PiGRAND: Physics-informed Graph Neural Diffusion for Intelligent Additive Manufacturing

2026-03-16

AI Summary

This work addresses the challenge of modeling heat conduction in additive manufacturing, where sensor data scarcity and unobservable thermal fields hinder accurate simulation. To overcome this, the authors propose a physics-informed graph neural diffusion method that integrates explicit Euler and implicit Crank-Nicolson schemes into a graph neural network framework, enabling physically consistent and efficient heat diffusion modeling across graph nodes. A novel graph construction strategy grounded in partial differential equation theory, combined with a tailored transfer learning mechanism, substantially reduces computational complexity while enhancing model generalization. Experimental results on 3D printing thermal imaging data demonstrate that the proposed approach significantly outperforms both GRAND and physics-informed neural networks (PINNs) in terms of prediction accuracy and computational efficiency.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Computer Vision: Diffusion Models for Vision
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

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

Problem

• heat transport
• additive manufacturing
• limited sensor data
• physics-informed learning
• thermal prediction

Innovation

• Physics-informed
• Graph Neural Diffusion
• Heat Transport
• Additive Manufacturing
• Transfer Learning