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math.NA2025
Dimension reduction for derivative-informed operator learning: An analysis of approximation errors
Dingcheng Luo, Thomas O'Leary-Roseberry, Peng Chen +1
We study the derivative-informed learning of nonlinear operators between infinite-dimensional separable Hilbert spaces by neural networks. Such operators can arise from the solutio…
math.NA2024
Gaussian mixture Taylor approximations of risk measures constrained by PDEs with Gaussian random field inputs
Dingcheng Luo, Joshua Chen, Peng Chen +1
This work considers the computation of risk measures for quantities of interest governed by PDEs with Gaussian random field parameters using Taylor approximations. While efficient,…
math.NA2020
Tensor train construction from tensor actions, with application to compression of large high order derivative tensors
Nick Alger, Peng Chen, Omar Ghattas
We present a method for converting tensors into tensor train format based on actions of the tensor as a vector-valued multilinear function. Existing methods for constructing tensor…