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.

翻译：在复杂几何结构上实现时空场的精确长时域预测是科学机器学习中的一个基础性挑战，其应用场景包括增材制造，其中温度历程决定着缺陷形成与力学性能。高保真仿真虽然精确但计算成本高昂，而尽管近期取得进展，机器学习方法在长时域温度与梯度预测方面仍面临困难。我们提出一种深度学习框架，用于直接在网格上预测完整温度历程，该框架以几何结构与工艺参数为条件，同时能在数千个时间步长上保持稳定性，并实现跨异构几何结构的泛化。该框架采用一种由两个在互补时间尺度上运行的耦合模型构成的时间多尺度架构。两个模型均依赖潜在循环图神经网络来捕捉网格上的时空动态，而变分图自编码器则提供紧凑的潜在表示，从而降低内存使用并提升训练稳定性。在模拟粉末床熔融数据上的实验表明，该框架能对不同几何结构实现精确且时间稳定的长时域预测，性能优于现有基线方法。尽管在二维场景中进行评估，但该框架具有通用性，可扩展至具有多尺度动态的物理驱动系统及三维几何结构。