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Maddu, S.* ; Sturm, D.* ; Müller, C.L. ; Sbalzarini, I.F.*

Inverse Dirichlet weighting enables reliable training of physics informed neural networks.

Mach. Learn.: Sci. Technol. 3:015026 (2022)
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Open Access Gold
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We characterize and remedy a failure mode that may arise from multi-scale dynamics with scale imbalances during training of deep neural networks, such as physics informed neural networks (PINNs). PINNs are popular machine-learning templates that allow for seamless integration of physical equation models with data. Their training amounts to solving an optimization problem over a weighted sum of data-fidelity and equation-fidelity objectives. Conflicts between objectives can arise from scale imbalances, heteroscedasticity in the data, stiffness of the physical equation, or from catastrophic interference during sequential training. We explain the training pathology arising from this and propose a simple yet effective inverse Dirichlet weighting strategy to alleviate the issue. We compare with Sobolev training of neural networks, providing the baseline of analytically epsilon-optimal training. We demonstrate the effectiveness of inverse Dirichlet weighting in various applications, including a multi-scale model of active turbulence, where we show orders of magnitude improvement in accuracy and convergence over conventional PINN training. For inverse modeling using sequential training, we find that inverse Dirichlet weighting protects a PINN against catastrophic forgetting.
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Publication type Article: Journal article
Document type Scientific Article
Keywords Physics-informed Neural Networks ; Multi-scale Modeling ; Active Turbulence ; Catastrophic Forgetting ; Multi-objective Training ; Gradient Flow Regularization; Algorithm
Language english
Publication Year 2022
HGF-reported in Year 2022
ISSN (print) / ISBN 2632-2153
e-ISSN 2632-2153
Journal Machine Learning: Science and Technology
Quellenangaben Volume: 3, Issue: 1, Pages: , Article Number: 015026 Supplement: ,
Publisher Institute of Physics Publishing (IOP)
Publishing Place Temple Circus, Temple Way, Bristol Bs1 6be, England
Reviewing status Peer reviewed
Institute(s) Institute of Computational Biology (ICB)
POF-Topic(s) 30205 - Bioengineering and Digital Health
Research field(s) Enabling and Novel Technologies
PSP Element(s) G-503800-001
Grants Saxon Ministry for Science, Culture and Tourism (SMWK)
German Research Foundation (DFG)
Center for Scalable Data Analytics and Artificial Intelligence (ScaDS.AI) Dresden/Leipzig - Federal Ministry of Education and Research (BMBF)
Center for Advanced Systems Understanding (CASUS) - Germany's Federal Ministry of Education and Research (BMBF)
DOI 10.1088/2632-2153/ac3712
WOS ID WOS:000755293800001
Scopus ID 85126707714
Erfassungsdatum 2022-06-01
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