gradient print 'generate observations' waveobj.update_m(lambda_init_fn) waveobj.solvefwd_cost() cost1 = waveobj.misfit print 'misfit = {}'.format(waveobj.misfit) myplot.plot_timeseries(waveobj.solfwd, 'p', 0, skip, fctV) # Plot data and observations fig = plt.figure() if len(obspts) > 9: fig.set_size_inches(20., 15.) for ii in range(len(obspts)): if len(obspts) == 4: ax = fig.add_subplot(2,2,ii+1) else: ax = fig.add_subplot(4,6,ii+1) ax.plot(waveobj.PDE.times, waveobj.dd[ii,:], 'k--') ax.plot(waveobj.PDE.times, waveobj.Bp[ii,:], 'b') ax.set_title('Plot'+str(ii)) fig.savefig(filename + '/observations.eps') print 'compute gradient' waveobj.solveadj_constructgrad() myplot.plot_timeseries(waveobj.soladj, 'v', 0, skip, fctV) MG = waveobj.MGv.array().copy() myplot.set_varname('grad') myplot.plot_vtk(waveobj.Grad) print 'check gradient with FD' Medium = np.zeros((5, Vl.dim())) for ii in range(5): smoothperturb = dl.Expression('sin(n*pi*x[0])*sin(n*pi*x[1])', n=ii+1) smoothperturb_fn = dl.interpolate(smoothperturb, Vl) Medium[ii,:] = smoothperturb_fn.vector().array() checkgradfd_med(waveobj, Medium, 1e-6, [1e-5, 1e-4]) print 'check Hessian with FD' checkhessfd_med(waveobj, Medium, 1e-6, [1e-1, 1e-2, 1e-3, 1e-4, 1e-5], False)