mlsanityData to 7 Oct 2026

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

arXiv 2207.01751 ↗First posted 4 Jul 2022cs.LG cs.AR cs.DCcited by 6

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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.

Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Builds on 8 of its 16 references that are in the map. First posted on arXiv 4 Jul 2022.

Builds on

8 of 16 references.

References · 8

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2015Automatic differentiation in machine learning: a surveycited by 846
  3. 2021Physics-informed neural networks with hard constraints for inverse designcited by 277
  4. 2015Tensorizing Neural Networkscited by 246
  5. 2020DeepReach: A Deep Learning Approach to High-Dimensional Reachabilitycited by 81
  6. 2019Bayesian Tensorized Neural Networks with Automatic Rank Selectioncited by 24
  7. 2020Towards Compact Neural Networks via End-to-End Training: A Bayesian Tensor Approach with Automatic Rank Determinationcited by 17
  8. 2020A Neural Network Approach Applied to Multi-Agent Optimal Controlcited by 14

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Cited by year

Citing papers per year: 2023: 3; 2024: 1; 2025: 2.

6 papers.

  1. 2023PIFON-EPT: MR-Based Electrical Property Tomography Using Physics-Informed Fourier Networkscited by 4
  2. 2023Real-Time FJ/MAC PDE Solvers via Tensorized, Back-Propagation-Free Optical PINN Trainingcited by 4
  3. 2024Separable Operator Networkscited by 4
  4. 2023Quantization-Aware and Tensor-Compressed Training of Transformers for Natural Language Understandingcited by 2
  5. 2025Tensor-Compressed and Fully-Quantized Training of Neural PDE Solverscited by 1
  6. 2025Experimental Demonstration of an Optical Neural PDE Solver via On-Chip PINN Trainingcited by 0