Issue with Enforcing Initial Conditions at t=0 in 2D Linear Elasticity Problem (proportional loading)

[IkramArif21]

Hi Lu Lu,

I’m working on a 2D linear elastic problem with a varying load using DeepXDE. In my simulation, the initial conditions (ICs) should ensure that all output parameters (displacements and stresses) are zero at t=0, since no load is applied initially. I’ve implemented the ICs in two ways—first as soft constraints and then via an output transform (hard constraints)—but I’m still observing nonzero values for the outputs at t=0.

Here’s how I defined my initial conditions as soft constraints:

_dde.IC(geomtime, ic_u1, lambda _, on_initial: on_initial, component=0),
dde.IC(geomtime, ic_u2, lambda , on_initial: on_initial, component=1),

And here’s my output transform for hard enforcing the conditions (for the displacements):

def output_transform(x, f):
# Enforce u1 = 0 and u2 = 0 on the left edge and at t=0
u1 = f[:, 0:1] * x[:, 0:1] * x[:, 1:2]
u2 = f[:, 1:2] * x[:, 0:1] * x[:, 1:2]
return tf.concat([u1, u2, f[:, 2:]], axis=1)

Despite these implementations, at t=0 the outputs for displacements and stresses are not zero as expected.

Questions:

1. What could be causing the initial condition not to be strictly enforced at t=0, even when using both soft and hard constraint formulations?

2. Are there any common pitfalls or issues in DeepXDE that might lead to this behavior in spatio-temporal domains?

3. Can anyone suggest modifications or debugging steps to help ensure that all output parameters are exactly zero at t=0?

Any insights or advice would be greatly appreciated.

Thanks in advance!