🐛[BUG]: Diffusion(time=True) in darcy_physics_informed/utils.py silently drops the time-derivative term #2020

Version

physicsnemo 2.1.1

On which installation method(s) does this occur?

No response

Describe the issue

In examples/cfd/darcy_physics_informed/utils.py, Diffusion builds the field as
T_var = Function(T)(*iv.values()) with iv = {x, y} (L52), and when time=True adds
T_var.diff(Symbol("t")) (L57). Since T_var does not depend on t, SymPy evaluates the
derivative to 0, so time=True silently produces the steady equation.

Expected: Derivative(u(x, y, t), t) - DDerivative(u, (x, 2)) - DDerivative(u, (y, 2))

Impact: both Darcy examples use time=False (darcy_physics_informed_fno.py L84,
darcy_physics_informed_deeponet.py L124), so they are unaffected. Anyone reusing the
class for a transient problem (the docstring advertises dT/dt) trains against the
steady equation with no warning.

Suggested fix (after L51):
if time:
iv["t"] = Symbol("t")
With it, the equation vanishes on the exact heat solution
T = exp(-2π²Dt)·sin(πx)·sin(πy) (max residual ~1e-6), and time=False equations are unchanged.

Minimum reproducible example

cd examples/cfd/darcy_physics_informed
python -c "from utils import Diffusion; print(Diffusion(T='u', D=1.0, time=True).equations)"
# {'diffusion_u': -1.0*Derivative(u(x, y), (x, 2)) - 1.0*Derivative(u(x, y), (y, 2))}   <- no d/dt term

Relevant log output

Environment details