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math.NA2026
Neural network approximation in discrete dual norms with adaptive test spaces
Tanakorn Udomworarat, Ignacio Brevis, Kristoffer G. van der Zee +1
In robust variational physics-informed neural networks (RVPINNs), the loss function is formulated in terms of the Riesz representative of the variational residual within a discrete…
math.NA2025
Neural network methods for Neumann series problems of Perron-Frobenius operators
T. Udomworarat, I. Brevis, M. Richter +2
Problems related to Perron-Frobenius operators (or transfer operators) have been extensively studied and applied across various fields. In this work, we propose neural network meth…