2024/04/27 by Shijun Cheng, Tariq Alkhalifah, Cheng, Shijun +1 · 1 citation
Computer Science · Engineering · #FOS: Physical sciences #Fault Detection and Control Systems #Geophysics (physics.geo-ph) #Neural Networks and Applications #Time Series Analysis and Forecasting
paper · pdf · doi:10.48550/arxiv.2404.17971
openalex publication_date 2024/04/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Using symbolic regression to discover physical laws from observed data is an emerging field. In previous work, we combined genetic algorithm (GA) and machine learning to present a data-driven method for discovering a wave equation. Although it managed to utilize the data to discover the two-dimensional (x,z) acoustic constant-density wave equation utt=v2(uxx+uzz) (subscripts of the wavefield, u, are second derivatives in time and space) in a homogeneous medium, it did not provide the complete equation form, where the velocity term is represented by a coefficient rather than directly given by v2. In this work, we redesign the framework, encoding both velocity information and candidate functional terms simultaneously. Thus, we use GA to simultaneously evolve the candidate functional and coefficient terms in the library. Also, we consider here the physics rationality and interpretability in the randomly generated potential wave equations, by ensuring that both-hand sides of the equation maintain balance in their physical units. We demonstrate this redesigned framework using the acoustic wave equation as an example, showing its ability to produce physically reasonable expressions of wave equations from noisy and sparsely observed data in both homogeneous and inhomogeneous media. Also, we demonstrate that our method can effectively discover wave equations from a more realistic observation scenario.