Adaptive Physics-informed Neural Networks: A Survey
Abstract: Physics-informed neural networks (PINNs) have emerged as a promising approach for solving partial differential equations (PDEs) using neural networks, particularly in data-scarce scenarios due to their unsupervised training capability. However, a key limitation is the
need for re-optimization with each change in PDE parameters, similar to the challenge in traditional numerical methods where each system of equations corresponds to a specific PDE instance. This characteristic poses a barrier to the widespread adoption of PINNs
across scientific and engineering applications. This survey explores research addressing this limitation through transfer learning and meta-learning, synthesizing insights to establish a foundation for efficient data generation strategies tailored to PINNs. These methods can potentially improve PINNs’ training efficiency, enabling quicker adaptation to new PDEs with fewer data and computational demands. While numerical methods directly solve systems of equations to derive solutions, neural networks implicitly learn solutions by adjusting their parameters. One notable advantage of neural networks lies in their capacity to abstract away from specific problem domains, enabling them to retain, discard, or adapt learned representations to efficiently address similar problems. By understanding how these techniques can be applied to PINNs, this survey seeks to identify promising directions for future research to enable the widespread adoption of PINNs across a wide range of scientific and engineering applications.
Submission Length: Long submission (more than 12 pages of main content)
Assigned Action Editor: ~Efstratios_Gavves1
Submission Number: 3382
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