In a changing climate, accurate and efficient Earth system models are needed to understand the impacts of climate change on atmospheric dynamics and extreme weather events - e.g., heat waves, floods, and droughts. This project proposes a mathematically rigorous method to develop AI-based stable and physically consistent global atmospheric models that can be reliably used to perform both short-term forecasting and long-term climate modeling at a fraction of the computational cost of current physics-based models, which may take years to develop otherwise. The proposed methodology leverages principles in deep learning theory and atmospheric physics to ensure physical consistency of the proposed AI models. Furthermore, the project aims to develop a framework for systematic evaluation of such physical consistency of AI-based models of the atmosphere that are grounded in physics, akin to traditional climate model development. This project contributes to a new paradigm of simulation sciences for geophysics, which is driven entirely through models trained on data. This would train and develop an interdisciplinary workforce that would perform cutting-edge research in atmospheric physics, scientific computing, and AI with a greater goal of addressing the pressing challenges of climate change.<br/><br/>Current AI models are trained on reanalysis data and demonstrate prediction skills that outperform numerical weather prediction models. Despite their superior performance in predicting certain atmospheric variables at short time scales, their long-term performance degrades quickly, and all these models either show numerical blow-up, or unphysical hallucinations beyond 15 day or 20-day lead times. The reason for such unphysical behavior in these models is the inability to preserve physical consistency of the predicted states especially in the small scales as well as the inability to integrate the states in time by considering the numerical stability criteria of such integrators. Hence, these models fail to provide any scientific insight into the climate statistics which require one to integrate the states of the atmosphere for hundreds of years, e.g., to estimate the risk of extreme events with long return periods, low-frequency variability of key climate processes, or estimate the response to external forcing. We propose to develop a physically-consistent long- term stable deep learning-based atmospheric emulator that incorporates boundary conditions and integrates the states of the atmosphere for hundreds of years. The key innovations in enabling such an emulator are (a) the understanding of limitations of deep learning models in preserving small-scale physical consistency and then alleviating it through hard- and soft-constraints inside the architecture of the model in an architecture-agnostic fashion and (b) enabling stability analysis of these models akin to traditional numerical stability analysis to restrict the model’s fastest growing eigenvalues. Such emulators, which are 10000x faster than Earth system models, will allow us to seamlessly generate a large ensemble of integrated states of the atmosphere enabling rigorous estimates of extremes and their uncertainties, computing responses to external forcings, and more.<br/><br/>This award by the Division of Research, Innovation, Synergies, and Education within the Directorate for Geosciences is jointly supported by the National Discovery Cloud for Climate initiative within the Office of Advanced Cyberinfrastructure within the Directorate for Computer and Information Science and Engineering.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.