Uncertainty-Aware Physics-Informed Neural Networks for Parametrizations in Ocean Modeling

Abstract:

The resolution of current ocean and climate models is limited by the computational cost of numerical solvers (Schneider et al., 2017). The combination of deep neural networks and differential equations, called physics-informed neural networks, promises to reduce the computational cost of ocean models and enable fast, global ocean projections at subgrid resolution (Rackauckas et al., 2020). Specifically, the use of deep neural networks to learn subgrid parametrizations, i.e., terms of a differential equation that capture small scale processes such as ocean turbulences, has decreased the computational cost of an ocean simulation by a factor up to 15000 (Rackauckas et al., 2020). The speed-up of learned parametrizations, however, comes at the cost of interpretability: neural networks are considered “black-box” models, partially, because they do not express predictive uncertainties (Amodei et al., 2016).

This work proposes scalable uncertainty-aware physics-informed neural networks (UA-PINNs) for the parametrization of ocean turbulence. The neural networks are modified with methods (e.g., MC-Dropout (Gal et al., 2016) and Bootstrapping (Osband et al., 2016)) to express epistemic uncertainty, i.e., the uncertainty in modeling the observed data distribution.

Preliminary results, in Fig. 1., show that UA-PINNs (blue) can 1) accurately infer the parameters of the Bousinessq approximation (red) to model the equilibration of temperature in a vertical ocean column, and 2) express the uncertainty in learning the parameters (shaded blue). The computational cost of estimating the uncertainty scales linearly with the number of samples drawn from the UA-PINNs and is still significantly lower in comparison to traditional numerical solvers.

Future work, will scale the approach to ocean large-eddy simulations and provide a benchmark and guarantees on the quality of the uncertainty estimates. The estimates could also be used for adaptive sampling, i.e., placing sensors (e.g., buoys or AUVs) at the most informative locations at sea to reduce uncertainty in ocean models. In summary, this work has proposed UA-PINNs: interpretable deep learning-based parametrizations in ocean modeling.