3 papers
math.NA2026
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…
math.NA2026
Adaptive Randomized Neural Networks with Locally Activation Function: Theory and Algorithm for Solving PDEs
Ran Bi, Weibing Deng
This paper establishes an approximation theory and develop an adaptive computational framework for randomized neural networks (RaNNs). For RaNNs of the form $\sum_{i=1}^{N} W_i σ(A…
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 presents considerable difficulties because strong form residuals become ill…