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Wave Physics as an Analog Recurrent Neural Network

arXiv 1904.12831 ↗First posted 29 Apr 2019physics.comp-ph cs.LG cs.NEcited by 43

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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.

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

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Citing papers per year: 2021: 9; 2022: 7; 2023: 5; 2024: 9; 2025: 9; 2026: 4.

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  1. 2021Deep physical neural networks enabled by a backpropagation algorithm for arbitrary physical systemscited by 128
  2. 2024Training of Physical Neural Networkscited by 49
  3. 2023Backpropagation-free Training of Deep Physical Neural Networkscited by 42
  4. 2021Self-learning Machines based on Hamiltonian Echo Backpropagationcited by 28
  5. 2023Deep Learning in Deterministic Computational Mechanicscited by 21
  6. 2022Learning Stochastic Dynamics with Statistics-Informed Neural Networkcited by 16
  7. 2022Geometry-Complete Perceptron Networks for 3D Molecular Graphscited by 16
  8. 2023Analogue and Physical Reservoir Computing Using Water Wavescited by 16
  9. 2022Polarization Multiplexed Diffractive Computing: All-Optical Implementation of a Group of Linear Transformations Through a Polarization-Encoded Diffractive Networkcited by 10
  10. 2022Dual adaptive training of photonic neural networkscited by 9
  11. 2024Arbitrary control over multimode wave propagation for machine learningcited by 9
  12. 2023Quantum-limited stochastic optical neural networks operating at a few quanta per activationcited by 8
31 more
  1. 2022Over-the-Air Split Machine Learning in Wireless MIMO Networkscited by 7
  2. 2024Towards Exact Gradient-based Training on Analog In-memory Computingcited by 7
  3. 2021Wave-based extreme deep learning based on non-linear time-Floquet entanglementcited by 6
  4. 2024Training all-mechanical neural networks for task learning through in situ backpropagationcited by 5
  5. 2025Analog In-memory Training on General Non-ideal Resistive Elements: The Impact of Response Functionscited by 5
  6. 2021Inverse Design of Grating Couplers Using the Policy Gradient Method from Reinforcement Learningcited by 3
  7. 2021Neural network is heterogeneous: Phase matters morecited by 3
  8. 2022Machine learning for knowledge acquisition and accelerated inverse-design for non-Hermitian systemscited by 3
  9. 2025Near-Equilibrium Propagation training in nonlinear wave systemscited by 3
  10. 2024PIC2O-Sim: A Physics-Inspired Causality-Aware Dynamic Convolutional Neural Operator for Ultra-Fast Photonic Device FDTD Simulationcited by 2
  11. 2025Blending Optimal Control and Biologically Plausible Learning for Noise-Robust Physical Neural Networkscited by 2
  12. 2025MAPS: Multi-Fidelity AI-Augmented Photonic Simulation and Inverse Design Infrastructurecited by 2
  13. 2025Model-free Optical Processors using In Situ Reinforcement Learning with Proximal Policy Optimizationcited by 2
  14. 2021Gaussian boson sampling and multi-particle event optimization by machine learning in the quantum phase spacecited by 1
  15. 2021Partial Differential Equations is All You Need for Generating Neural Architectures -- A Theory for Physical Artificial Intelligence Systemscited by 1
  16. 2022Physical Computing for Materials Acceleration Platformscited by 1
  17. 2026Physical Foundation Models: Fixed hardware implementations of large-scale neural networkscited by 1
  18. 2021Tensor Network for Supervised Learning at Finite Temperaturecited by 0
  19. 2021Acceleration Method for Learning Fine-Layered Optical Neural Networkscited by 0
  20. 2023An Analysis of Physics-Informed Neural Networkscited by 0
  21. 2024Unified, Verifiable Neural Simulators for Electromagnetic Wave Inverse Problemscited by 0
  22. 2024Gradient-based Design of Computational Granular Crystalscited by 0
  23. 2024Training a multilayer dynamical spintronic network with standard machine learning tools to perform time series classificationcited by 0
  24. 2024Discovery and inversion of the viscoelastic wave equation in inhomogeneous mediacited by 0
  25. 2025Traveling Waves Integrate Spatial Information Through Timecited by 0
  26. 2025Synergizing Deep Learning and Full-Waveform Inversion: Bridging Data-Driven and Theory-Guided Approaches for Enhanced Seismic Imagingcited by 0
  27. 2025Mechanical in-sensor computing: a programmable meta-sensor for structural damage classification without external electronic powercited by 0
  28. 2025BioOSS: A Bio-Inspired Oscillatory State System with Spatio-Temporal Dynamicscited by 0
  29. 2026Laser interferometry as a robust neuromorphic platform for machine learningcited by 0
  30. 2026Fully Analog Resonant Recurrent Neural Network via Metacircuitcited by 0
  31. 2026RAOA: Alternating-Operator Neural Computation with Programmable Radio Propagationcited by 0