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math.NA2026
CI-PINN: Causal Integral Physics-Informed Neural Network for Solving Evolution Equations
Xiaodong Feng, Ziyu Sun, Tao Tang +2
Physics-informed neural networks (PINNs) solve partial differential equations (PDEs) by incorporating governing physical laws into the training loss. For evolution equations, howev…
cs.LG2026
Deep Adaptive Dimension Reduction for Bayesian Inference in Inverse Problems
Yueyang Wang, Xili Wang, Kejun Tang +3
Solving high-dimensional PDE-governed inverse problems is often challenging due to complex non-Gaussian posterior distributions, expensive forward model evaluations, and misspecifi…
stat.ML2026
Amortized Filtering and Smoothing with Conditional Normalizing Flows
Tiangang Cui, Xiaodong Feng, Chenlong Pei +2
Bayesian filtering and smoothing are central to data assimilation in nonlinear dynamical systems. Recent advances in deep generative models provide flexible approximations of the a…