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

Benjamin Uhrich, Tim Häntschel, Erhard Rahm

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

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

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
Paper Structure (22 sections, 26 equations, 11 figures, 5 tables)

This paper contains 22 sections, 26 equations, 11 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Heat Transfer Modelling
  4. Physics-informed Learning
  5. Differential-Equation-inspired Neural Architectures
  6. Graph Neural Networks
  7. Graph Neural Diffusion
  8. Methodology
  9. Data Transformation
  10. Graph Construction from Thermal Images
  11. Numerical Models for the Graph Diffusion Process
  12. Neural Diffusion Models on Graphs
  13. Regularizing Loss Functions
  14. Results in the Application of Powder Bed Fusion
  15. Heat Transfer Prediction based on Thermal Images
  16. ...and 7 more sections

Figures (11)

  • Figure 1: Graph Construction Algorithm - Step 1: Generating point cloud, Step 2: Pruning method, Step 3: Delaunay triangulation, Step 4: Alpha shape, Step 5: Simplicial 3-complex.
  • Figure 2: Flowchart - Graph construction and physics-informed graph neural diffusion
  • Figure 3: Geometry of Printed Objects - Photographs of high quality components, strongly deformed component P9 and CAD models
  • Figure 4: Temporal-Spatial Graph - graph model development for layer 100, 250, 500 (rows). Left column: point cloud, middle column: Simplicial Complex, right column: Alpha Shape
  • Figure 5: 4D-Heat Transport Prediction - Heat transport evolution for layer 100, 250, 350, 500. As time progresses, the component's temperature increases, reaching a maximum at the upper portion and subsequently declining towards the base.
  • ...and 6 more figures