Joint Physics-informed and Data-driven Complex Dynamical System Solvers

Several scientifically major tasks such as weather forecasting leads to highly complex and high-dimensional dynamical systems whose solutions are challenging to obtain. Classical solvers using numerical methods should be run over and over as the environment changes. Furthermore, classical solvers are slow and expensive to implement. Such solvers typically require fine-grained discretizations, which leads to an increased run-time. Recently, it has been shown that AI and ML methods can significantly accelerate solving highly complex dynamical systems such as high-resolution weather prediction [1,2], which is backed by substantial investments by major companies such as NVIDIA and Deepmind.  In this project, our idea is to apply a novel and knowledge-driven approach to write the solution as a composition of a physics-inspired mechanical part and data-driven residual part. We inject the knowledge using highly-efficient numerical solvers based on substantial preliminary work done at the DSB group at UiO combined with SoTA ML-driven architectures and algorithms developed by the researchers from the departments of computer science and math and statistics through Integreat to substantially improve performance of the current weather prediction solvers, which will have huge scientific impacts.