Stable Long-Horizon Spatiotemporal Prediction on Meshes Using Latent Multiscale Recurrent Graph Neural Networks

TL;DR

A deep learning framework for predicting full temperature histories directly on meshes, conditioned on geometry and process parameters, while maintaining stability over thousands of time steps and generalizing across heterogeneous geometries is proposed.

Abstract

Accurate long-horizon prediction of spatiotemporal fields on complex geometries is a fundamental challenge in scientific machine learning, with applications such as additive manufacturing where temperature histories govern defect formation and mechanical properties. High-fidelity simulations are accurate but computationally costly, and despite recent advances, machine learning methods remain challenged by long-horizon temperature and gradient prediction. We propose a deep learning framework for predicting full temperature histories directly on meshes, conditioned on geometry and process parameters, while maintaining stability over thousands of time steps and generalizing across heterogeneous geometries. The framework adopts a temporal multiscale architecture composed of two coupled models operating at complementary time scales. Both models rely on a latent recurrent graph neural network to capture spatiotemporal dynamics on meshes, while a variational graph autoencoder provides a compact latent representation that reduces memory usage and improves training stability. Experiments on simulated powder bed fusion data demonstrate accurate and temporally stable long-horizon predictions across diverse geometries, outperforming existing baseline. Although evaluated in two dimensions, the framework is general and extensible to physics-driven systems with multiscale dynamics and to three-dimensional geometries.

Figures (17)

• Figure 1: Example of printed geometry. Metallic powder is in gray, the final printed part is in blue and the part boundaries are highlighted in green.
• Figure 2: Temperature field snapshots for a fixed printed geometry at multiple time steps. The green lines indicate the part boundaries, enclosing the solid metallic region. The temperature is simulated for both metallic part and the surrounding powder.
• Figure 3: Overview of the LM-RGNN architecture and its main components, including the latent-RGNN and the VGAE.
• Figure 4: Temporal MAE (t-MAE) on the test set for the interlayer model, compared with its full-dimensional (non-latent) counterpart.
• Figure 5: Temporal MAE (t-MAE) on the test set for the intralayer model, compared with its ablated variants.