Learning-guided Kansa collocation for forward and inverse PDEs beyond linearity
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.
698ad28e1b2dc6b37d61b234
Zheyuan Hu
claimed_verified
2026-02-10T09:04:34.533Z
653053c6657ae56cdb5c490b
https://cdn-avatars.huggingface.co/v1/production/uploads/653053c6657ae56cdb5c490b/Zl0bZZ7-tD9AR6muE8esU.png
Peter Hu
Peter2023HuggingFace
user
Peter2023HuggingFace
698ad28e1b2dc6b37d61b235
Weitao Chen
698ad28e1b2dc6b37d61b236
Cengiz Öztireli
698ad28e1b2dc6b37d61b237
Chenliang Zhou
698ad28e1b2dc6b37d61b238
Fangcheng Zhong
Learning-guided Kansa collocation for forward and inverse PDEs beyond linearity
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.
Research explores PDE solvers including neural frameworks for scientific simulations, examining forward solutions, inverse problems, and equation discovery across multi-variable and non-linear systems.
PDE solvers neural PDE solvers scientific simulation forward solution inverse problems equation discovery CNF multi-dependent-variable non-linear settings