Ali Ramadhan

Xin Kai Lee, Ali Ramadhan, Andre Souza et al.

NORi is a machine-learned (ML) parameterization of ocean boundary layer turbulence that is physics-based and augmented with neural networks. NORi stands for neural ordinary differential equations (NODEs) Richardson number (Ri) closure. The physical parameterization is controlled by a Richardson number-dependent diffusivity and viscosity. The NODEs are trained to capture the entrainment through the base of the boundary layer, which cannot be represented with a local diffusive closure. The parameterization is trained using large-eddy simulations in an "a posteriori" fashion, where parameters are calibrated with a loss function that explicitly depends on the actual time-integrated variables of interest rather than the instantaneous subgrid fluxes, which are inherently noisy. NORi is designed for the realistic nonlinear equation of state of seawater and demonstrates excellent prediction and generalization capabilities in capturing entrainment dynamics under different convective strengths, oceanic background stratifications, rotation strengths, and surface wind forcings. NORi is numerically stable for at least 100 years of integration time in large-scale simulations, despite only being trained on 2-day horizons, and can be run with time steps as long as one hour. The highly expressive neural networks, combined with a physically-rigorous base closure, prove to be a robust paradigm for designing parameterizations for climate models where data requirements are drastically reduced, inference performance can be directly targeted and optimized, and numerical stability is implicitly encouraged during training.

Christopher Rackauckas, Yingbo Ma, Julius Martensen et al.

In the context of science, the well-known adage "a picture is worth a thousand words" might well be "a model is worth a thousand datasets." In this manuscript we introduce the SciML software ecosystem as a tool for mixing the information of physical laws and scientific models with data-driven machine learning approaches. We describe a mathematical object, which we denote universal differential equations (UDEs), as the unifying framework connecting the ecosystem. We show how a wide variety of applications, from automatically discovering biological mechanisms to solving high-dimensional Hamilton-Jacobi-Bellman equations, can be phrased and efficiently handled through the UDE formalism and its tooling. We demonstrate the generality of the software tooling to handle stochasticity, delays, and implicit constraints. This funnels the wide variety of SciML applications into a core set of training mechanisms which are highly optimized, stabilized for stiff equations, and compatible with distributed parallelism and GPU accelerators.