Learning-guided Kansa collocation for forward and inverse PDEs beyond linearity
Abstract
Partial Differential Equations are precise in modelling the physical, biological and graphical phenomena. However, the numerical methods suffer from the curse of dimensionality, high computation costs and domain-specific discretization. We aim to explore pros and cons of different PDE solvers, and apply them to specific scientific simulation problems, including forwarding solution, inverse problems and equations discovery. In particular, we extend the recent CNF (NeurIPS 2023) framework solver to coupled and non-linear settings, together with down-stream applications. The outcomes include implementation of selected methods, self-tuning techniques, evaluation on benchmark problems and a comprehensive survey of neural PDE solvers and scientific simulation applications.
Cite
@article{arxiv.2602.07970,
title = {Learning-guided Kansa collocation for forward and inverse PDEs beyond linearity},
author = {Zheyuan Hu and Weitao Chen and Cengiz Öztireli and Chenliang Zhou and Fangcheng Zhong},
journal= {arXiv preprint arXiv:2602.07970},
year = {2026}
}
Comments
Accepted for poster presentation at the ICLR 2026 Artificial Intelligence and Partial Differential Equations (AI&PDE) Workshop. Fangcheng Zhong and Chenliang Zhou are co-corresponding authors