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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…
physics.flu-dyn2026
Finite basis physics-informed neural networks with hard constraints for viscous fluid flow in highly perforated domains
Jeeeun Lee, Denis Korolev, Miro Duhovic +1
In this work, viscous fluid flow governed by the Stokes equations in highly perforated domains is studied using physics-informed neural networks (PINNs). Perforated microstructures…
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…