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math.NA2026
Preconditioning and Numerical Stability in Neural Network Training for Parametric PDEs
Markus Bachmayr, Wolfgang Dahmen, Chenguang Duan +1
In the context of training neural network-based approximations of solutions of parameter-dependent PDEs, we investigate the effect of preconditioning via well-conditioned frame rep…
math.NA2024
Variationally Correct Neural Residual Regression for Parametric PDEs: On the Viability of Controlled Accuracy
Markus Bachmayr, Wolfgang Dahmen, Mathias Oster
This paper is about learning the parameter-to-solution map for systems of partial differential equations (PDEs) that depend on a potentially large number of parameters covering all…