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.
A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks
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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.
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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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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.