Learning-guided Kansa collocation for forward and inverse PDEs beyond linearity

Peter Hu, Weitao Chen, Cengiz Öztireli, Chenliang Zhou, Fangcheng Zhong

Learning-guided Kansa collocation for forward and inverse PDEs beyond linearity: 0 upvotes on Hugging Face Daily Papers, #48 of 58 papers on 2026-02-10. Day-by-day upvote history.

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 multi-dependent-variable 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.

Paper page on Hugging Face · arXiv

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