Title: A Physics-Informed Spatiotemporal Deep Learning Framework for Turbulent Systems Show Chinese title

Title: 基于物理信息的时空深度学习框架用于湍流系统

Abstract: 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-B\'enard 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. Show Chinese abstract

Abstract: 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，对这些系统的直接数值模拟（DNS）在计算上可能非常昂贵。 为了解决这个问题，我们提出了一种新颖的物理信息时空代理模型，用于雷利-贝纳德对流（RBC），这是对流流体流动的一个典型例子。 我们的方法结合了卷积神经网络，用于空间维度降维，以及一种受大型语言模型启发的创新循环架构，以模拟长程时间动态。 推理过程受到控制偏微分方程的惩罚，以确保物理可解释性。 由于RBC表现出湍流行为，我们使用一个保形预测框架来量化不确定性。 该模型再现了RBC动力学的关键物理特征，同时显著降低了计算成本，为长期模拟提供了一种可扩展的DNS替代方案。