An effective physics-informed neural operator framework for predicting wavefields

2025/07/22 by Xiao Ma, Tariq Alkhalifah, Ma, Xiao +1 · 2 citations
Computer Science · Physics and Astronomy · #Advanced Optical Sensing Technologies #FOS: Computer and information sciences #FOS: Physical sciences #Geophysics (physics.geo-ph) #Machine Learning (cs.LG) #Model Reduction and Neural Networks #Neural Networks and Reservoir Computing

paper · pdf · doi:10.48550/arxiv.2507.16431

openalex publication_date 2025/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Solving the wave equation is fundamental for geophysical applications. However, numerical solutions of the Helmholtz equation face significant computational and memory challenges. Therefore, we introduce a physics-informed convolutional neural operator (PICNO) to solve the Helmholtz equation efficiently. The PICNO takes both the background wavefield corresponding to a homogeneous medium and the velocity model as input function space, generating the scattered wavefield as the output function space. Our workflow integrates PDE constraints directly into the training process, enabling the neural operator to not only fit the available data but also capture the underlying physics governing wave phenomena. PICNO allows for high-resolution reasonably accurate predictions even with limited training samples, and it demonstrates significant improvements over a purely data-driven convolutional neural operator (CNO), particularly in predicting high-frequency wavefields. These features and improvements are important for waveform inversion down the road.

Citations

• Seismic wavefield solutions via physics-guided generative neural operator
• Scientific Machine Learning Seismology
• Learned frequency-domain scattered wavefield solutions using neural operators
• Operator SVD with Neural Networks via Nested Low-Rank Approximation
• Seismic traveltime simulation for variable velocity models using physics-informed Fourier neural operator
• Neural Eikonal solver: Improving accuracy of physics-informed neural networks for solving eikonal equation in case of caustics
• FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators
• Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next
• Scientific Machine Learning Through Physics–Informed Neural Networks: Where we are and What’s Next
• Physics-Informed Neural Operator for Learning Partial Differential Equations
• OpenFWI: Large-Scale Multi-Structural Benchmark Datasets for Seismic Full Waveform Inversion
• Physics‐Informed Neural Networks (PINNs) for Wave Propagation and Full Waveform Inversions
• Wavefield solutions from machine learned functions
• Physics-informed machine learning
• Fourier Neural Operator for Parametric Partial Differential Equations
• Neural Operator: Graph Kernel Network for Partial Differential Equations
• Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators
• Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

Cited by

• Learning from Imperfect Labels: A Physics-Aware Neural Operator with Application to DAS Data Denoising
• Velocity model building from seismic images using a Convolutional Neural Operator

Related

• Wavefield solutions from machine learned functions
• Learned frequency-domain scattered wavefield solutions using neural operators
• Physics-guided Full Waveform Inversion using Encoder-Solver Convolutional Neural Networks
• Solving the wave equation with physics-informed deep learning
• Is it time to swish? Comparing activation functions in solving the Helmholtz equation using physics-informed neural networks