Fluid thermodynamics underpins atmospheric dynamics, climate science, industrial applications, and energy systems. However, direct numerical simulations (DNS) of such systems can be computationally prohibitive. To address this, we present a novel physics-informed spatiotemporal surrogate model for Rayleigh-Benard convection (RBC), a canonical example of convective fluid flow. Our approach combines convolutional neural networks, for spatial dimension reduction, with an innovative recurrent architecture, inspired by large language models, to model long-range temporal dynamics. Inference is penalized with respect to the governing partial differential equations to ensure physical interpretability. Since RBC exhibits turbulent behavior, we quantify uncertainty using a conformal prediction framework. This model replicates key physical features of RBC dynamics while significantly reducing computational cost, offering a scalable alternative to DNS for long-term simulations.

翻译：流体热力学是大气动力学、气候科学、工业应用和能源系统的基础。然而，对此类系统进行直接数值模拟（DNS）的计算成本可能过高。为解决这一问题，我们提出了一种新颖的基于物理信息的时空替代模型，用于研究瑞利-贝纳德对流（RBC）——对流流体流动的典型示例。我们的方法结合了用于空间降维的卷积神经网络，以及一种受大语言模型启发的创新循环架构，以建模长程时间动力学。通过相对于控制偏微分方程对推理过程施加惩罚，确保了模型的物理可解释性。由于RBC表现出湍流行为，我们使用保形预测框架来量化不确定性。该模型在显著降低计算成本的同时，复现了RBC动力学的关键物理特征，为长期模拟提供了一种可扩展的DNS替代方案。