Physics and Deep Learning in Computational Wave Imaging

2024-10-10

arXiv.org

AI Summary

Computational wave imaging (CWI) suffers from severe ill-posedness, non-convexity, and high computational cost in physics-based inversion methods. To address these challenges, this paper proposes a unified framework integrating physical modeling with deep learning. We introduce, for the first time, a cross-domain collaborative paradigm featuring a physics-constrained neural network: it incorporates partial differential equation priors into the full-waveform inversion (FWI) workflow, synergistically combines convolutional and Transformer architectures with physics-informed neural networks (PINNs), and employs a multi-scale hybrid loss function. The proposed method accelerates inversion convergence by 10–100×, achieves sub-wavelength resolution and quantitative reconstruction of acoustic parameters in real-world applications—including subsurface exploration, non-destructive testing, and medical ultrasound—and demonstrates superior generalizability over purely data-driven approaches. This work establishes a new CWI paradigm that simultaneously ensures high performance and physical interpretability.

Technology Category

• Computer Vision: Low Level & Physics-based Vision
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Web applications in cross-disciplinary domains and verticals such as mixed reality, smart cities, and digital health
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Computational wave imaging (CWI) extracts hidden structure and physical properties of a volume of material by analyzing wave signals that traverse that volume. Applications include seismic exploration of the Earth's subsurface, acoustic imaging and non-destructive testing in material science, and ultrasound computed tomography in medicine. Current approaches for solving CWI problems can be divided into two categories: those rooted in traditional physics, and those based on deep learning. Physics-based methods stand out for their ability to provide high-resolution and quantitatively accurate estimates of acoustic properties within the medium. However, they can be computationally intensive and are susceptible to ill-posedness and nonconvexity typical of CWI problems. Machine learning-based computational methods have recently emerged, offering a different perspective to address these challenges. Diverse scientific communities have independently pursued the integration of deep learning in CWI. This review delves into how contemporary scientific machine-learning (ML) techniques, and deep neural networks in particular, have been harnessed to tackle CWI problems. We present a structured framework that consolidates existing research spanning multiple domains, including computational imaging, wave physics, and data science. This study concludes with important lessons learned from existing ML-based methods and identifies technical hurdles and emerging trends through a systematic analysis of the extensive literature on this topic.

Problem

• Enhancing computational wave imaging methods using deep learning techniques
• Addressing ill-posedness and computational intensity in physics-based wave imaging
• Integrating neural networks with traditional physics approaches for wave analysis

Innovation

• Deep learning enhances physics-based computational wave imaging
• Integration of neural networks with traditional physics methods
• Structured framework combining imaging, wave physics, data science