🤖 AI Summary
To address key limitations of physics-informed neural networks (PINNs) in acoustic field reconstruction—including heavy reliance on training data, susceptibility to local minima, poor interpretability, and limited generalizability—this paper proposes a novel *data-free* PINN. Our method directly embeds the fundamental solution of the 3D wave equation into neuron-level operations, establishing the first complex-valued “point neuron” architecture. This design intrinsically enforces exact compliance with the wave equation, enabling physically consistent acoustic field inversion from sparse microphone measurements—*without any training*. The resulting framework provides strong physical constraints, full interpretability, and robust cross-scenario generalization. Experiments demonstrate that our approach significantly outperforms two state-of-the-art PINN baselines under challenging conditions: strong reverberation, high noise levels, and extremely sparse sampling (e.g., only four microphones).
📝 Abstract
Machine learning and neural networks have advanced numerous research domains, but challenges such as large training data requirements and inconsistent model performance hinder their application in certain scientific problems. To overcome these challenges, researchers have investigated integrating physics principles into machine learning models, mainly through (i) physics-guided loss functions, generally termed as physics-informed neural networks, and (ii) physics-guided architectural design. While both approaches have demonstrated success across multiple scientific disciplines, they have limitations including being trapped to a local minimum, poor interpretability, and restricted generalizability beyond sampled data range. This paper proposes a new physics-informed neural network (PINN) architecture that combines the strengths of both approaches by embedding the fundamental solution of the wave equation into the network architecture, enabling the learned model to strictly satisfy the wave equation. The proposed point neuron learning method can model an arbitrary sound field based on microphone observations without any dataset. Compared to other PINN methods, our approach directly processes complex numbers, offers better interpretability, and can be generalized to out-of-sample scenarios. We evaluate the versatility of the proposed architecture by a sound field reconstruction problem in a reverberant environment. Results indicate that the point neuron method outperforms two competing methods and can efficiently handle noisy environments with sparse microphone observations.