def multiparam_combinations(dirname):
sim = BatchSimulator(dirname, N=256, lambda2=1, overwrite=True)
base_params = {
"alpha": 1,
"mu_scale": 1.8,
"max_t": 80,
"modes": 21,
"order": 2,
"dt": 1e-3
}
# lambda4 is the coefficient by the fourth derivative u_xxxx,
# lambda2 is the coefficient by the second derivative term u_xx.
estimate_params = [
"lambda2", "lambda4", "nonlinear_coeff", "lambda1", "lambda3"
]
initial_guesses = []
for included in itertools.product([False, True], repeat=5):
# Skip the boring case of nothing to estimate.
if not any(included):
continue
initial_guess = {}
for is_included, param_name in zip(included, estimate_params):
if is_included:
initial_guess[param_name] = 2
initial_guesses.append(initial_guess)
sim.run_batch(base_params, ranges={"initial_guess": initial_guesses})
def probe_order(dirname):
sim = BatchSimulator(dirname, N=512, lambda2=1, overwrite=True)
base_params = {
"alpha": 1,
"mu_scale": 1.8,
"max_t": 60,
"modes": 21,
"timestepper": "rk4"
}
base_params["initial_guess"] = {"lambda2": 2}
ranges = {"dt": [1e-2, 1e-3, 5e-3, 1e-4, 5e-4], "order": [1, 2, 3]}
sim.run_batch(base_params, ranges=ranges)
def high_spatial_res(dirname):
sim = BatchSimulator(dirname, N=1024, lambda2=1, overwrite=True)
base_params = {
"alpha": 1,
"mu_scale": 1.8,
"order": 3,
"max_t": 45,
"modes": 21,
"timestepper": "rk4"
}
base_params["initial_guess"] = {"lambda2": 2}
sim.run_batch(base_params, ranges={"dt": [2.5e-4], "modes": [42, 84, 168]})
results = SimulationResults(dirname)
df = results.get_summary()
print(df)
print(df[["dt", "modes", "lambda2_error"]])
def mu_alpha_convergence(dirname):
"""Vary mu_scale and alpha - and see how the convergence rate changes.
"""
sim = BatchSimulator(dirname, N=512, lambda2=1, overwrite=True)
base_params = {
"alpha": 1,
"mu_scale": 1.8,
"order": 3,
"max_t": 60,
"dt": 1e-3,
"modes": 21,
"timestepper": "rk4",
"initial_guess": {
"lambda2": 2
}
}
ranges = {
"alpha": [.1, .5, 1, 5, 10, 50, 100],
"mu_scale": [5e-4, .001, .005, .01, .05, .1, .5, 1, 1.4, 1.8]
}
sim.run_batch(base_params, ranges=ranges, grid=False) # No grid search.
def explore_alpha(dirname):
sim = BatchSimulator(dirname, N=512, lambda2=1, overwrite=True)
base_params = {
"alpha": 1,
"mu_scale": 1.8,
"order": 3,
"max_t": 60,
"dt": 1e-3,
"modes": 21,
"timestepper": "rk4"
}
ranges = {
"initial_guess": [{
"lambda2": 2
}, {
"lambda2": 2,
"lambda4": 2,
"nonlinear_coeff": 2
}],
"alpha": [.5, 1, 10, 100, None]
}
sim.run_batch(base_params, ranges=ranges)
def interpolator_scan(dirname):
"""Do a parameter scan over interpolators.
We vary both the functional form (piecewise-linear, cubic, Fourier modes,
etc) and the dimension.
"""
sim = BatchSimulator(dirname, N=512, lambda2=1, overwrite=True)
# modes = [4, 8, 16, 21, 32, 48, 64, 96, 128]
# interpolators = [None, "cubic", "linear"]
# None stands for the standard Fourier interpolator.
# Use a much smaller mu.
base_params = {
"alpha": 1,
"mu_scale": .01,
"order": 3,
"max_t": 60,
"dt": 1e-3,
"modes": 21,
"timestepper": "rk4",
"initial_guess": {
"lambda2": 2
}
}
pointwise_modes = list(range(34, 48, 2))
fourier_modes = list(range(17, 22))
# mu_scales = [1e-3, 1e-2, 1e-1]
pointwise_params = sim.get_param_list(base_params,
ranges={
"modes":
pointwise_modes,
"pointwise_interpolation":
["cubic", "quadratic", "linear"],
"mu_scale": [.01]
})
fourier_params = sim.get_param_list(base_params,
ranges={
"modes": fourier_modes,
"mu_scale": [1.8]
})
# sim.run_batch(base_params, ranges={
# "modes": modes,
# "pointwise_interpolation": interpolators}
# )
sim.run_simulations_low(pointwise_params + fourier_params)