2021): Deep emulators for differentiation, forecasting, and parametrization in Earth science simulators. Journal of Advances in Modeling Earth Systems, 13, e2021MS002554, doi:10.1029/2021MS002554, & (
To understand and predict large, complex, and chaotic systems, Earth scientists build simulators from physical laws. Simulators generalize better to new scenarios, require fewer tunable parameters, and are more interpretable than nonphysical deep learning, but procedures for obtaining their derivatives with respect to their inputs are often unavailable. These missing derivatives limit the application of many important tools for forecasting, model tuning, sensitivity analysis, or subgrid-scale parametrization. Here, we propose to overcome this limitation with deep emulator networks that learn to calculate the missing derivatives. By training directly on simulation data without analyzing source code or equations, this approach supports simulators in any programming language on any hardware without specialized routines for each case. To demonstrate the effectiveness of our approach, we train emulators on complete or partial system states of the chaotic Lorenz-96 simulator and evaluate the accuracy of their dynamics and derivatives as a function of integration time and training data set size. We further demonstrate that emulator-derived derivatives enable accurate 4D-Var data assimilation and closed-loop training of parametrizations. These results provide a basis for further combining the parsimony and generality of physical models with the power and flexibility of machine learning.
Plain Language Summary:
Many Earth science simulators are implemented as monolithic programs that calculate changes in the state of a system over time. In many cases, using or improving these simulators also requires the derivatives of their outputs with respect to inputs, which describe how future states depend on past states. These derivatives can be difficult or costly to compute. Several recent studies have applied deep learning (DL) to simulation data to construct emulators of their dynamics. Here, we use the fact that DL models can be easily and automatically differentiated to obtain approximate derivatives of the original simulator and test this idea on a simple and common chaotic model of the atmosphere. We verify in several experiments that the emulator derivatives, which require neither additional training nor extensive postprocessing to obtain, can indeed be used as a valid substitute for the derivatives of the simulator.