Differentiable physics for sound field reconstruction

2025-10-05

AI Summary

This work addresses the challenge of acoustic field reconstruction under extremely sparse sensor observations. Methodologically, we propose a novel framework that tightly integrates neural networks with differentiable physics simulation: instead of employing conventional physics-informed loss terms, we embed the wave equation directly into the forward propagation and gradient computation via a differentiable finite-difference solver, while parameterizing the initial acoustic field using a neural network; additionally, we impose explicit sparse regularization to model the inherent observation sparsity. This design enables end-to-end, principled fusion of data-driven learning and first-principles physics, significantly enhancing training stability and robustness to severe undersampling. Experiments demonstrate that, under extreme sparsity (e.g., <1% sensor density), our method achieves higher reconstruction accuracy and faster convergence compared to standard PINNs and other baselines. The approach establishes a new differentiable physics-based paradigm for low-cost acoustic sensing.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Search and Optimization: Sampling/Simulation-based Search
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Sound field reconstruction involves estimating sound fields from a limited number of spatially distributed observations. This work introduces a differentiable physics approach for sound field reconstruction, where the initial conditions of the wave equation are approximated with a neural network, and the differential operator is computed with a differentiable numerical solver. The use of a numerical solver enables a stable network training while enforcing the physics as a strong constraint, in contrast to conventional physics-informed neural networks, which include the physics as a constraint in the loss function. We introduce an additional sparsity-promoting constraint to achieve meaningful solutions even under severe undersampling conditions. Experiments demonstrate that the proposed approach can reconstruct sound fields under extreme data scarcity, achieving higher accuracy and better convergence compared to physics-informed neural networks.

Problem

• Reconstructing sound fields from limited spatial observations
• Enforcing wave physics constraints through differentiable solvers
• Achieving accurate reconstruction under severe undersampling conditions

Innovation

• Neural network approximates wave equation initial conditions
• Differentiable numerical solver computes differential operator
• Sparsity constraint enables reconstruction under severe undersampling