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

📝 Original Info

• Title: Tensor-Compressed and Fully-Quantized Training of Neural PDE Solvers
• ArXiv ID: 2512.09202
• Date: 2025-12-10
• Authors: Jinming Lu, Jiayi Tian, Yequan Zhao, Hai Li, Zheng Zhang

📝 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 resourceconstrained 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 mixedprecision 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...

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