用物理约束深度学习模拟湍流对流，大幅降低计算成本。
A Physics-Informed Spatiotemporal Deep Learning Framework for Turbulent Systems
- 结合卷积网络与类大模型时序结构，捕捉空间与长程时间动态。
- 在保持物理一致性前提下，实现对瑞利-贝纳德对流的高精度模拟。
- 适合气候、能源等领域需长期仿真的研究者使用。
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，直接数值模拟（DNS）这类系统计算代价极高。为此，我们提出一种新型物理信息引导的时空代理模型，用于经典对流流动案例——瑞利-贝纳德对流（RBC）。该方法结合卷积神经网络进行空间降维，以及受大语言模型启发的创新循环架构，以建模长程时间动态。推理过程通过惩罚机制施加控制偏微分方程约束，确保物理可解释性。由于RBC呈现湍流行为，我们采用共形预测框架量化不确定性。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，为长期模拟提供了可扩展的替代方案。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。