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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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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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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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.