Sensitivity-Constrained Neural Operators for Data-Efficient Forward and Inverse Modeling of Partial Differential Equation Systems
Neural operators provide fast surrogates for partial differential equation (PDE) solvers, but their reliability can degrade for high-dimensional spatial inputs and inverse or repeated inference. State-only training constrains solution values but not the learned input--output response. We study sensitivity-constrained neural operators (SC-NOs), which augment standard training with sampled solver-derived Jacobian supervision. Selected sensitivities from differentiable solvers or discrete adjoints are matched during training, allowing response information to be amortized across minibatches without imposing the full Jacobian at every update. We evaluate SC-NO on advection--diffusion and RANS-...
| Authors | Abdolmehdi Behroozi, Chaopeng Shen, Daniel Kifer et al. |
|---|---|
| Primary category | cs.LG |
| Published | 30 August 2026 |
| Last updated at source | 30 August 2026 |
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