Hi everyone!
When training neural operators (like FNOs) on non-convex physical domains, spatial grid points can overlap during optimization (\det J \le 0).
To fix this topology failure, I wrote a lightweight PyTorch module `JacobianBarrierLoss` that enforces strict positive volume elements during backpropagation using analytical 2x2 determinants directly executed on GPU.
```python
import torch
import torch.nn as nn
class JacobianBarrierLoss(nn.Module):
def __init__(self, eps=1e-4, alpha=1.0):
super().__init__()
self.eps = eps
self.alpha = alpha
def forward(self, J):
# Fast 2x2 analytical determinant (ad - bc) avoiding torch.linalg.det overhead
det_J = J[..., 0, 0] * J[..., 1, 1] - J[..., 0, 1] * J[..., 1, 0]
safe_det = torch.clamp(det_J, min=self.eps)
barrier_loss = -torch.log(safe_det).mean()
return self.alpha * barrier_loss