Physics-Informed Regional Climate Models With Reduced-Order Neural Networks

The patent segments the climate modeling problem into two distinct components: a reduced-order model (ROM) that captures dominant spatial patterns through proper orthogonal decomposition, and a neural network that predicts temporal evolution. This segmentation allows each component to be optimized independently, with the ROM providing accurate spatial structures and the neural network providing fast temporal predictions, thereby resolving the contradiction between accuracy and computational speed.

The patent replaces the traditional physics-based mechanical climate model with a data-driven neural network component that learns temporal dynamics from historical data. This substitution maintains accuracy by learning from observed patterns while dramatically reducing computational cost, as the neural network can be trained once and then provides rapid predictions without requiring repeated complex physical calculations.

The patent applies segmentation by separating spatial and temporal dimensions through proper orthogonal decomposition. The spatial component is captured in the ROM basis functions which represent dominant patterns at various scales, while the temporal component is handled by the neural network. This allows the model to achieve high effective resolution for regional details without requiring a full high-resolution grid throughout the entire domain, thereby reducing overall complexity.

The patent uses partial action by focusing computational resources on capturing the most significant spatial patterns through a limited number of ROM basis functions. Rather than resolving all possible spatial scales equally, the model concentrates on the dominant modes that capture the essential climate variability, achieving high precision for the most important features while avoiding the exponential complexity increase that would result from fully resolving all scales.

The patent segments the modeling approach into a physics-informed ROM component that ensures physical consistency through proper orthogonal decomposition of the governing equations, and a data-driven neural network component that provides rapid temporal predictions. The ROM maintains physical consistency by being derived from the underlying physics, while the neural network accelerates computation by learning from pre-computed trajectories, thus resolving the contradiction between reliability and speed.

The patent applies preliminary action by pre-computing the ROM basis functions and training the neural network on historical climate data before actual forecasting. This upfront preparation creates a surrogate model that can then provide rapid predictions without requiring repeated complex physics calculations during operational forecasting, thereby achieving both physical consistency and computational speed.