Parameterized Representations via Implicit Stochastic Modulation for High-Dimensional and High-Order Neural PDE Solvers
Solving high-dimensional and high-order PDEs is challenged by the coupled growth of spatial dimensionality and derivative order. Recent stochastic derivative estimators reduce this cost by replacing full derivative tensors with randomized dimension or Taylor estimators, but they are mostly designed for fixed physical parameters and require retraining for each new parameter. We show that direct conditional parameterization of such solvers entangles physical parameters with the high-order automatic differentiation graph, causing extra memory growth and parameter-induced variance amplification. We propose Parameterized Representations via Implicit Stochastic Modulation (PRISM), a plug-and-pl...
| Authors | Zhangyong Liang, Huanhuan Gao |
|---|---|
| Primary category | cs.LG |
| Published | 20 June 2026 |
| Last updated at source | 20 June 2026 |
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