Enhancing deep learning-based field reconstruction with a differentiable learning framework

Abstract

Achieving accurate reconstructions of complex high-dimensional fields from sparse sensors remains a long-standing challenge. Frequently, reconstruction performance is mainly constrained by models and placement. The placement of sparse and prohibitive experimental sensors restricts information quality, resulting in formidable reconstruction tasks. Despite deep learning-based models having made strides, they typically lack the ability to co-optimize sensor placement. The joint optimization of high-dimensional neural network parameters versus low-dimensional sensor placement further poses significant difficulties. Here we present a general bilevel differentiable learning framework that effectively integrates models with sensor placement optimization (DSPO), enabling the dynamical search for the placement and accurate global field reconstruction. Within this framework, models are complemented with a differentiable operator to achieve the differentiability of placement. A gradient-based optimizer further empowers models by dynamically updating placement. The alternating optimization strategy is adopted to efficiently solve the joint optimization. We demonstrate the efficiency and generalizability of the DSPO on baseline models across various scenarios, including periodic and acyclic physical fields, regular and irregular grid datasets, and noisy and noiseless observations. Our results show that the DSPO significantly improves the reconstruction accuracy of models and robustness and advances baseline models comparable with the state-of-the-art performance. Our framework provides a new and general paradigm for the practical use of neural networks and placement optimization techniques for real-world applications.