用物理约束提升3D打印热场预测，精度与速度双突破
PiGRAND: Physics-informed Graph Neural Diffusion for Intelligent Additive Manufacturing
- 构建物理感知图神经扩散模型，融合微分方程先验
- 在3D打印热图像上实现比GRAND和PINNs更高的精度与效率
- 适合工业界做增材制造过程仿真与优化的科研人员
热传输的深入理解对优化3D打印等工程应用至关重要。由于传感器数据有限，且部分测量成本高、难获取，结合机器学习与物理模型成为新趋势。本文提出物理信息图神经扩散框架PiGRAND，通过高效图构建降低计算复杂度，并借鉴显式欧拉与隐式克兰克-尼科尔斯方法建模连续热传导，利用子学习模型确保图节点间扩散准确性。同时引入高效迁移学习提升计算性能。在3D打印热图像数据集上评估表明，相比传统图神经扩散（GRAND）与物理信息神经网络（PINNs），PiGRAND在预测精度与计算效率上均有显著提升。该优势源于将偏微分方程（PDEs）理论推导的物理规律嵌入学习模型。代码已开源：https://github.com/bu32loxa/PiGRAND。
原文摘要 · Abstract (English)
A comprehensive understanding of heat transport is essential for optimizing various mechanical and engineering applications, including 3D printing. Recent advances in machine learning, combined with physics-based models, have enabled a powerful fusion of numerical methods and data-driven algorithms. This progress is driven by the availability of limited sensor data in various engineering and scientific domains, where the cost of data collection and the inaccessibility of certain measurements are high. To this end, we present PiGRAND, a Physics-informed graph neural diffusion framework. In order to reduce the computational complexity of graph learning, an efficient graph construction procedure was developed. Our approach is inspired by the explicit Euler and implicit Crank-Nicolson methods for modeling continuous heat transport, leveraging sub-learning models to secure the accurate diffusion across graph nodes. To enhance computational performance, our approach is combined with efficient transfer learning. We evaluate PiGRAND on thermal images from 3D printing, demonstrating significant improvements in prediction accuracy and computational performance compared to traditional graph neural diffusion (GRAND) and physics-informed neural networks (PINNs). These enhancements are attributed to the incorporation of physical principles derived from the theoretical study of partial differential equations (PDEs) into the learning model. The PiGRAND code is open-sourced on GitHub: https://github.com/bu32loxa/PiGRAND
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