Tensor-Compressed and Fully-Quantized Training of Neural PDE Solvers

• URL: http://arxiv.org/abs/2512.09202v1
• Date: Wed, 10 Dec 2025 00:00:34 GMT
• Title: Tensor-Compressed and Fully-Quantized Training of Neural PDE Solvers
• Authors: Jinming Lu, Jiayi Tian, Yequan Zhao, Hai Li, Zheng Zhang,
• Abstract summary: We present a framework that enables scalable and energy-efficient PINN training on edge devices.<n>This work enables real-time PDE solving on edge devices and paves the way for energy-efficient scientific computing at scale.
• Score: 10.320585073024455
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Physics-Informed Neural Networks (PINNs) have emerged as a promising paradigm for solving partial differential equations (PDEs) by embedding physical laws into neural network training objectives. However, their deployment on resource-constrained platforms is hindered by substantial computational and memory overhead, primarily stemming from higher-order automatic differentiation, intensive tensor operations, and reliance on full-precision arithmetic. To address these challenges, we present a framework that enables scalable and energy-efficient PINN training on edge devices. This framework integrates fully quantized training, Stein's estimator (SE)-based residual loss computation, and tensor-train (TT) decomposition for weight compression. It contributes three key innovations: (1) a mixed-precision training method that use a square-block MX (SMX) format to eliminate data duplication during backpropagation; (2) a difference-based quantization scheme for the Stein's estimator that mitigates underflow; and (3) a partial-reconstruction scheme (PRS) for TT-Layers that reduces quantization-error accumulation. We further design PINTA, a precision-scalable hardware accelerator, to fully exploit the performance of the framework. Experiments on the 2-D Poisson, 20-D Hamilton-Jacobi-Bellman (HJB), and 100-D Heat equations demonstrate that the proposed framework achieves accuracy comparable to or better than full-precision, uncompressed baselines while delivering 5.5x to 83.5x speedups and 159.6x to 2324.1x energy savings. This work enables real-time PDE solving on edge devices and paves the way for energy-efficient scientific computing at scale.

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