Collaborative Research: Scientific Computing Assisted Machine Learning for Wave Imaging

Computational wave imaging, vital for uncovering hidden properties in diverse fields of science and engineering, such as materials science, medicine, and geoscience, faces significant challenges. Traditional methods struggle with the inherent complexity and computational demands of such problems. Although deep learning offers promise for these scientific inverse problems, its efficacy is hindered by the scarcity of labeled data, often due to costly experiments and expertise requirements. This underscores the need for innovative approaches that circumvent data limitations in wave imaging. This project seeks to optimize the potential of deep learning in computational wave imaging by introducing techniques to address data scarcity and improve generalizability, aiming to drastically lessen deep learning's dependence on extensive labeled datasets, efficiently generate high-quality training data, and greatly improve deep learning's capacity to solve real-world problems. It also emphasizes educational integration and interdisciplinary collaboration, and promotes the sharing of open-source computer codes and datasets, enhancing the broader scientific community’s ability to conduct research and providing educators with valuable tools for teaching computational and data-enabled science, engineering, and mathematics. Physical principles will be integrated with advanced deep learning models in hybrid learning strategies. Hybrid strategies involve efficient wave simulations results which can address the challenges of data and label scarcity, and the weak generalizability in computational wave imaging. A novel self-supervised learning method will be introduced, which can uncover hidden physical principles within the latent space. Preliminary investigations have revealed an “Auto-Linear” phenomenon, where features from different physical domains automatically correlate linearly. This discovery allows for simultaneous forward and inverse modeling, significantly enhancing performance in imaging tasks that lack paired data. Efficient wave simulations will also be developed. They will involve high-order methods for effective forward propagation and backpropagation, with explicit Runge-Kutta time stepping for non-stiff problems and A-stable implicit Runge-Kutta time stepping for stiff problems, combined with Fourier or spectral element spatial approximations. Furthermore, integral-based methods with asymptotic short-time Green's function will be developed for problems with point-source-like source functions. This configuration is designed to simulate wave propagation with high accuracy and minimal sampling requirements in both time and space, thus avoiding the pollution effect and promising a leap in simulation efficiency and quality. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.