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

arXiv: https://arxiv.org/abs/2408.16969 · HTML: https://mlsanity.com/paper/2408.16969/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 61 references that are in the map.
- First posted on arXiv 30 Aug 2024.

## Builds on (most cited first, 22 of 22)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Fundamentals of Recurrent Neural Network (RNN) and Long Short-Term Memory (LSTM) Network](https://mlsanity.com/paper/1808.03314/) (2018)
- [Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10561/) (2017)
- [Cormorant: Covariant Molecular Neural Networks](https://mlsanity.com/paper/1906.04015/) (2019)
- [Theory-guided Data Science: A New Paradigm for Scientific Discovery from Data](https://mlsanity.com/paper/1612.08544/) (2016)
- [Machine learning in cardiovascular flows modeling: Predicting arterial blood pressure from non-invasive 4D flow MRI data using physics-informed neural networks](https://mlsanity.com/paper/1905.04817/) (2019)
- [Physics-informed Autoencoders for Lyapunov-stable Fluid Flow Prediction](https://mlsanity.com/paper/1905.10866/) (2019)
- [Learning in Sinusoidal Spaces with Physics-Informed Neural Networks](https://mlsanity.com/paper/2109.09338/) (2021)
- [Physics-Guided Machine Learning for Scientific Discovery: An Application in Simulating Lake Temperature Profiles](https://mlsanity.com/paper/2001.11086/) (2020)
- [Physics-Driven Deep Learning for Computational Magnetic Resonance Imaging](https://mlsanity.com/paper/2203.12215/) (2022)
- [Physics guided neural networks for modelling of non-linear dynamics](https://mlsanity.com/paper/2205.06858/) (2022)
- [Physics-informed neural networks for myocardial perfusion MRI quantification](https://mlsanity.com/paper/2011.12844/) (2020)
- [Room impulse response reconstruction with physics-informed deep learning](https://mlsanity.com/paper/2401.01206/) (2024)
- [Implicit neural representation with physics-informed neural networks for the reconstruction of the early part of room impulse responses](https://mlsanity.com/paper/2306.11509/) (2023)
- [Physics-informed neural networks for one-dimensional sound field predictions with parameterized sources and impedance boundaries](https://mlsanity.com/paper/2109.11313/) (2021)
- [Physics-Informed Neural Network for Volumetric Sound field Reconstruction of Speech Signals](https://mlsanity.com/paper/2403.09524/) (2024)
- [Physics-informed convolutional neural network with bicubic spline interpolation for sound field estimation](https://mlsanity.com/paper/2207.10937/) (2022)
- [Sound Field Estimation around a Rigid Sphere with Physics-informed Neural Network](https://mlsanity.com/paper/2307.14013/) (2023)
- [Circumvent spherical Bessel function nulls for open sphere microphone arrays with physics informed neural network](https://mlsanity.com/paper/2308.00242/) (2023)
- [An Active Noise Control System Based on Soundfield Interpolation Using a Physics-informed Neural Network](https://mlsanity.com/paper/2309.10605/) (2023)

## Built on by (most cited first, 2 of 2)

- [Fundamental Survey on Neuromorphic Based Audio Classification](https://mlsanity.com/paper/2502.15056/) (2025)
- [Gaussian Process Regression of Steering Vectors With Physics-Aware Deep Composite Kernels for Augmented Listening](https://mlsanity.com/paper/2509.02571/) (2025)

## Abstract (arXiv)

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.