Dual variational neural network decouples p-Laplace into linear Poisson and divergence-free minimization subproblems approximated by two NNs, with error analysis from vector inequalities and statistical learning theory, showing robust convergence for p near 1 and large p.
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beignet replaces random Fourier feature embeddings in PINNs with a trainable multi-resolution Fourier feature pyramid, achieving higher accuracy on PDE benchmarks with fewer parameters and near machine precision residuals on the inviscid Burgers blowup using Adam.
A multi-agent LLM framework, ATHENA, autonomously designs and refines numerical PDE solvers and physics-informed models, reportedly beating expert-authored baselines.
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Dual Variational Neural Network for the $p$-Laplace Problem
Dual variational neural network decouples p-Laplace into linear Poisson and divergence-free minimization subproblems approximated by two NNs, with error analysis from vector inequalities and statistical learning theory, showing robust convergence for p near 1 and large p.
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Fourier Feature Pyramids for Physics-Informed Neural Networks
beignet replaces random Fourier feature embeddings in PINNs with a trainable multi-resolution Fourier feature pyramid, achieving higher accuracy on PDE benchmarks with fewer parameters and near machine precision residuals on the inviscid Burgers blowup using Adam.
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ATHENA: Agentic Team for Hierarchical Evolutionary Numerical Algorithms
A multi-agent LLM framework, ATHENA, autonomously designs and refines numerical PDE solvers and physics-informed models, reportedly beating expert-authored baselines.