A Physics-Informed Convolutional Long Short Term Memory Statistical Model for Fluid Thermodynamics Simulations

Fluid thermodynamics underpins atmospheric dynamics, climate science, industrial applications, and energy systems. However, direct numerical simulations (DNS) of such systems are computationally prohibitive. To address this, we present a novel physics-informed spatio-temporal surrogate model for Rayleigh-B\'enard convection (RBC), a canonical example of convective fluid flow. Our approach combines convolutional neural networks for spatial feature extraction with an innovative recurrent architecture inspired by large language models, comprising a context builder and a sequence generator to capture temporal dynamics. Inference is penalized with respect to the governing partial differential equations to ensure physical interpretability. Given the sensitivity of turbulent convection to initial conditions, we quantify uncertainty using a conformal prediction framework. This model replicates key features of RBC dynamics while significantly reducing computational cost, offering a scalable alternative to DNS for long-term simulations.