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math.OC2026
Tensor-Train Compressed Separable PINNs: A Curvature-Aware Optimization Framework for Parametric PDEs in High Dimensions
Denis Korolev, Martin Eigel
In this work, we develop a second-order optimization framework for physics-informed neural networks (PINNs) applied to high-dimensional parametric partial differential equations (P…
math.OC2026
Layerwise goal-oriented adaptivity for neural ODEs: an optimal control perspective
Michael Hintermüller, Michael Hinze, Denis Korolev
In this work, we propose a novel layerwise adaptive construction method for neural network architectures. Our approach is based on a goal--oriented dual-weighted residual technique…
math.OC2023★ 3 cited
A hybrid physics-informed neural network based multiscale solver as a partial differential equation constrained optimization problem
Michael Hintermüller, Denis Korolev
In this work, we study physics-informed neural networks (PINNs) constrained by partial differential equations (PDEs) and their application in approximating PDEs with two characteri…