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20242026
most citedR-adaptive DeepONet: Learning Solution Operators for PDEs with Discontinuous Solutions Using an R-adaptive Strategy

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math.NA2025

A Two-stage Adaptive Lifting PINN Framework for Solving Viscous Approximations to Hyperbolic Conservation Laws

Yameng Zhu, Weibing Deng, Ran Bi

Training physics-informed neural networks (PINNs) for hyperbolic conservation laws near the inviscid limit is challenging because shock discontinuities invalidate classical strong-…

math.NA2025

Extended Interface Physics-Informed Neural Networks Method for Moving Interface Problems

Ran Bi, Weibing Deng, Yameng Zhu

Physics-informed neural networks (PINNs) have emerged as an effective class of mesh-free methods for solving partial differential equations (PDEs), particularly on complex geometri…