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name: deep_ritz_residual_trial_network description: Build smooth residual trial networks for Deep Ritz variational PDE objectives.

Deep Ritz Residual Trial Network

When To Use

Use this skill when a variational PDE solver needs a scalar neural trial function u(x; theta) whose spatial gradients can be differentiated. Do not use it for mesh-only PDE discretizations.

Inputs

• Spatial dimension.
• Hidden width and residual block count.
• Activation choice, preferably cubic ReLU for Poisson-style Deep Ritz losses.
• Coordinate batch with gradient tracking enabled when a loss needs grad_x u.

Outputs

• A trainable scalar model.
• Forward values shaped [batch, 1].
• Input-gradient compatibility for energy losses.

Workflow

1. Project coordinates into hidden width.
2. Apply residual blocks with two affine transformations and smooth activation.
3. Apply a final linear readout.
4. Keep the model independent of any original implementation repository.

Validation

Run:

python tests/test_residual_network.py

Limitations

The helper uses PyTorch when available. If PyTorch is unavailable, tests still validate architecture metadata and deterministic parameter counting, but recovery should record that full autograd training is blocked.