# TT-PINN: A Tensor-Compressed Neural PDE Solver for Edge Computing

arXiv: https://arxiv.org/abs/2207.01751 · HTML: https://mlsanity.com/paper/2207.01751/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 16 references that are in the map.
- First posted on arXiv 4 Jul 2022.

## Builds on (most cited first, 8 of 8)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Physics-informed neural networks with hard constraints for inverse design](https://mlsanity.com/paper/2102.04626/) (2021)
- [Tensorizing Neural Networks](https://mlsanity.com/paper/1509.06569/) (2015)
- [DeepReach: A Deep Learning Approach to High-Dimensional Reachability](https://mlsanity.com/paper/2011.02082/) (2020)
- [Bayesian Tensorized Neural Networks with Automatic Rank Selection](https://mlsanity.com/paper/1905.10478/) (2019)
- [Towards Compact Neural Networks via End-to-End Training: A Bayesian Tensor Approach with Automatic Rank Determination](https://mlsanity.com/paper/2010.08689/) (2020)
- [A Neural Network Approach Applied to Multi-Agent Optimal Control](https://mlsanity.com/paper/2011.04757/) (2020)

## Built on by (most cited first, 7 of 7)

- [Separable Operator Networks](https://mlsanity.com/paper/2407.11253/) (2024)
- [PIFON-EPT: MR-Based Electrical Property Tomography Using Physics-Informed Fourier Networks](https://mlsanity.com/paper/2302.11883/) (2023)
- [Real-Time FJ/MAC PDE Solvers via Tensorized, Back-Propagation-Free Optical PINN Training](https://mlsanity.com/paper/2401.00413/) (2023)
- [Quantization-Aware and Tensor-Compressed Training of Transformers for Natural Language Understanding](https://mlsanity.com/paper/2306.01076/) (2023)
- [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)
- [S2-PINN: Stochastic Separable Physics-Informed Neural Networks](https://mlsanity.com/paper/2610.03303/) (2026)

## Abstract (arXiv)

Physics-informed neural networks (PINNs) have been increasingly employed due to their capability of modeling complex physics systems. To achieve better expressiveness, increasingly larger network sizes are required in many problems. This has caused challenges when we need to train PINNs on edge devices with limited memory, computing and energy resources. To enable training PINNs on edge devices, this paper proposes an end-to-end compressed PINN based on Tensor-Train decomposition. In solving a Helmholtz equation, our proposed model significantly outperforms the original PINNs with few parameters and achieves satisfactory prediction with up to 15× overall parameter reduction.