def test_initial_value_problem_without_exact_solution():
diff_eq = PopulationGrowthEquation()
cp = ConstrainedProblem(diff_eq)
ic = ContinuousInitialCondition(cp, lambda _: np.array([0.]))
ivp = InitialValueProblem(cp, (0., 2.), ic)
assert not ivp.has_exact_solution
with pytest.raises(RuntimeError):
ivp.exact_y(2.)
def test_pidon_operator_on_ode_with_analytic_solution():
set_random_seed(0)
r = 4.
y_0 = 1.
diff_eq = PopulationGrowthEquation(r)
cp = ConstrainedProblem(diff_eq)
t_interval = (0., .25)
ic = ContinuousInitialCondition(cp, lambda _: np.array([y_0]))
sampler = UniformRandomCollocationPointSampler()
pidon = PIDONOperator(sampler, .001, True)
training_loss_history, test_loss_history = pidon.train(
cp,
t_interval,
training_data_args=DataArgs(
y_0_functions=[ic.y_0],
n_domain_points=25,
n_batches=5,
n_ic_repeats=5
),
model_args=ModelArgs(
latent_output_size=1,
trunk_hidden_layer_sizes=[50, 50, 50],
),
optimization_args=OptimizationArgs(
optimizer=optimizers.SGD(),
epochs=100,
verbose=False
),
secondary_optimization_args=SecondaryOptimizationArgs(
max_iterations=100,
verbose=False
)
)
assert len(training_loss_history) == 101
assert len(test_loss_history) == 0
assert training_loss_history[-1].weighted_total_loss.numpy() < 5e-5
ivp = InitialValueProblem(
cp,
t_interval,
ic,
lambda _ivp, t, x: np.array([y_0 * np.e ** (r * t)])
)
solution = pidon.solve(ivp)
assert solution.d_t == .001
assert solution.discrete_y().shape == (250, 1)
analytic_y = np.array([ivp.exact_y(t) for t in solution.t_coordinates])
assert np.mean(np.abs(analytic_y - solution.discrete_y())) < 1e-3
assert np.max(np.abs(analytic_y - solution.discrete_y())) < 2.5e-3
def test_initial_value_problem():
y_0 = 100
r = .5
diff_eq = PopulationGrowthEquation(r)
cp = ConstrainedProblem(diff_eq)
ic = ContinuousInitialCondition(cp, lambda _: np.array([y_0]))
ivp = InitialValueProblem(
cp, (0., 2.), ic, lambda _ivp, t, x: np.array([y_0 * np.e**(r * t)]))
assert ivp.has_exact_solution
assert ivp.constrained_problem == cp
assert ivp.t_interval == (0., 2.)
assert ivp.initial_condition == ic
assert np.allclose(ivp.exact_y(0.), [y_0])
def test_ode_operator_on_ode_with_analytic_solution():
r = .02
y_0 = 100.
diff_eq = PopulationGrowthEquation(r)
cp = ConstrainedProblem(diff_eq)
ic = ContinuousInitialCondition(cp, lambda _: np.array([y_0]))
ivp = InitialValueProblem(
cp, (0., 10.), ic, lambda _ivp, t, x: np.array([y_0 * np.e**(r * t)]))
op = ODEOperator('DOP853', 1e-4)
solution = op.solve(ivp)
assert solution.d_t == 1e-4
assert solution.discrete_y().shape == (1e5, 1)
analytic_y = np.array([ivp.exact_y(t) for t in solution.t_coordinates])
assert np.allclose(analytic_y, solution.discrete_y())