Layerwise goal-oriented adaptivity for neural ODEs: An optimal control perspective
Authors
- Hintermüller, Michael
ORCID: 0000-0001-9471-2479 - Hinze, Michael
- Korolev, Denis
ORCID: 0000-0001-5686-7699
2020 Mathematics Subject Classification
- 65K10 65M50 68T07
Keywords
- Resnet, neural ODEs, parameter identification/learning, adaptive neural network
DOI
Abstract
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.
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