def test_reversibility(sde_cls):
batch_size = 32
state_size = 4
t_size = 20
dt = 0.1
brownian_size = {
NOISE_TYPES.scalar: 1,
NOISE_TYPES.diagonal: state_size,
NOISE_TYPES.general: 2,
NOISE_TYPES.additive: 2
}[sde_cls.noise_type]
class MinusSDE(torch.nn.Module):
def __init__(self, sde):
self.noise_type = sde.noise_type
self.sde_type = sde.sde_type
self.f = lambda t, y: -sde.f(-t, y)
self.g = lambda t, y: -sde.g(-t, y)
sde = sde_cls(d=state_size, m=brownian_size, sde_type='stratonovich')
minus_sde = MinusSDE(sde)
y0 = torch.full((batch_size, state_size), 0.1)
ts = torch.linspace(0, (t_size - 1) * dt, t_size)
bm = torchsde.BrownianInterval(t0=ts[0], t1=ts[-1], size=(batch_size, brownian_size))
ys, (f, g, z) = torchsde.sdeint(sde, y0, ts, bm=bm, method='reversible_heun', dt=dt, extra=True)
backward_ts = -ts.flip(0)
backward_ys = torchsde.sdeint(minus_sde, ys[-1], backward_ts, bm=torchsde.ReverseBrownian(bm),
method='reversible_heun', dt=dt, extra_solver_state=(-f, -g, z))
backward_ys = backward_ys.flip(0)
torch.testing.assert_allclose(ys, backward_ys, rtol=1e-6, atol=1e-6)
def _test_sdeint(sde, bm, method, adaptive, logqp, device, should_fail, options):
y0 = torch.ones(batch_size, d, device=device)
ts = torch.linspace(t0, t1, steps=T, device=device)
if adaptive and method == 'euler' and sde.noise_type != 'additive':
ctx = pytest.warns(UserWarning)
else:
ctx = _nullcontext()
# Using `f` as drift.
with torch.no_grad():
try:
with ctx:
ans = torchsde.sdeint(sde, y0, ts, bm, method=method, dt=dt, adaptive=adaptive, logqp=logqp,
options=options)
except ValueError:
if should_fail:
return
raise
else:
if should_fail:
pytest.fail("Expected an error; did not get one.")
if logqp:
ans, log_ratio = ans
assert log_ratio.shape == (T - 1, batch_size)
assert ans.shape == (T, batch_size, d)
# Using `h` as drift.
with torch.no_grad():
with ctx:
ans = torchsde.sdeint(sde, y0, ts, bm, method=method, dt=dt, adaptive=adaptive, names={'drift': 'h'},
logqp=logqp, options=options)
if logqp:
ans, log_ratio = ans
assert log_ratio.shape == (T - 1, batch_size)
assert ans.shape == (T, batch_size, d)
def inspect_strong_order():
batch_size, d, m = 4096, 5, 5
t0, t1 = ts = torch.tensor([0., 5.]).to(device)
dts = tuple(2**-i for i in range(1, 9))
y0 = torch.ones(batch_size, d).to(device)
sde = Ex3Additive(d=d).to(device)
euler_mses_ = []
srk_mses_ = []
with torch.no_grad():
bm = BrownianPath(t0=t0, w0=torch.zeros(
batch_size,
m).to(device)) # It's important to have the correct size!!!
for dt in tqdm.tqdm(dts):
# Only take end value.
_, ys_euler = sdeint(sde,
y0=y0,
ts=ts,
dt=dt,
bm=bm,
method='euler')
_, ys_srk = sdeint(sde,
y0=y0,
ts=ts,
dt=dt,
bm=bm,
method='srk',
options={'trapezoidal_approx': False})
_, ys_analytical = sde.analytical_sample(y0=y0, ts=ts, bm=bm)
euler_mse = compute_mse(ys_euler, ys_analytical)
srk_mse = compute_mse(ys_srk, ys_analytical)
euler_mse_, srk_mse_ = to_numpy(euler_mse, srk_mse)
euler_mses_.append(euler_mse_)
srk_mses_.append(srk_mse_)
del euler_mse_, srk_mse_
# Divide the log-error by 2, since textbook strong orders are represented so.
log = lambda x: np.log(np.array(x))
euler_slope, _, _, _, _ = stats.linregress(log(dts), log(euler_mses_) / 2)
srk_slope, _, _, _, _ = stats.linregress(log(dts), log(srk_mses_) / 2)
plt.figure()
plt.plot(dts, euler_mses_, label=f'euler(k={euler_slope:.4f})')
plt.plot(dts, srk_mses_, label=f'srk(k={srk_slope:.4f})')
plt.xscale('log')
plt.yscale('log')
plt.legend()
img_dir = os.path.join('.', 'diagnostics', 'plots', 'srk_additive')
makedirs_if_not_found(img_dir)
plt.savefig(os.path.join(img_dir, 'rate'))
plt.close()
def _test_sdeint(self, sde, bm, adaptive, method, dt):
# Using `f` as drift.
with torch.no_grad():
ans = sdeint(sde, y0, ts, bm, method=method, dt=dt, adaptive=adaptive)
self.assertEqual(ans.shape, (T, batch_size, d))
# Using `h` as drift.
with torch.no_grad():
ans = sdeint(sde, y0, ts, bm, method=method, dt=dt, adaptive=adaptive, names={'drift': 'h'})
self.assertEqual(ans.shape, (T, batch_size, d))
def test_rename_methods(self):
# Test renaming works with a subset of names when `logqp=False`.
sde = basic_sde.CustomNamesSDE().to(device)
ans = sdeint(sde, y0, ts, dt=dt, names={'drift': 'forward'})
self.assertEqual(ans.shape, (T, batch_size, d))
# Test renaming works with a subset of names when `logqp=True`.
sde = basic_sde.CustomNamesSDELogqp().to(device)
ans = sdeint(sde, y0, ts, dt=dt, names={'drift': 'forward', 'prior_drift': 'w'}, logqp=True)
self.assertEqual(ans[0].shape, (T, batch_size, d))
self.assertEqual(ans[1].shape, (T - 1, batch_size))
def test_srk_determinism(self):
# srk for additive.
sde = basic_sde.AdditiveSDE(d=d, m=m).to(device)
ys1 = sdeint(sde, y0, ts, bm=bm_general, adaptive=False, method='srk', dt=dt)
ys2 = sdeint(sde, y0, ts, bm=bm_general, adaptive=False, method='srk', dt=dt)
self.tensorAssertAllClose(ys1, ys2)
# srk for diagonal.
sde = basic_sde.BasicSDE1(d=d).to(device)
ys1 = sdeint(sde, y0, ts, bm=bm_diagonal, adaptive=False, method='srk', dt=dt)
ys2 = sdeint(sde, y0, ts, bm=bm_diagonal, adaptive=False, method='srk', dt=dt)
self.tensorAssertAllClose(ys1, ys2)
def inspect_rate():
batch_size, d, m = 4096, 5, 5
t0, t1 = ts = torch.tensor([0., 5.]).to(device)
dts = tuple(2**-i for i in range(1, 10))
y0 = torch.ones(batch_size, d).to(device)
sde = Ex3Additive(d=d).to(device)
euler_mses_ = []
srk_mses_ = []
with torch.no_grad():
bm = BrownianPath(t0=t0, w0=torch.zeros(
batch_size,
m).to(device)) # It's important to have the correct size!!!
for dt in dts:
# Only take end value.
_, ys_euler = sdeint(sde,
y0=y0,
ts=ts,
dt=dt,
bm=bm,
method='euler')
_, ys_srk = sdeint(sde,
y0=y0,
ts=ts,
dt=dt,
bm=bm,
method='srk',
options={'trapezoidal_approx': False})
_, ys_analytical = sde.analytical_sample(y0=y0, ts=ts, bm=bm)
euler_mse = compute_mse(ys_euler, ys_analytical)
srk_mse = compute_mse(ys_srk, ys_analytical)
euler_mse_, srk_mse_ = to_numpy(euler_mse, srk_mse)
euler_mses_.append(euler_mse_)
srk_mses_.append(srk_mse_)
plt.figure()
plt.plot(dts, euler_mses_, label='euler')
plt.plot(dts, srk_mses_, label='srk')
plt.xscale('log')
plt.yscale('log')
plt.legend()
img_dir = os.path.join('.', 'diagnostics', 'plots', 'srk_additive')
makedirs_if_not_found(img_dir)
plt.savefig(os.path.join(img_dir, 'rate'))
plt.close()
def sample(self, x0, ts, noise_std, normalize):
"""Sample data for training. Store data normalization constants if necessary."""
xs = torchsde.sdeint(self, x0, ts)
if normalize:
mean, std = torch.mean(xs, dim=(0, 1)), torch.std(xs, dim=(0, 1))
xs.sub_(mean).div_(std).add_(torch.randn_like(xs) * noise_std)
return xs
def forward(self, xs, ts, noise_std, adjoint=False, method="euler"):
# Contextualization is only needed for posterior inference.
ctx = self.encoder(torch.flip(xs, dims=(0, )))
ctx = torch.flip(ctx, dims=(0, ))
self.contextualize((ts, ctx))
if adjoint:
# Must use the argument `adjoint_params`, since `ctx` is not part of the input to `f`, `g`, and `h`.
adjoint_params = ((ctx, ) + tuple(self.f_net.parameters()) +
tuple(self.g_nets.parameters()) +
tuple(self.h_net.parameters()))
_xs, log_ratio = torchsde.sdeint_adjoint(
self,
xs[0],
ts,
adjoint_params=adjoint_params,
dt=1e-2,
logqp=True,
method=method)
else:
_xs, log_ratio = torchsde.sdeint(self,
xs[0],
ts,
dt=1e-2,
logqp=True,
method=method)
xs_dist = Normal(loc=_xs, scale=noise_std)
log_pxs = xs_dist.log_prob(xs).sum(dim=(0, 2)).mean()
log_ratio = log_ratio.sum(dim=0).mean()
return log_pxs, log_ratio
def test_sdeint_tuplesde(self):
y0_ = (y0,) # Make tuple input.
sde = basic_sde.TupleSDE(d=d).to(device)
bm = lambda t: (bm_diagonal(t),)
with torch.no_grad():
ans = sdeint(sde, y0_, ts, bm, method='euler', dt=dt)
self.assertTrue(isinstance(ans, tuple))
def time_func():
ys = sdeint(geometric_bm,
y0,
ts,
adaptive=False,
dt=ts[1],
options={'trapezoidal_approx': True})
def sample(self, x0, ts, bm=None):
return torchsde.sdeint(self,
x0,
ts,
names={'drift': 'h'},
dt=1e-3,
bm=bm)
def _time_sdeint_bp(sde, y0, ts, bm):
now = time.perf_counter()
sde.zero_grad()
y0 = y0.clone().requires_grad_(True)
ys = torchsde.sdeint(sde, y0, ts, bm, method='euler')
ys.sum().backward()
return time.perf_counter() - now
def test_rename_methods(device):
"""Test renaming works with a subset of names."""
sde = problems.CustomNamesSDE().to(device)
y0 = torch.ones(batch_size, d, device=device)
ts = torch.linspace(t0, t1, steps=T, device=device)
ans = torchsde.sdeint(sde, y0, ts, dt=dt, names={'drift': 'forward'})
assert ans.shape == (T, batch_size, d)
def test_rename_methods_logqp(device):
"""Test renaming works with a subset of names when `logqp=True`."""
sde = problems.CustomNamesSDELogqp().to(device)
y0 = torch.ones(batch_size, d, device=device)
ts = torch.linspace(t0, t1, steps=T, device=device)
ans = torchsde.sdeint(sde, y0, ts, dt=dt, names={'drift': 'forward', 'prior_drift': 'w'}, logqp=True)
assert ans[0].shape == (T, batch_size, d)
assert ans[1].shape == (T - 1, batch_size)
def inspect_rate():
batch_size, d = 4096, 10
t0, t1 = ts = torch.tensor([0., 5.]).to(device)
dts = tuple(2 ** -i for i in range(1, 10))
y0 = torch.ones(batch_size, d).to(device)
sde = Ex2(d=d).to(device)
euler_mses_ = []
milstein_mses_ = []
srk_mses_ = []
with torch.no_grad():
bm = BrownianPath(t0=t0, w0=torch.zeros(batch_size, 1).to(device))
for dt in dts:
# Only take end value.
_, ys_euler = sdeint(sde, y0=y0, ts=ts, dt=dt, bm=bm, method='euler')
_, ys_milstein = sdeint(sde, y0=y0, ts=ts, dt=dt, bm=bm, method='milstein')
_, ys_srk = sdeint(sde, y0=y0, ts=ts, dt=dt, bm=bm, method='srk')
_, ys_analytical = sde.analytical_sample(y0=y0, ts=ts, bm=bm)
euler_mse = compute_mse(ys_euler, ys_analytical)
milstein_mse = compute_mse(ys_milstein, ys_analytical)
srk_mse = compute_mse(ys_srk, ys_analytical)
euler_mse_, milstein_mse_, srk_mse_ = to_numpy(euler_mse, milstein_mse, srk_mse)
euler_mses_.append(euler_mse_)
milstein_mses_.append(milstein_mse_)
srk_mses_.append(srk_mse_)
plt.figure()
plt.plot(dts, euler_mses_, label='euler')
plt.plot(dts, milstein_mses_, label='milstein')
plt.plot(dts, srk_mses_, label='srk')
plt.xscale('log')
plt.yscale('log')
plt.legend()
img_dir = os.path.join('.', 'diagnostics', 'plots', 'srk_scalar')
makedirs_if_not_found(img_dir)
plt.savefig(os.path.join(img_dir, 'rate'))
plt.close()
def trajectory(self, x: torch.Tensor, s_span: torch.Tensor):
x = self._prep_sdeint(x)
sol = torchsde.sdeint(self.defunc,
x,
s_span,
rtol=self.rtol,
atol=self.atol,
method=self.solver,
dt=self.ds)
return sol
def _autograd(self, x):
self.defunc.intloss, self.defunc.sensitivity = self.intloss, self.sensitivity
return torchsde.sdeint(self.defunc,
x,
self.s_span,
rtol=self.rtol,
atol=self.atol,
adaptive=self.adaptive,
method=self.solver,
dt=self.ds)[-1]
def sample_p(self, ts, batch_size, eps=None, bm=None):
eps = torch.randn(batch_size, 1).to(
self.py0_mean) if eps is None else eps
y0 = self.py0_mean + eps * self.py0_std
return sdeint(self,
y0,
ts,
bm=bm,
method='srk',
dt=args.dt,
names={'drift': 'h'})
def sample_q(self, vis_span, n_sim, eps=None, bm=None, dt=0.01):
"""
:param vis_span:
:param n_sim:
:param eps:
:param bm:
:param dt:
"""
eps = torch.randn(n_sim, 1).to(self.qy0_mean) if eps is None else eps
y0 = self.qy0_mean + eps.to(self.device) * self.qy0_std
return torchsde.sdeint(self.defunc, y0, vis_span, bm=bm, method='srk', dt=dt)
def inspect_samples():
batch_size, d, m = 32, 1, 5
steps = 10
ts = torch.linspace(0., 5., steps=steps).to(device)
t0 = ts[0]
dt = 3e-1
y0 = torch.ones(batch_size, d).to(device)
sde = AdditiveSDE(d=d, m=m).to(device)
with torch.no_grad():
bm = BrownianPath(t0=t0, w0=torch.zeros(batch_size, m).to(device))
ys_em = sdeint(sde, y0=y0, ts=ts, dt=dt, bm=bm, method='euler')
ys_srk = sdeint(sde,
y0=y0,
ts=ts,
dt=dt,
bm=bm,
method='srk',
options={'trapezoidal_approx': False})
ys_true = sdeint(sde, y0=y0, ts=ts, dt=1e-3, bm=bm, method='euler')
ys_em = ys_em.squeeze().t()
ys_srk = ys_srk.squeeze().t()
ys_true = ys_true.squeeze().t()
ts_, ys_em_, ys_srk_, ys_true_ = to_numpy(ts, ys_em, ys_srk, ys_true)
# Visualize sample path.
img_dir = os.path.join('.', 'diagnostics', 'plots', 'srk_additive')
makedirs_if_not_found(img_dir)
for i, (ys_em_i, ys_srk_i,
ys_true_i) in enumerate(zip(ys_em_, ys_srk_, ys_true_)):
plt.figure()
plt.plot(ts_, ys_em_i, label='em')
plt.plot(ts_, ys_srk_i, label='srk')
plt.plot(ts_, ys_true_i, label='true')
plt.legend()
plt.savefig(os.path.join(img_dir, f'{i}'))
plt.close()
def inspect_samples(y0: Tensor,
ts: Vector,
dt: Scalar,
sde: BaseSDE,
bm: BaseBrownian,
img_dir: str,
methods: Tuple[str, ...],
options: Optional[Tuple] = None,
vis_dim=0,
dt_true: Optional[float] = 2**-14,
labels: Optional[Tuple[str, ...]] = None):
if options is None:
options = (None, ) * len(methods)
if labels is None:
labels = methods
sde = copy.deepcopy(sde).requires_grad_(False)
solns = [
sdeint(sde, y0, ts, bm, method=method, dt=dt, options=options_)
for method, options_ in zip(methods, options)
]
method_for_true = 'euler' if sde.sde_type == SDE_TYPES.ito else 'midpoint'
true = sdeint(sde, y0, ts, bm, method=method_for_true, dt=dt_true)
labels += ('true', )
solns += [true]
# (T, batch_size, d) -> (T, batch_size) -> (batch_size, T).
solns = [soln[..., vis_dim].t() for soln in solns]
for i, samples in enumerate(zip(*solns)):
utils.swiss_knife_plotter(img_path=os.path.join(img_dir, f'{i}'),
plots=[{
'x': ts,
'y': sample,
'label': label,
'marker': 'x'
} for sample, label in zip(samples, labels)])
def inspect_sample():
batch_size, d = 32, 1
steps = 100
ts = torch.linspace(0., 5., steps=steps).to(device)
t0 = ts[0]
dt = 1e-1
y0 = torch.ones(batch_size, d).to(device)
sde = Ex2(d=d).to(device)
sde.noise_type = "scalar"
with torch.no_grad():
bm = BrownianPath(t0=t0, w0=torch.zeros_like(y0))
ys_euler = sdeint(sde, y0=y0, ts=ts, dt=dt, bm=bm, method='euler')
ys_milstein = sdeint(sde, y0=y0, ts=ts, dt=dt, bm=bm, method='milstein')
ys_srk = sdeint(sde, y0=y0, ts=ts, dt=dt, bm=bm, method='srk', options={'trapezoidal_approx': False})
ys_analytical = sde.analytical_sample(y0=y0, ts=ts, bm=bm)
ys_euler = ys_euler.squeeze().t()
ys_milstein = ys_milstein.squeeze().t()
ys_srk = ys_srk.squeeze().t()
ys_analytical = ys_analytical.squeeze().t()
ts_, ys_euler_, ys_milstein_, ys_srk_, ys_analytical_ = to_numpy(
ts, ys_euler, ys_milstein, ys_srk, ys_analytical)
# Visualize sample path.
img_dir = os.path.join('.', 'diagnostics', 'plots', 'srk_scalar')
makedirs_if_not_found(img_dir)
for i, (ys_euler_i, ys_milstein_i, ys_srk_i, ys_analytical_i) in enumerate(
zip(ys_euler_, ys_milstein_, ys_srk_, ys_analytical_)):
plt.figure()
plt.plot(ts_, ys_euler_i, label='euler')
plt.plot(ts_, ys_milstein_i, label='milstein')
plt.plot(ts_, ys_srk_i, label='srk')
plt.plot(ts_, ys_analytical_i, label='analytical')
plt.legend()
plt.savefig(os.path.join(img_dir, f'{i}'))
plt.close()
def sde_sample(self,
batch_size=64,
tau=1.,
t=None,
y=None,
dt=1e-2,
tweedie_correction=True):
self.module.eval()
t = torch.tensor([-self.t1, -self.t0],
device=self.device) if t is None else t
y = self.sample_t1_marginal(batch_size, tau) if y is None else y
ys = torchsde.sdeint(self, y.flatten(start_dim=1), t, dt=dt)
ys = ys.view(len(t), *y.size())
if tweedie_correction:
ys[-1] = self.tweedie_correction(self.t0, ys[-1], dt)
return ys
def test_specialised_functions(sde_type, method):
vector = torch.randn(m)
fg = problems.FGSDE(sde_type, vector)
f_and_g = problems.FAndGSDE(sde_type, vector)
g_prod = problems.GProdSDE(sde_type, vector)
f_and_g_prod = problems.FAndGProdSDE(sde_type, vector)
f_and_g_with_g_prod1 = problems.FAndGGProdSDE1(sde_type, vector)
f_and_g_with_g_prod2 = problems.FAndGGProdSDE2(sde_type, vector)
y0 = torch.randn(batch_size, d)
outs = []
for sde in (fg, f_and_g, g_prod, f_and_g_prod, f_and_g_with_g_prod1, f_and_g_with_g_prod2):
bm = torchsde.BrownianInterval(t0, t1, (batch_size, m), entropy=45678)
outs.append(torchsde.sdeint(sde, y0, [t0, t1], dt=dt, bm=bm)[1])
for o in outs[1:]:
# Equality of floating points, because we expect them to do everything exactly the same.
assert o.shape == outs[0].shape
assert (o == outs[0]).all()
def sample_q(self, vis_span, n_sim, eps=None, bm=None, dt=0.01):
"""[summary]
Args:
vis_span ([type]): [description]
n_sim ([type]): [description]
eps ([type], optional): [description]. Defaults to None.
bm ([type], optional): [description]. Defaults to None.
dt (float, optional): [description]. Defaults to 0.01.
Returns:
[type]: [description]
"""
eps = torch.randn(n_sim, 1).to(self.qy0_mean) if eps is None else eps
y0 = self.qy0_mean + eps.to(self.device) * self.qy0_std
return torchsde.sdeint(self.defunc,
y0,
vis_span,
bm=bm,
method='srk',
dt=dt)
def forward(self, ts, batch_size):
# ts has shape (t_size,) and corresponds to the points we want to evaluate the SDE at.
###################
# Actually solve the SDE.
###################
init_noise = torch.randn(batch_size,
self._initial_noise_size,
device=ts.device)
x0 = self._initial(init_noise)
xs = torchsde.sdeint(self._func, x0, ts, method='midpoint',
dt=1.0) # shape (t_size, batch_size, hidden_size)
xs = xs.transpose(0, 1) # switch t_size and batch_size
ys = self._readout(xs)
###################
# Normalise the data to the form that the discriminator expects, in particular including time as a channel.
###################
t_size = ts.size(0)
ts = ts.unsqueeze(0).unsqueeze(-1).expand(batch_size, t_size, 1)
return torchcde.linear_interpolation_coeffs(torch.cat([ts, ys], dim=2))
def forward(self, eps: torch.Tensor, s_span=None):
"""[summary]
Args:
eps (torch.Tensor): [description]
s_span ([type], optional): [description]. Defaults to None.
Returns:
[type]: [description]
"""
eps = eps.to(self.qy0_std)
x0 = self.qy0_mean + eps * self.qy0_std
qy0 = Normal(loc=self.qy0_mean, scale=self.qy0_std)
py0 = Normal(loc=self.py0_mean, scale=self.py0_std)
logqp0 = kl_divergence(qy0, py0).sum(1).mean(0) # KL(time=0).
if s_span is not None:
s_span_ext = s_span
else:
s_span_ext = self.s_span.cpu()
zs, logqp = torchsde.sdeint(sde=self.defunc,
x0=x0,
s_span=s_span_ext,
rtol=self.rtol,
atol=self.atol,
logqp=True,
options=self.options,
adaptive=self.adaptive,
method=self.solver)
logqp = logqp.sum(0).mean(0)
log_ratio = logqp0 + logqp # KL(time=0) + KL(path).
return zs, log_ratio
def forward(self, ts, batch_size, eps=None):
eps = torch.randn(batch_size, 1).to(
self.qy0_std) if eps is None else eps
y0 = self.qy0_mean + eps * self.qy0_std
qy0 = Normal(loc=self.qy0_mean, scale=self.qy0_std)
py0 = Normal(loc=self.py0_mean, scale=self.py0_std)
logqp0 = kl_divergence(qy0, py0).sum(1).mean(0) # KL(time=0).
# `trapezoidal_approx` is for SRK. Disabling it gives better performance.
if args.adjoint:
zs, logqp = sdeint_adjoint(self,
y0,
ts,
logqp=True,
method=args.method,
dt=args.dt,
adaptive=args.adaptive,
rtol=args.rtol,
atol=args.atol,
options={'trapezoidal_approx': False})
else:
zs, logqp = sdeint(self,
y0,
ts,
logqp=True,
method=args.method,
dt=args.dt,
adaptive=args.adaptive,
rtol=args.rtol,
atol=args.atol,
options={'trapezoidal_approx': False})
logqp = logqp.sum(0).mean(0)
log_ratio = logqp0 + logqp # KL(time=0) + KL(path).
return zs, log_ratio
def get_data(batch_size, device):
class OrnsteinUhlenbeckSDE(torch.nn.Module):
sde_type = 'ito'
noise_type = 'scalar'
def __init__(self, mu, theta, sigma):
super(OrnsteinUhlenbeckSDE, self).__init__()
self.register_buffer('mu', torch.as_tensor(mu))
self.register_buffer('theta', torch.as_tensor(theta))
self.register_buffer('sigma', torch.as_tensor(sigma))
def f(self, t, y):
return self.mu * t - self.theta * y
def g(self, t, y):
return self.sigma.expand(y.size(0), 1, 1)
dataset_size = 8192
t_size = 64
ou_sde = OrnsteinUhlenbeckSDE(mu=0.02, theta=0.1, sigma=0.4).to(device)
y0 = torch.rand(dataset_size, device=device).unsqueeze(-1) * 2 - 1
ts = torch.linspace(0, t_size - 1, t_size, device=device)
ys = torchsde.sdeint(ou_sde, y0, ts, dt=1e-1)
###################
# To demonstrate how to handle irregular data, then here we additionally drop some of the data (by setting it to
# NaN.)
###################
ys_num = ys.numel()
to_drop = torch.randperm(ys_num)[:int(0.3 * ys_num)]
ys.view(-1)[to_drop] = float('nan')
###################
# Typically important to normalise data. Note that the data is normalised with respect to the statistics of the
# initial data, _not_ the whole time series. This seems to help the learning process, presumably because if the
# initial condition is wrong then it's pretty hard to learn the rest of the SDE correctly.
###################
y0_flat = ys[0].view(-1)
y0_not_nan = y0_flat.masked_select(~torch.isnan(y0_flat))
ys = (ys - y0_not_nan.mean()) / y0_not_nan.std()
###################
# As discussed, time must be included as a channel for the discriminator.
###################
ys = torch.cat([
ts.unsqueeze(0).unsqueeze(-1).expand(dataset_size, t_size, 1),
ys.transpose(0, 1)
],
dim=2)
# shape (dataset_size=1000, t_size=100, 1 + data_size=3)
###################
# Package up.
###################
data_size = ys.size(
-1
) - 1 # How many channels the data has (not including time, hence the minus one).
ys_coeffs = torchcde.linear_interpolation_coeffs(ys) # as per neural CDEs.
dataset = torch.utils.data.TensorDataset(ys_coeffs)
dataloader = torch.utils.data.DataLoader(dataset,
batch_size=batch_size,
shuffle=True)
return ts, data_size, dataloader
