Efficient PINNs: Multi-Head Unimodular Regularization of the Solutions Space

• URL: http://arxiv.org/abs/2501.12116v1
• Date: Tue, 21 Jan 2025 13:25:56 GMT
• Title: Efficient PINNs: Multi-Head Unimodular Regularization of the Solutions Space
• Authors: Pedro Tarancón-Álvarez, Pablo Tejerina-Pérez, Raul Jimenez, Pavlos Protopapas,
• Abstract summary: We present a machine learning framework to facilitate the solution of nonlinear multiscale differential equations and, especially, inverse problems using Physics-Informed Neural Networks (PINNs) This framework is based on what is called multihead (MH) training, which involves training the network to learn a general space of all solutions for a given set of equations with certain variability, rather than learning a specific solution of the system. We show that the multihead approach, combined with the regularization, significantly improves the efficiency of PINNs by facilitating the transfer learning process thereby enabling the finding of solutions for nonlinear, coupled, and multiscale
• Score: 1.4061979259370274
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• Abstract: We present a machine learning framework to facilitate the solution of nonlinear multiscale differential equations and, especially, inverse problems using Physics-Informed Neural Networks (PINNs). This framework is based on what is called multihead (MH) training, which involves training the network to learn a general space of all solutions for a given set of equations with certain variability, rather than learning a specific solution of the system. This setup is used with a second novel technique that we call Unimodular Regularization (UR) of the latent space of solutions. We show that the multihead approach, combined with the regularization, significantly improves the efficiency of PINNs by facilitating the transfer learning process thereby enabling the finding of solutions for nonlinear, coupled, and multiscale differential equations.

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