Kindly ask for any ideas about how I can debug the following PyTorch error. Here's an example adapted from the official example about the inverse modeling of the reaction-diffusion system:
"""Backend supported: tensorflow.compat.v1, tensorflow, pytorch, paddle"""
import deepxde as dde
import numpy as np
import torch
def gen_traindata():
data = np.load("reaction.npz")
t, x, ca, cb = data["t"], data["x"], data["Ca"], data["Cb"]
X, T = np.meshgrid(x, t)
X = np.reshape(X, (-1, 1))
T = np.reshape(T, (-1, 1))
Ca = np.reshape(ca, (-1, 1))
Cb = np.reshape(cb, (-1, 1))
return np.hstack((X, T)), Ca, Cb
kf = dde.Variable(0.05)
D = dde.Variable(1.0)
def pde(x, y):
ca, cb = y[:, 0:1], y[:, 1:2]
dca_t = dde.grad.jacobian(y, x, i=0, j=1)
dca_xx = dde.grad.hessian(y, x, component=0, i=0, j=0)
dcb_t = dde.grad.jacobian(y, x, i=1, j=1)
dcb_xx = dde.grad.hessian(y, x, component=1, i=0, j=0)
eq_a = dca_t - 1e-3 * D * dca_xx + kf * ca * cb ** 2
eq_b = dcb_t - 1e-3 * D * dcb_xx + 2 * kf * ca * cb ** 2
return [eq_a, eq_b]
def fun_bc(x):
return 1 - x[:, 0:1]
###### main changes start from here ##########
# def fun_init(x):
# return np.exp(-20 * x[:, 0:1])
x0 = dde.Variable(0.2)
def fun_init(x):
return torch.exp(-10 * (dde.backend.as_tensor(x[:, 0:1]) - x0)**2)
###### main changes end here ##########
geom = dde.geometry.Interval(0, 1)
timedomain = dde.geometry.TimeDomain(0, 10)
geomtime = dde.geometry.GeometryXTime(geom, timedomain)
bc_a = dde.icbc.DirichletBC(
geomtime, fun_bc, lambda _, on_boundary: on_boundary, component=0
)
bc_b = dde.icbc.DirichletBC(
geomtime, fun_bc, lambda _, on_boundary: on_boundary, component=1
)
ic1 = dde.icbc.IC(geomtime, fun_init, lambda _,
on_initial: on_initial, component=0)
ic2 = dde.icbc.IC(geomtime, fun_init, lambda _,
on_initial: on_initial, component=1)
observe_x, Ca, Cb = gen_traindata()
# simplification
print(observe_x.shape, Ca.shape, Cb.shape)
observe_x = observe_x[::20, :]
Ca = Ca[::20, :]
Cb = Cb[::20, :]
#--
observe_y1 = dde.icbc.PointSetBC(observe_x, Ca, component=0)
observe_y2 = dde.icbc.PointSetBC(observe_x, Cb, component=1)
data = dde.data.TimePDE(
geomtime,
pde,
[bc_a, bc_b, ic1, ic2, observe_y1, observe_y2],
num_domain=1000,
num_boundary=100,
num_initial=100,
# anchors=observe_x,
num_test=1000,
)
net = dde.nn.FNN([2] + [20] * 2 + [2], "tanh", "Glorot uniform")
model = dde.Model(data, net)
model.compile("adam", lr=0.001, external_trainable_variables=[kf, D, x0])
variable = dde.callbacks.VariableValue([kf, D, x0], period=100)
losshistory, train_state = model.train(iterations=200, callbacks=[variable])
# dde.saveplot(losshistory, train_state, issave=True, isplot=True)
I ran this example on a Ubuntu 22.04 computer with python 3.10, deepxde 1.11.0 and torch 2.2.2+cu121. The error messages I got are
Traceback (most recent call last):
File "~/.../test-unknowninit.py", line 87, in <module>
losshistory, train_state = model.train(iterations=200, callbacks=[variable])
File "~/miniforge3/envs/de/lib/python3.10/site-packages/deepxde/utils/internal.py", line 22, in wrapper
result = f(*args, **kwargs)
File "~/miniforge3/envs/de/lib/python3.10/site-packages/deepxde/model.py", line 650, in train
self._train_sgd(iterations, display_every)
File "~/miniforge3/envs/de/lib/python3.10/site-packages/deepxde/model.py", line 668, in _train_sgd
self._train_step(
File "~/miniforge3/envs/de/lib/python3.10/site-packages/deepxde/model.py", line 562, in _train_step
self.train_step(inputs, targets, auxiliary_vars)
File "~/miniforge3/envs/de/lib/python3.10/site-packages/deepxde/model.py", line 362, in train_step
self.opt.step(closure)
File "~/miniforge3/envs/de/lib/python3.10/site-packages/torch/optim/optimizer.py", line 385, in wrapper
out = func(*args, **kwargs)
File "~/miniforge3/envs/de/lib/python3.10/site-packages/torch/optim/optimizer.py", line 76, in _use_grad
ret = func(self, *args, **kwargs)
File "~/miniforge3/envs/de/lib/python3.10/site-packages/torch/optim/adam.py", line 146, in step
loss = closure()
File "~/miniforge3/envs/de/lib/python3.10/site-packages/deepxde/model.py", line 359, in closure
total_loss.backward()
File "~/miniforge3/envs/de/lib/python3.10/site-packages/torch/_tensor.py", line 522, in backward
torch.autograd.backward(
File "~/miniforge3/envs/de/lib/python3.10/site-packages/torch/autograd/__init__.py", line 266, in backward
Variable._execution_engine.run_backward( # Calls into the C++ engine to run the backward pass
RuntimeError: Trying to backward through the graph a second time (or directly access saved tensors after they have already been freed). Saved intermediate values of the graph are freed when you call .backward() or autograd.grad(). Specify retain_graph=True if you need to backward through the graph a second time or if you need to access saved tensors after calling backward.
Specifically, the error occurs at total_loss.backward() during the 2nd iteration in train_step (in model.py).
Some detailed explanations of the codes: The difference from the official example is that I include a trainable variable x0 in the fun_init used to create the initial conditions ic1, ic2. Specifically, the function is changed from
def fun_init(x):
return np.exp(-20 * x[:, 0:1])
to
def fun_init(x):
return torch.exp(-10 * (dde.backend.as_tensor(x[:, 0:1]) - x0)**2)
which assumes that the initial distribution is centered at an unknown
. Noticing that the input of fun_init will be a Numpy array, I change np to torch and add a dde.backend.as_tensor such that the computations are compatible with the torch.Tensor variable x0.
The problem stems from deepxde trying to use cached initial/boundary values instead of newly calculated ones. A detailed explanation has been posted in the discussion panel of deepxde.