S$^{2}$-PINN: Stochastic Separable Physics-Informed Neural Networks
Uncertainty quantification (UQ) for random partial differential equations (PDEs) is ubiquitous in computational science and engineering. However, classical spectral solvers for this class of problems face the curse of dimensionality, and existing neural solvers often ignore the stochastic structure that makes moments and calibration tractable. We introduce a stochastic separable physics-informed neural network, dubbed S$^{2}$-PINN, that represents the solution $u(t,\mathbf{x},\mathbf{Z})$ of a random PDE with a learnable Gaussian spatial dictionary, Fourier temporal features, and a generalized polynomial chaos (gPC) stochastic basis, coupled by a low-rank Canonical Polyadic (CP) tensor de...
| Authors | Zhendong Li, Akwum Onwunta |
|---|---|
| Primary category | cs.LG |
| Published | 2 October 2026 |
| Last updated at source | 2 October 2026 |
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