ArticleAdvances in neural information processing systems2024
Newton Informed Neural Operator for Solving Nonlinear Partial Differential Equations.
Article in Advances in neural information processing systems, 2024. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 6 papers.
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Who cites it
6 citing papers in PubMed.
- PatternFormer: Learning Multiple Solution Patterns in Reaction-Diffusion Systems.Research square · 2026Article
- Broadband Electromagnetic Field Prediction at Unseen Wavelengths via Physics-Guided Neural Operators.Nanophotonics (Berlin, Germany) · 2026Article
- ZENN: A thermodynamics-inspired computational framework for heterogeneous data-driven modeling.Proceedings of the National Academy of Sciences of the United States of America · 2026Article
- Laplacian Eigenfunction-Based Neural Operator for Learning Nonlinear Reaction-Diffusion Dynamics.Journal of computational physics · 2025Article
- Automatic Differentiation is Essential in Training Neural Networks for Solving Differential Equations.Journal of scientific computing · 2025Article
- Learn Singularly Perturbed Solutions via Homotopy Dynamics.Proceedings of machine learning research · 2025Article
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Authors and funding
3 authors.
Funding
Abstract
Solving nonlinear partial differential equations (PDEs) with multiple solutions is essential in various fields, including physics, biology, and engineering. However, traditional numerical methods, such as finite element and finite difference methods, often face challenges when dealing with nonlinear solvers, particularly in the presence of multiple solutions. These methods can become computationally expensive, especially when relying on solvers like Newton's method, which may struggle with ill-posedness near bifurcation points. In this paper, we propose a novel approach, the Newton Informed Neural Operator, which learns the Newton solver for nonlinear PDEs. Our method integrates traditional numerical techniques with the Newton nonlinear solver, efficiently learning the nonlinear mapping at each iteration. This approach allows us to compute multiple solutions in a single learning process while requiring fewer supervised data points than existing neural network methods.
Identifiers
40196134PMC11973962What OpenQuestion holds
Registered trials
Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.