# Wave Physics as an Analog Recurrent Neural Network

arXiv: https://arxiv.org/abs/1904.12831 · HTML: https://mlsanity.com/paper/1904.12831/

## Key facts

- Cited by 43 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Apr 2019.

## Built on by (most cited first, 30 of 43)

- [Deep physical neural networks enabled by a backpropagation algorithm for arbitrary physical systems](https://mlsanity.com/paper/2104.13386/) (2021)
- [Training of Physical Neural Networks](https://mlsanity.com/paper/2406.03372/) (2024)
- [Backpropagation-free Training of Deep Physical Neural Networks](https://mlsanity.com/paper/2304.11042/) (2023)
- [Self-learning Machines based on Hamiltonian Echo Backpropagation](https://mlsanity.com/paper/2103.04992/) (2021)
- [Deep Learning in Deterministic Computational Mechanics](https://mlsanity.com/paper/2309.15421/) (2023)
- [Learning Stochastic Dynamics with Statistics-Informed Neural Network](https://mlsanity.com/paper/2202.12278/) (2022)
- [Geometry-Complete Perceptron Networks for 3D Molecular Graphs](https://mlsanity.com/paper/2211.02504/) (2022)
- [Analogue and Physical Reservoir Computing Using Water Waves](https://mlsanity.com/paper/2306.09095/) (2023)
- [Polarization Multiplexed Diffractive Computing: All-Optical Implementation of a Group of Linear Transformations Through a Polarization-Encoded Diffractive Network](https://mlsanity.com/paper/2203.13482/) (2022)
- [Dual adaptive training of photonic neural networks](https://mlsanity.com/paper/2212.06141/) (2022)
- [Arbitrary control over multimode wave propagation for machine learning](https://mlsanity.com/paper/2402.17750/) (2024)
- [Quantum-limited stochastic optical neural networks operating at a few quanta per activation](https://mlsanity.com/paper/2307.15712/) (2023)
- [Over-the-Air Split Machine Learning in Wireless MIMO Networks](https://mlsanity.com/paper/2210.04742/) (2022)
- [Towards Exact Gradient-based Training on Analog In-memory Computing](https://mlsanity.com/paper/2406.12774/) (2024)
- [Wave-based extreme deep learning based on non-linear time-Floquet entanglement](https://mlsanity.com/paper/2107.08564/) (2021)
- [Training all-mechanical neural networks for task learning through in situ backpropagation](https://mlsanity.com/paper/2404.15471/) (2024)
- [Analog In-memory Training on General Non-ideal Resistive Elements: The Impact of Response Functions](https://mlsanity.com/paper/2502.06309/) (2025)
- [Inverse Design of Grating Couplers Using the Policy Gradient Method from Reinforcement Learning](https://mlsanity.com/paper/2107.00088/) (2021)
- [Neural network is heterogeneous: Phase matters more](https://mlsanity.com/paper/2111.02014/) (2021)
- [Machine learning for knowledge acquisition and accelerated inverse-design for non-Hermitian systems](https://mlsanity.com/paper/2204.13376/) (2022)
- [Near-Equilibrium Propagation training in nonlinear wave systems](https://mlsanity.com/paper/2510.16084/) (2025)
- [PIC2O-Sim: A Physics-Inspired Causality-Aware Dynamic Convolutional Neural Operator for Ultra-Fast Photonic Device FDTD Simulation](https://mlsanity.com/paper/2406.17810/) (2024)
- [Blending Optimal Control and Biologically Plausible Learning for Noise-Robust Physical Neural Networks](https://mlsanity.com/paper/2502.19053/) (2025)
- [MAPS: Multi-Fidelity AI-Augmented Photonic Simulation and Inverse Design Infrastructure](https://mlsanity.com/paper/2503.01046/) (2025)
- [Model-free Optical Processors using In Situ Reinforcement Learning with Proximal Policy Optimization](https://mlsanity.com/paper/2507.05583/) (2025)
- [Gaussian boson sampling and multi-particle event optimization by machine learning in the quantum phase space](https://mlsanity.com/paper/2102.12142/) (2021)
- [Partial Differential Equations is All You Need for Generating Neural Architectures -- A Theory for Physical Artificial Intelligence Systems](https://mlsanity.com/paper/2103.08313/) (2021)
- [Physical Computing for Materials Acceleration Platforms](https://mlsanity.com/paper/2208.08566/) (2022)
- [Physical Foundation Models: Fixed hardware implementations of large-scale neural networks](https://mlsanity.com/paper/2604.27911/) (2026)
- [Tensor Network for Supervised Learning at Finite Temperature](https://mlsanity.com/paper/2104.05439/) (2021)

## Abstract (arXiv)

Analog machine learning hardware platforms promise to be faster and more energy-efficient than their digital counterparts. Wave physics, as found in acoustics and optics, is a natural candidate for building analog processors for time-varying signals. Here we identify a mapping between the dynamics of wave physics, and the computation in recurrent neural networks. This mapping indicates that physical wave systems can be trained to learn complex features in temporal data, using standard training techniques for neural networks. As a demonstration, we show that an inverse-designed inhomogeneous medium can perform vowel classification on raw audio signals as their waveforms scatter and propagate through it, achieving performance comparable to a standard digital implementation of a recurrent neural network. These findings pave the way for a new class of analog machine learning platforms, capable of fast and efficient processing of information in its native domain.