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.

CESAR: A Convolutional Echo State AutoencodeR for High-Resolution Wind Forecasting

An accurate and timely assessment of wind speed and energy output allows an efficient planning and management of this resource on the power grid. Wind energy, especially at high resolution, calls for the development of nonlinear statistical models able to capture complex dependencies in space and time. This work introduces a Convolutional Echo State AutoencodeR (CESAR), a spatio-temporal, neural network-based model which first extracts the spatial features with a deep convolutional autoencoder, and then models their dynamics with an echo state network. We also propose a two-step approach to also allow for computationally affordable inference, while also performing uncertainty quantification. We focus on a high-resolution simulation in Riyadh (Saudi Arabia), an area where wind farm planning is currently ongoing, and show how CESAR is able to provide improved forecasting of wind speed and power for proposed building sites by up to 17% against the best alternative methods.

Modeling High-Resolution Spatio-Temporal Wind with Deep Echo State Networks and Stochastic Partial Differential Equations

In the past decades, clean and renewable energy has gained increasing attention due to a global effort on carbon footprint reduction. In particular, Saudi Arabia is gradually shifting its energy portfolio from an exclusive use of oil to a reliance on renewable energy, and, in particular, wind. Modeling wind for assessing potential energy output in a country as large, geographically diverse and understudied as Saudi Arabia is a challenge which implies highly non-linear dynamic structures in both space and time. To address this, we propose a spatio-temporal model whose spatial information is first reduced via an energy distance-based approach and then its dynamical behavior is informed by a sparse and stochastic recurrent neural network (Echo State Network). Finally, the full spatial data is reconstructed by means of a non-stationary stochastic partial differential equation-based approach. Our model can capture the fine scale wind structure and produce more accurate forecasts of both wind speed and energy in lead times of interest for energy grid management and save annually as much as one million dollar against the closest competitive model.