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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-…
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…
R-adaptive DeepONet: Learning Solution Operators for PDEs with Discontinuous Solutions Using an R-adaptive Strategy
Yameng Zhu, Jingrun Chen, Weibing Deng
DeepONet has recently been proposed as a representative framework for learning nonlinear mappings between function spaces. However, when it comes to approximating solution operator…
XI-DeepONet: An operator learning method for elliptic interface problems
Ran Bi, Jingrun Chen, Weibing Deng
Scientific computing has been an indispensable tool in applied sciences and engineering, where traditional numerical methods are often employed due to their superior accuracy guara…