Recent advancements in physics-informed machine learning have contributed to solving partial differential equations through means of a neural network. Following this, several physics-informed neural network works have followed to solve inverse problems arising in structural health monitoring. Other works involving physics-informed neural networks solve the wave equation with partial data and modeling wavefield data generator for efficient sound data generation. While a lot of work has been done to show that partial differential equations can be solved and identified using a neural network, little work has been done the same with more basic machine learning (ML) models. The advantage with basic ML models is that the parameters learned in a simpler model are both more interpretable and extensible. For applications such as ultrasonic nondestructive evaluation, this interpretability is essential for trustworthiness of the methods and characterization of the material system under test. In this work, we show an interpretable, physics-informed representation learning framework that can analyze data across multiple dimensions (e.g., two dimensions of space and one dimension of time). The algorithm comes with convergence guarantees. In addition, our algorithm provides interpretability of the learned model as the parameters correspond to the individual solutions extracted from data. We demonstrate how this algorithm functions with wavefield videos.
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CoPhy-PGNN: Learning Physics-guided Neural Networks with Competing Loss Functions for Solving Eigenvalue Problems
Physics-guided Neural Networks (PGNNs) represent an emerging class of neural networks that are trained using physics-guided (PG) loss functions (capturing violations in network outputs with known physics), along with the supervision contained in data. Existing work in PGNNs has demonstrated the efficacy of adding single PG loss functions in the neural network objectives, using constant trade-off parameters, to ensure better generalizability. However, in the presence of multiple PG functions with competing gradient directions, there is a need to adaptively tune the contribution of different PG loss functions during the course of training to arrive at generalizable solutions. We demonstrate the presence of competing PG losses in the generic neural network problem of solving for the lowest (or highest) eigenvector of a physics-based eigenvalue equation, which is commonly encountered in many scientific problems. We present a novel approach to handle competing PG losses and demonstrate its efficacy in learning generalizable solutions in two motivating applications of quantum mechanics and electromagnetic propagation. All the code and data used in this work are available at https://github.com/jayroxis/Cophy-PGNN.
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- Award ID(s):
- 2026710
- PAR ID:
- 10227099
- Date Published:
- Journal Name:
- ACM Transactions on Intelligent Systems and Technology
- ISSN:
- 2157-6904
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1145/3530911
