Learning Nonlinear Finite Element Solution Operators using Multilayer Perceptrons and Energy Minimization

arXiv:2412.04596 · cs.LG, cs.NA, math.NA · Submitted 2024-12-05 · Read on arXiv

cs.LG, cs.NA, math.NA

Submitted: 2024-12-05

Updated: 2026-09-28

Code: https://github.com/nmwsharp/neural-physics-subspaces

Terminology

• Loss Function — 1× in this paper · explained in 2 episodes
• Multilayer Perceptron (MLP) — 1× in this paper · explained in 2 episodes

Sources

• Accelerating the convergence of Newton's method for nonlinear elliptic PDEs using Fourier neural operators
• Neural Operator: Graph Kernel Network for Partial Differential Equations
• Fourier Neural Operator for Parametric Partial Differential Equations

Related papers

• Polynomial-Augmented Neural Networks (PANNs) with Weak Orthogonality Constraints for Enhanced Function and PDE Approximation
• AIRL-S: Unifying Reinforcement Learning and Search-Based Test-Time Scaling via Adversarial Inverse Reinforcement Learning
• Transformers as Bayesian In-Context Experimenters: Smoothness-Adaptive Efficient ATE Estimation
• Convergence issues in Relational Concept Analysis based on AOC-posets
• Beliefs Beyond Posteriors: The Predictive Cost of ELBO Binding
• Understanding Diffusion Models via Ratio-Based Function Approximation with SignReLU Networks