def test_lotka_volterra():
alpha, beta, delta, gamma = 1, 1, 1, 1
lotka_volterra = lambda x, y, t : [diff(x, t) - (alpha*x - beta*x*y),
diff(y, t) - (delta*x*y - gamma*y)]
init_vals_lv = [
IVP(t_0=0.0, x_0=1.5),
IVP(t_0=0.0, x_0=1.0)
]
nets_lv = [
FCNN(hidden_units=(32, 32), actv=SinActv),
FCNN(hidden_units=(32, 32), actv=SinActv),
]
solution_lv, _ = solve_system(ode_system=lotka_volterra, conditions=init_vals_lv,
t_min=0.0, t_max=12, nets=nets_lv, max_epochs=12000,
monitor=Monitor(t_min=0.0, t_max=12, check_every=100))
ts = np.linspace(0, 12, 100)
prey_net, pred_net = solution_lv(ts, as_type='np')
def dPdt(P, t):
return [P[0]*alpha - beta*P[0]*P[1], delta*P[0]*P[1] - gamma*P[1]]
P0 = [1.5, 1.0]
Ps = odeint(dPdt, P0, ts)
prey_num = Ps[:,0]
pred_num = Ps[:,1]
assert isclose(prey_net, prey_num, atol=0.1).all()
assert isclose(pred_net, pred_num, atol=0.1).all()
print('Lotka Volterra test passed.')
def test_get_internals():
parametric_circle = lambda x1, x2, t: [diff(x1, t) - x2, diff(x2, t) + x1]
init_vals_pc = [
IVP(t_0=0.0, u_0=0.0),
IVP(t_0=0.0, u_0=1.0),
]
solver = Solver1D(
ode_system=parametric_circle,
conditions=init_vals_pc,
t_min=0.0,
t_max=2 * np.pi,
)
solver.fit(max_epochs=1)
internals = solver.get_internals()
assert isinstance(internals, dict)
internals = solver.get_internals(return_type='list')
assert isinstance(internals, dict)
internals = solver.get_internals(return_type='dict')
assert isinstance(internals, dict)
internals = solver.get_internals(['generator', 'n_batches'], return_type='dict')
assert isinstance(internals, dict)
internals = solver.get_internals(['generator', 'n_batches'], return_type='list')
assert isinstance(internals, list)
internals = solver.get_internals('train_generator')
assert isinstance(internals, BaseGenerator)
def get_solution(use_single: bool) -> Solution:
conditions = [IVP(t0, u0), IVP(t1, u1)]
if use_single:
net = FCNN(1, 2)
for i, cond in enumerate(conditions):
cond.set_impose_on(i)
return Solution(net, None, conditions)
else:
nets = [FCNN(1, 1), FCNN(1, 1)]
return Solution(None, nets, conditions)
def get_solution(use_single: bool) -> Solution1D:
conditions = [IVP(t0, u0), IVP(t1, u1)]
if use_single:
net = FCNN(1, 2)
with warns(DeprecationWarning):
for i, cond in enumerate(conditions):
cond.set_impose_on(i)
return Solution1D(net, conditions)
else:
nets = [FCNN(1, 1), FCNN(1, 1)]
return Solution1D(nets, conditions)
def test_monitor():
exponential = lambda x, t: diff(x, t) - x
init_val_ex = IVP(t_0=0.0, x_0=1.0)
solution_ex, _ = solve(ode=exponential, condition=init_val_ex,
t_min=0.0, t_max=2.0,
max_epochs=3,
monitor=Monitor(t_min=0.0, t_max=2.0, check_every=1))
print('Monitor test passed.')
def test_ode_system():
parametric_circle = lambda x1, x2, t: [diff(x1, t) - x2, diff(x2, t) + x1]
init_vals_pc = [IVP(t_0=0.0, x_0=0.0), IVP(t_0=0.0, x_0=1.0)]
solution_pc, _ = solve_system(
ode_system=parametric_circle,
conditions=init_vals_pc,
t_min=0.0,
t_max=2 * np.pi,
max_epochs=5000,
)
ts = np.linspace(0, 2 * np.pi, 100)
x1_net, x2_net = solution_pc(ts, as_type='np')
x1_ana, x2_ana = np.sin(ts), np.cos(ts)
assert isclose(x1_net, x1_ana, atol=0.1).all()
assert isclose(x2_net, x2_ana, atol=0.1).all()
print('solve_system basic test passed.')
def test_monitor():
exponential = lambda u, t: diff(u, t) - u
init_val_ex = IVP(t_0=0.0, u_0=1.0)
solution_ex, _ = solve(ode=exponential,
condition=init_val_ex,
t_min=0.0,
t_max=2.0,
max_epochs=3,
monitor=Monitor(t_min=0.0, t_max=2.0,
check_every=1))
def test_ode_system():
parametric_circle = lambda u1, u2, t: [diff(u1, t) - u2, diff(u2, t) + u1]
init_vals_pc = [IVP(t_0=0.0, u_0=0.0), IVP(t_0=0.0, u_0=1.0)]
solution_pc, loss_history = solve_system(
ode_system=parametric_circle,
conditions=init_vals_pc,
t_min=0.0,
t_max=2 * np.pi,
max_epochs=10,
)
assert isinstance(solution_pc, Solution)
assert isinstance(loss_history, dict)
keys = ['train_loss', 'valid_loss']
for key in keys:
assert key in loss_history
assert isinstance(loss_history[key], list)
assert len(loss_history[keys[0]]) == len(loss_history[keys[1]])
def test_ode_ivp():
oscillator = lambda x, t: diff(x, t, order=2) + x
init_val_ho = IVP(t_0=0.0, x_0=0.0, x_0_prime=1.0)
solution_ho, _ = solve(ode=oscillator, condition=init_val_ho,
max_epochs=3000,
t_min=0.0, t_max=2*np.pi)
ts = np.linspace(0, 2*np.pi, 100)
x_net = solution_ho(ts, as_type='np')
x_ana = np.sin(ts)
assert isclose(x_net, x_ana, atol=0.1).all()
print('IVP basic test passed.')
def test_ode():
def mse(x, t):
true_x = torch.sin(t)
return torch.mean((x - true_x) ** 2)
exponential = lambda x, t: diff(x, t) - x
init_val_ex = IVP(t_0=0.0, x_0=1.0)
solution_ex, _ = solve(ode=exponential, condition=init_val_ex,
t_min=0.0, t_max=2.0, shuffle=False,
max_epochs=2000, return_best=True, metrics={'mse': mse})
ts = np.linspace(0, 2.0, 100)
x_net = solution_ex(ts, as_type='np')
x_ana = np.exp(ts)
assert isclose(x_net, x_ana, atol=0.1).all()
print('solve basic test passed.')
def test_ode():
def mse(u, t):
true_u = torch.sin(t)
return torch.mean((u - true_u) ** 2)
exponential = lambda u, t: diff(u, t) - u
init_val_ex = IVP(t_0=0.0, u_0=1.0)
solution_ex, loss_history = solve(ode=exponential, condition=init_val_ex,
t_min=0.0, t_max=2.0, shuffle=False,
max_epochs=10, return_best=True, metrics={'mse': mse})
assert isinstance(solution_ex, Solution1D)
assert isinstance(loss_history, dict)
keys = ['train_loss', 'valid_loss']
for key in keys:
assert key in loss_history
assert isinstance(loss_history[key], list)
assert len(loss_history[keys[0]]) == len(loss_history[keys[1]])
def test_train_generator():
exponential = lambda x, t: diff(x, t) - x
init_val_ex = IVP(t_0=0.0, x_0=1.0)
train_gen = Generator1D(size=32, t_min=0.0, t_max=2.0, method='uniform')
solution_ex, _ = solve(ode=exponential, condition=init_val_ex,
t_min=0.0, t_max=2.0,
train_generator=train_gen,
max_epochs=3)
train_gen = Generator1D(size=32, t_min=0.0, t_max=2.0, method='equally-spaced')
solution_ex, _ = solve(ode=exponential, condition=init_val_ex,
t_min=0.0, t_max=2.0,
train_generator=train_gen,
max_epochs=3)
train_gen = Generator1D(size=32, t_min=0.0, t_max=2.0, method='equally-spaced-noisy')
solution_ex, _ = solve(ode=exponential, condition=init_val_ex,
t_min=0.0, t_max=2.0,
train_generator=train_gen,
max_epochs=3)
train_gen = Generator1D(size=32, t_min=0.0, t_max=2.0, method='equally-spaced-noisy', noise_std=0.01)
solution_ex, _ = solve(ode=exponential, condition=init_val_ex,
t_min=0.0, t_max=2.0,
train_generator=train_gen,
max_epochs=3)
train_gen = Generator1D(size=32, t_min=np.log10(0.1), t_max=np.log10(2.0), method='log-spaced')
solution_ex, _ = solve(ode=exponential, condition=init_val_ex,
t_min=0.1, t_max=2.0,
train_generator=train_gen,
max_epochs=3)
train_gen = Generator1D(size=32, t_min=np.log10(0.1), t_max=np.log10(2.0), method='log-spaced-noisy')
solution_ex, _ = solve(ode=exponential, condition=init_val_ex,
t_min=0.1, t_max=2.0,
train_generator=train_gen,
max_epochs=3)
train_gen = Generator1D(size=32, t_min=np.log10(0.1), t_max=np.log10(2.0), method='log-spaced-noisy', noise_std=0.01)
solution_ex, _ = solve(ode=exponential, condition=init_val_ex,
t_min=0.1, t_max=2.0,
train_generator=train_gen,
max_epochs=3)
with raises(ValueError):
train_gen = Generator1D(size=32, t_min=0.0, t_max=2.0, method='magic')
print('ExampleGenerator test passed.')