Update direction selection for PINN training is cast as a Chebyshev-center problem in the dual cone, yielding an efficient dual formulation with nonconvex convergence guarantees and automatic recovery of scale robustness and simultaneous descent.
When and why pinns fail to train: A neural tangent kernel perspective.Journal of Computational Physics, 449:110768
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A multi-network PINN with NTK-based adaptive weighting jointly estimates source functions, velocity, diffusion parameters, and the solution field in advection-diffusion PDEs from noisy sparse data.
MC² corrects low-budget Monte Carlo solutions for elliptic PDEs with a single-pass neural network to match the accuracy of 1000× more Monte Carlo samples while outperforming classical and learned baselines.
ResearchEVO automates the discover-then-explain cycle by evolving algorithms via fitness-driven LLM co-evolution and generating grounded, anti-hallucination research papers through sentence-level RAG.
The Neural Basis Method uses a predefined neural basis space and operator residual metric to deliver accurate single solves and fast parametric learning for multiscale Darcian dynamics.
citing papers explorer
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Chebyshev Center-Based Direction Selection for Multi-Objective Optimization and Training PINNs
Update direction selection for PINN training is cast as a Chebyshev-center problem in the dual cone, yielding an efficient dual formulation with nonconvex convergence guarantees and automatic recovery of scale robustness and simultaneous descent.
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Physics-Informed Neural Networks for Joint Source and Parameter Estimation in Advection-Diffusion Equations
A multi-network PINN with NTK-based adaptive weighting jointly estimates source functions, velocity, diffusion parameters, and the solution field in advection-diffusion PDEs from noisy sparse data.
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MC$^2$: Monte Carlo Correction for Fast Elliptic PDE Solving
MC² corrects low-budget Monte Carlo solutions for elliptic PDEs with a single-pass neural network to match the accuracy of 1000× more Monte Carlo samples while outperforming classical and learned baselines.
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ResearchEVO: An End-to-End Framework for Automated Scientific Discovery and Documentation
ResearchEVO automates the discover-then-explain cycle by evolving algorithms via fitness-driven LLM co-evolution and generating grounded, anti-hallucination research papers through sentence-level RAG.
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Solving and learning advective multiscale Darcian dynamics with the Neural Basis Method
The Neural Basis Method uses a predefined neural basis space and operator residual metric to deliver accurate single solves and fast parametric learning for multiscale Darcian dynamics.