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

TL;DR

This paper introduces a novel physics-informed neural network architecture that embeds the wave equation's fundamental solution, enabling accurate sound field modeling without datasets, with improved interpretability and generalizability over existing methods.

Contribution

The paper presents a new PINN architecture that directly incorporates the wave equation's fundamental solution, enhancing model performance and interpretability in sound field reconstruction.

Findings

Outperforms existing PINN methods in sound field reconstruction

Handles noisy and sparse microphone data effectively

Provides better interpretability and generalizability

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.