Point Neuron Learning: A New Physics-Informed Neural Network Architecture
This work addresses the problem of sound field reconstruction in reverberant environments for researchers in acoustics and physics-informed machine learning, offering an incremental improvement by combining existing approaches with a novel architectural design.
The paper tackles the challenge of large training data requirements and inconsistent performance in neural networks for scientific problems by proposing a new physics-informed neural network architecture that embeds the wave equation's fundamental solution, enabling sound field reconstruction without any dataset and outperforming competing methods in noisy, sparse observation environments.
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.