Alternating Levenberg-Marquardt Training of Physics-Informed Neural Networks with Fourier-Enhanced Features

arXiv:2608.05892 · cs.LG, math.NA · Submitted 2026-08-06 · Read on arXiv

Yulun Wu, Matthieu Barreau, Miguel Aguiar, Karl H. Johansson

cs.LG, math.NA

Submitted: 2026-08-06

Comments: 53 pages, 18 figures, 6 tables

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Spectral Bias — 17× in this paper · explained in 2 episodes
• Adam — 14× in this paper · explained in 3 episodes
• Benchmark — 11× in this paper · explained in 2 episodes
• Accuracy — 8× in this paper · explained in 1 episode
• Latent Space — 6× in this paper · explained in 7 episodes
• Residual-Based Attention — 5× in this paper
• Conservation Laws — 4× in this paper · explained in 3 episodes
• Physics-Informed Neural Networks (PINNs) — 4× in this paper · explained in 8 episodes
• Representation Learning — 4× in this paper · explained in 3 episodes
• Ablation — 3× in this paper · explained in 1 episode
• Convergence Guarantees — 3× in this paper · explained in 3 episodes
• Diffusion Model — 3× in this paper · explained in 10 episodes
• Embeddings — 3× in this paper · explained in 2 episodes
• Hyperparameters — 3× in this paper · explained in 2 episodes
• Inverse Problem — 3× in this paper · explained in 2 episodes
• Latent Representation — 3× in this paper · explained in 2 episodes
• Active Learning — 2× in this paper · explained in 6 episodes
• Decoupling — 2× in this paper · explained in 2 episodes
• DeepONet — 2× in this paper · explained in 2 episodes
• Diffusion Models — 2× in this paper · explained in 9 episodes
• Entanglement — 2× in this paper · explained in 5 episodes
• Failure Modes — 2× in this paper · explained in 3 episodes
• Robustness — 2× in this paper · explained in 6 episodes
• Training Objective — 2× in this paper · explained in 3 episodes
• Transformer — 2× in this paper · explained in 2 episodes
• Ablation Study — 1× in this paper · explained in 3 episodes
• Composition — 1× in this paper · explained in 2 episodes
• Expressivity — 1× in this paper · explained in 2 episodes
• Fidelity — 1× in this paper · explained in 2 episodes
• Flow Matching — 1× in this paper · explained in 22 episodes
• Generalization — 1× in this paper · explained in 14 episodes
• Inductive Bias — 1× in this paper · explained in 3 episodes
• Inverse Design — 1× in this paper · explained in 2 episodes
• Kernel Ridge Regression — 1× in this paper · explained in 2 episodes
• Papers — 1× in this paper · explained in 3 episodes
• Parameterization — 1× in this paper · explained in 2 episodes
• Performance Gap — 1× in this paper · explained in 2 episodes
• Physical Constraints — 1× in this paper · explained in 7 episodes
• Residual Connections — 1× in this paper · explained in 3 episodes
• Residual-based Attention (RBA) — 1× in this paper · explained in 2 episodes
• Singular Value Decomposition (SVD) — 1× in this paper · explained in 3 episodes
• Uncertainty Quantification — 1× in this paper · explained in 9 episodes

Sources

• Source-Guided Flow Matching
• Complex Physics-Informed Neural Network
• Iterative Training of Physics-Informed Neural Networks with Fourier-enhanced Features
• Adam: A Method for Stochastic Optimization

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