Learning Generalized Quasi-Geostrophic Models Using Deep Neural Numerical Models
This work addresses the challenge of modeling complex dynamical systems in physics, specifically for oceanographers, by introducing a hybrid approach that integrates machine learning with traditional numerical methods, though it appears incremental as it builds on existing physical theories.
The authors tackled the problem of discovering hidden physical laws in dynamical systems by proposing Deep Neural Numerical Models (DNNMs), which combine prior physical knowledge with neural networks, and applied this to upper ocean dynamics for Sea Surface Height prediction, achieving results that connect to the established Quasi-Geostrophic model.
We introduce a new strategy designed to help physicists discover hidden laws governing dynamical systems. We propose to use machine learning automatic differentiation libraries to develop hybrid numerical models that combine components based on prior physical knowledge with components based on neural networks. In these architectures, named Deep Neural Numerical Models (DNNMs), the neural network components are used as building-blocks then deployed for learning hidden variables of underlying physical laws governing dynamical systems. In this paper, we illustrate an application of DNNMs to upper ocean dynamics, more precisely the dynamics of a sea surface tracer, the Sea Surface Height (SSH). We develop an advection-based fully differentiable numerical scheme, where parts of the computations can be replaced with learnable ConvNets, and make connections with the single-layer Quasi-Geostrophic (QG) model, a baseline theory in physical oceanography developed decades ago.