mlsanityData to 7 Oct 2026

Real-Time FJ/MAC PDE Solvers via Tensorized, Back-Propagation-Free Optical PINN Training

arXiv 2401.00413 ↗First posted 31 Dec 2023cs.LG cs.ET eess.SPcited by 4

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Abstract (arXiv)

Solving partial differential equations (PDEs) numerically often requires huge computing time, energy cost, and hardware resources in practical applications. This has limited their applications in many scenarios (e.g., autonomous systems, supersonic flows) that have a limited energy budget and require near real-time response. Leveraging optical computing, this paper develops an on-chip training framework for physics-informed neural networks (PINNs), aiming to solve high-dimensional PDEs with fJ/MAC photonic power consumption and ultra-low latency. Despite the ultra-high speed of optical neural networks, training a PINN on an optical chip is hard due to (1) the large size of photonic devices, and (2) the lack of scalable optical memory devices to store the intermediate results of back-propagation (BP). To enable realistic optical PINN training, this paper presents a scalable method to avoid the BP process. We also employ a tensor-compressed approach to improve the convergence and scalability of our optical PINN training. This training framework is designed with tensorized optical neural networks (TONN) for scalable inference acceleration and MZI phase-domain tuning for textitin-situ optimization. Our simulation results of a 20-dim HJB PDE show that our photonic accelerator can reduce the number of MZIs by a factor of 1.17× 103, with only 1.36 J and 1.15 s to solve this equation. This is the first real-size optical PINN training framework that can be applied to solve high-dimensional PDEs.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 14 of its 31 references that are in the map. First posted on arXiv 31 Dec 2023.

Builds on

14 of 31 references.

References · 14

  1. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  2. 2018signSGD: Compressed Optimisation for Non-Convex Problemscited by 561
  3. 2020Photonics for artificial intelligence and neuromorphic computingcited by 111
  4. 2020DeepReach: A Deep Learning Approach to High-Dimensional Reachabilitycited by 81
  5. 2018Training of photonic neural networks through in situ backpropagationcited by 45
  6. 2022Experimentally realized in situ backpropagation for deep learning in nanophotonic neural networkscited by 43
  7. 2020Efficient On-Chip Learning for Optical Neural Networks Through Power-Aware Sparse Zeroth-Order Optimizationcited by 24
  8. 2021L2ight: Enabling On-Chip Learning for Optical Neural Networks via Efficient in-situ Subspace Optimizationcited by 21
  9. 2023Forward-Forward Training of an Optical Neural Networkcited by 19
  10. 2021Silicon Photonic Architecture for Training Deep Neural Networks with Direct Feedback Alignmentcited by 17
  11. 2020A Neural Network Approach Applied to Multi-Agent Optimal Controlcited by 14
  12. 2023Tensor-Compressed Back-Propagation-Free Training for (Physics-Informed) Neural Networkscited by 12
2 more
  1. 2022TT-PINN: A Tensor-Compressed Neural PDE Solver for Edge Computingcited by 6
  2. 2023PIFON-EPT: MR-Based Electrical Property Tomography Using Physics-Informed Fourier Networkscited by 4

Built on by

Cited by year

Citing papers per year: 2024: 1; 2025: 3.

4 papers.

  1. 2024Poor Man's Training on MCUs: A Memory-Efficient Quantized Back-Propagation-Free Approachcited by 5
  2. 2025Ultra Memory-Efficient On-FPGA Training of Transformers via Tensor-Compressed Optimizationcited by 3
  3. 2025Tensor-Compressed and Fully-Quantized Training of Neural PDE Solverscited by 1
  4. 2025Experimental Demonstration of an Optical Neural PDE Solver via On-Chip PINN Trainingcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025KD-PINN: Knowledge-Distilled PINNs for ultra-low-latency real-time neural PDE solvers
  2. 2024Streamlined optical training of large-scale modern deep learning architectures with direct feedback alignment
  3. 2025Wave-PDE Nets: Trainable Wave-Equation Layers as an Alternative to Attention
  4. 2025Sub-Sequential Physics-Informed Learning with State Space Model
  5. 2026Oscillatory State-Space Models as Inductive Biases for Physics-Informed Neural PDE Solvers
  6. 2023LatentPINNs: Generative physics-informed neural networks via a latent representation learning
  7. 2025Lang-PINN: From Language to Physics-Informed Neural Networks via a Multi-Agent Framework
  8. 2025PINN Balls: Scaling Second-Order Methods for PINNs with Domain Decomposition and Adaptive Sampling