Fourier-diagonalized natural gradients coincide with Sobolev mirror descent when their spectral symbols match and are otherwise preconditioned by it, yielding a new Spectral Natural Gradient implementation.
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MH-PINN compactifies unbounded domains with mapping and enforces wave boundary conditions through network architecture for efficient, accurate simulations.
A single trained parameterized NA-PINN coupled to FDM delivers low-error solutions for gravity-driven draining across multiple time steps and initial conditions without retraining or simulation data.
A multi-agent LLM framework, ATHENA, autonomously designs and refines numerical PDE solvers and physics-informed models, reportedly beating expert-authored baselines.
citing papers explorer
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Fourier-Diagonalized Natural Gradients and Sobolev Mirror Descent
Fourier-diagonalized natural gradients coincide with Sobolev mirror descent when their spectral symbols match and are otherwise preconditioned by it, yielding a new Spectral Natural Gradient implementation.
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Mapping-based Hard-constrained Physics-Informed Neural Networks for unbounded wave problems
MH-PINN compactifies unbounded domains with mapping and enforces wave boundary conditions through network architecture for efficient, accurate simulations.
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A Numerical Method for Coupling Parameterized Physics-Informed Neural Networks and FDM for Advanced Thermal-Hydraulic System Simulation
A single trained parameterized NA-PINN coupled to FDM delivers low-error solutions for gravity-driven draining across multiple time steps and initial conditions without retraining or simulation data.
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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.