Silvana Montoya-Noguera

arXiv2026

Evaluation of Sampling Strategies and Physics-Informed Kolmogorov--Arnold Networks in Unbounded Domains

Physics-informed neural networks (PINNs) have emerged as an effective approach for solving partial differential equations (PDEs) by incorporating physical laws into the learning process. However, their application to infinite and semi-infinite domains remains challenging due to the difficulty of representing unbounded regions with a finite number of training points. This work evaluates physics-informed learning strategies for inverse PDE problems in unbounded domains, focusing on the influence of sampling strategies based on uniform, Gaussian, and exponential distributions, and on the use of conventional multilayer perceptrons (MLPs) and Kolmogorov--Arnold Networks (KANs) within the PINN framework. The proposed benchmark considers manufactured inverse problems on infinite and semi-infinite domains, enabling quantitative assessment of reconstruction accuracy and computational efficiency. Results show that Gaussian and exponential sampling, controlled through explicit distribution parameters, improve reconstruction accuracy in the far field and offer a direct mechanism for embedding problem-specific prior knowledge into training. PIKANs, whose edge-based functional representation is grounded in the Kolmogorov--Arnold representation theorem, match or exceed the accuracy of MLP-based PINNs while requiring fewer neurons, though their spline-based formulation increases the computational cost of training, inference, and derivative evaluation.

cs.LG↗

arXiv2026

A Scoping Review of Physics Informed Machine Learning for Wave Propagation Modeling in Seismology

Standard numerical methods accurately simulate seismic waves but are computationally expensive, particularly for inverse problems. Some machine-learning-based alternatives have emerged, promising to reduce cost while preserving physical accuracy. This scoping review, drawing on OpenAlex and Scopus, maps physics-informed machine learning applications to seismic wave propagation based on partial differential equations, classifying selected studies by problem type (forward or inverse) and learning strategy to uncover trends, patterns, and gaps. Results show that these methods have been applied to both forward modeling and inversion, often matching standard numerical accuracy at lower cost. We identified three mechanisms for incorporating physical knowledge into models: observational, inductive, and learning bias. We implemented a PyTorch replication of the original PINN framework to test methodological reproducibility of a representative method, obtaining results consistent with and, in most cases, more accurate than those originally reported. Based on the reviewed literature, we identified limitations in benchmarking consistency, training cost, and scalability to three-dimensional and experimentally validated problems. We conclude that while standard numerical methods remain foundational, physics-informed machine learning serves as a complementary tool valuable for inverse problems and surrogate modeling, with future work needing consistent benchmarking, hybrid formulations, and validation under realistic geophysical conditions. The continued development of these methods, particularly through hybrid formulations and reproducible benchmarking, may broaden their role in seismological workflows, although realizing this potential will need addressing current limitations in scalability.

physics.comp-ph↗