Layerwise goal-oriented adaptivity for neural ODEs: an optimal control perspective

Fuente: arXiv
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Main Authors: Hintermüller, Michael, Hinze, Michael, Korolev, Denis
Format: Preprint
Published: 2026
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author Hintermüller, Michael
Hinze, Michael
Korolev, Denis
author_facet Hintermüller, Michael
Hinze, Michael
Korolev, Denis
contents 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 for the optimal control of neural differential equations. This leads to an ordinary differential equation constrained optimization problem with controls acting as coefficients and a specific loss function. We implement our approach on the basis of a DG(0) Galerkin discretization of the neural ODE, leading to an explicit Euler time marching scheme. For the optimization we use steepest descent. Finally, we apply our method to the construction of neural networks for the classification of data sets, where we present results for a selection of well known examples from the literature.
format Preprint
id arxiv_https___arxiv_org_abs_2601_07397
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Layerwise goal-oriented adaptivity for neural ODEs: an optimal control perspective
Hintermüller, Michael
Hinze, Michael
Korolev, Denis
Optimization and Control
Artificial Intelligence
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 for the optimal control of neural differential equations. This leads to an ordinary differential equation constrained optimization problem with controls acting as coefficients and a specific loss function. We implement our approach on the basis of a DG(0) Galerkin discretization of the neural ODE, leading to an explicit Euler time marching scheme. For the optimization we use steepest descent. Finally, we apply our method to the construction of neural networks for the classification of data sets, where we present results for a selection of well known examples from the literature.
title Layerwise goal-oriented adaptivity for neural ODEs: an optimal control perspective
topic Optimization and Control
Artificial Intelligence
url https://arxiv.org/abs/2601.07397