The work introduces a modulation-based analytical method for singularity proofs in singular PDEs and refines ML techniques like PINNs and KANs to identify blowup solutions, with application to the open 3D Keller-Segel problem.
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A multi-agent LLM framework, ATHENA, autonomously designs and refines numerical PDE solvers and physics-informed models, reportedly beating expert-authored baselines.
Frequency-adaptive tensor neural networks are proposed to overcome the frequency principle in TNNs for high-dimensional multi-scale problems by incorporating random Fourier features and 1D DFT on component functions.
A systematic review of Kolmogorov-Arnold Networks that maps their relation to Kolmogorov superposition theory, MLPs, and kernels, examines basis-function design choices, summarizes performance advances, and supplies a practitioner's selection guide plus open challenges.
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Singularity Formation: Synergy in Theoretical, Numerical and Machine Learning Approaches
The work introduces a modulation-based analytical method for singularity proofs in singular PDEs and refines ML techniques like PINNs and KANs to identify blowup solutions, with application to the open 3D Keller-Segel problem.
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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.
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Frequency-adaptive tensor neural networks for high-dimensional multi-scale problems
Frequency-adaptive tensor neural networks are proposed to overcome the frequency principle in TNNs for high-dimensional multi-scale problems by incorporating random Fourier features and 1D DFT on component functions.
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A Practitioner's Guide to Kolmogorov-Arnold Networks
A systematic review of Kolmogorov-Arnold Networks that maps their relation to Kolmogorov superposition theory, MLPs, and kernels, examines basis-function design choices, summarizes performance advances, and supplies a practitioner's selection guide plus open challenges.