Physics-Informed Parallel Neural Networks with self-adaptive loss weighting for the identification of continuous structural systems

Physics-Informed Neural Networks (PINNs) are being applied to forward and inverse problems in various science and engineering disciplines, integrating physical principles into the learning process. In line with this, the previously proposed Physics-Informed Parallel Neural Networks (PIPNNs) framework addresses the inverse structural identification problem of continuous structural systems, particularly for handling inherent discontinuities in the system such as interior supports and dissimilar element properties. The PIPNNs framework accommodates structural discontinuities by dividing the computational domain into subdomains, each uniquely represented through a parallelized and interconnected Neural Network (NN) architecture. However, these parallel NNs pose a challenge due to the increased number of terms in the loss function, making network training more complex. The main contribution of this paper is the development of a Neural Tangent Kernel (NTK)-based self-adaptive loss weighting mechanism within the PIPNNs framework to address the challenges of dissimilar convergence rates of loss terms during the training of multiple NNs, ensuring balanced convergence across various physical constraints and subdomains. Guided by NTK theory, which describes the evolution of fully connected NNs during training by gradient descent, the self-adaptive weighting approach developed here adaptively alters the weights for each loss component throughout the NNs training process. These weights, determined based upon the eigenvalues of the NTK matrix of the PIPNNs, adjust the convergence rates of each loss term to achieve a balanced convergence, while requiring less training data. In the context of the inverse problem and structural identification, the NTK matrix is derived by considering not only the training evolution of the parallel NNs but also the changes in unknown structural parameters during the training process. The NTK-enhanced PIPNNs framework is verified and validated against an alternative independent model, and its accuracy is assessed through the application of numerical examples of several continuous structural systems, including bars, beams, and plates.

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Work Title Physics-Informed Parallel Neural Networks with self-adaptive loss weighting for the identification of continuous structural systems
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Open Access
Creators
  1. Rui Zhang
  2. Gordon P. Warn
  3. Aleksandra Radlińska
License In Copyright (Rights Reserved)
Work Type Article
Publisher
  1. Computer Methods in Applied Mechanics and Engineering
Publication Date July 1, 2024
Publisher Identifier (DOI)
  1. https://doi.org/10.1016/j.cma.2024.117042
Deposited February 03, 2025

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  • Added Creator Gordon P. Warn
  • Added Creator Aleksandra Radlińska
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