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

arXiv: https://arxiv.org/abs/2401.00413 · HTML: https://mlsanity.com/paper/2401.00413/

## Key facts

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

## Builds on (most cited first, 14 of 14)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [signSGD: Compressed Optimisation for Non-Convex Problems](https://mlsanity.com/paper/1802.04434/) (2018)
- [Photonics for artificial intelligence and neuromorphic computing](https://mlsanity.com/paper/2011.00111/) (2020)
- [DeepReach: A Deep Learning Approach to High-Dimensional Reachability](https://mlsanity.com/paper/2011.02082/) (2020)
- [Training of photonic neural networks through in situ backpropagation](https://mlsanity.com/paper/1805.09943/) (2018)
- [Experimentally realized in situ backpropagation for deep learning in nanophotonic neural networks](https://mlsanity.com/paper/2205.08501/) (2022)
- [Efficient On-Chip Learning for Optical Neural Networks Through Power-Aware Sparse Zeroth-Order Optimization](https://mlsanity.com/paper/2012.11148/) (2020)
- [L2ight: Enabling On-Chip Learning for Optical Neural Networks via Efficient in-situ Subspace Optimization](https://mlsanity.com/paper/2110.14807/) (2021)
- [Forward-Forward Training of an Optical Neural Network](https://mlsanity.com/paper/2305.19170/) (2023)
- [Silicon Photonic Architecture for Training Deep Neural Networks with Direct Feedback Alignment](https://mlsanity.com/paper/2111.06862/) (2021)
- [A Neural Network Approach Applied to Multi-Agent Optimal Control](https://mlsanity.com/paper/2011.04757/) (2020)
- [Tensor-Compressed Back-Propagation-Free Training for (Physics-Informed) Neural Networks](https://mlsanity.com/paper/2308.09858/) (2023)
- [TT-PINN: A Tensor-Compressed Neural PDE Solver for Edge Computing](https://mlsanity.com/paper/2207.01751/) (2022)
- [PIFON-EPT: MR-Based Electrical Property Tomography Using Physics-Informed Fourier Networks](https://mlsanity.com/paper/2302.11883/) (2023)

## Built on by (most cited first, 4 of 4)

- [Poor Man's Training on MCUs: A Memory-Efficient Quantized Back-Propagation-Free Approach](https://mlsanity.com/paper/2411.05873/) (2024)
- [Ultra Memory-Efficient On-FPGA Training of Transformers via Tensor-Compressed Optimization](https://mlsanity.com/paper/2501.06663/) (2025)
- [Tensor-Compressed and Fully-Quantized Training of Neural PDE Solvers](https://mlsanity.com/paper/2512.09202/) (2025)
- [Experimental Demonstration of an Optical Neural PDE Solver via On-Chip PINN Training](https://mlsanity.com/paper/2501.00742/) (2025)

## 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.