S$^{2}$-PINN: Stochastic Separable Physics-Informed Neural Networks
Read the original on arXiv Machine Learning →The paper introduces S$^{2}$-PINN, a stochastic separable physics-informed neural network that models the solution of random partial differential equations using a learnable Gaussian spatial dictionary, Fourier temporal features, and a generalized polynomial chaos stochastic basis linked by a low-rank Canonical Polyadic tensor core. Training employs a hybrid strong-form and gPC-projected residual loss, and theoretical analysis shows the separable class is dense in $L^2$ and that the projected residual matches a stochastic Galerkin constraint. Experiments on four manufactured benchmarks and additional Poisson, Darcy, Navier–Stokes, and inverse problems demonstrate that S$^{2}$-PINN achieves higher mean and variance accuracy, better calibration, and fewer parameters than nine baselines, supporting stochastic separability as an effective design principle for physics-informed neural UQ.
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