Point Neuron Learning: A New Physics-Informed Neural Network Architecture

TL;DR

The paper tackles the challenge of reconstructing sound fields with limited data while enforcing physical laws. It introduces Point Neuron Learning, a physics-informed architecture that embeds the Helmholtz Green function into neural units, enabling exact adherence to the wave equation and processing of complex-valued fields. Through reverberant-room experiments, the method outperforms a conventional harmonics-based approach and a representative PINN, especially under sparse measurements and noise, while offering improved interpretability and generalization. The work suggests broad applicability to other wave-propagation problems beyond acoustics.

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. 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 and offers better interpretability and generalizability. 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.

Figures (9)

• Figure 1: Illustration of the target region $\Omega$, observation points, and sound sources.
• Figure 2: Network architecture of point neuron learning. Top: the point neuron building block. Bottom: the architecture overview with $V$ number of point neurons.
• Figure 3: Experimental setup. The sound field over the circular target region $\Omega$ is estimated. (a) Microphones are uniformly placed over the edge of the target region. (b) Microphones are arbitrarily placed in the target region.
• Figure 4: NMSE and MAC with respect to the frequency with circular microphone placement: (a) NMSE (b) MAC.
• Figure 5: Sound field reconstruction and NSE distribution with circular microphone distribution at 900 Hz for different methods. The target region is bounded by the black circle: (a) Original (b) Proposed (c) PINN (d) Harmonics-based (e) NSE of proposed (f) NSE of PINN (g) NSE of harmonics-based.