Combining machine learning with knowledge-based modeling for scalable forecasting and subgrid-scale closure of large, complex, spatiotemporal systems.

Alexander Wikner,Istvan Szunyogh,Michelle Girvan,Andrew Pomerance,Troy Arcomano,Jaideep Pathak,Edward Ott,Brian Hunt

doi:10.1063/5.0005541

Abstract

We consider the commonly encountered situation (e.g., in weather forecast) where the goal is to predict the time evolution of a large, spatiotemporally chaotic dynamical system when we have access to both time series data of previous system states and an imperfect model of the full system dynamics. Specifically, we attempt to utilize machine learning as the essential tool for integrating the use of past data into predictions. In order to facilitate scalability to the common scenario of interest where the spatiotemporally chaotic system is very large and complex, we propose combining two approaches: (i) a parallel machine learning prediction scheme and (ii) a hybrid technique for a composite prediction system composed of a knowledge-based component and a machine learning-based component. We demonstrate that not only can this method combining (i) and (ii) be scaled to give excellent performance for very large systems but also that the length of time series data needed to train our multiple, parallel machine learning components is dramatically less than that necessary without parallelization. Furthermore, considering cases where computational realization of the knowledge-based component does not resolve subgrid-scale processes, our scheme is able to use training data to incorporate the effect of the unresolved short-scale dynamics upon the resolved longer-scale dynamics (subgrid-scale closure).

Highlights

In order to facilitate scalability to the common scenario of interest where the spatiotemporally chaotic system is very large and complex, we propose combining two approaches: (i) a parallel machine learning prediction scheme and (ii) a hybrid technique for a composite prediction system composed of a knowledge-based component and a machine learning-based component
We describe a machine learning technique, Combined Hybrid-Parallel Prediction (CHyPP), that can potentially be applied to this situation and demonstrate its efficacy on test systems
We address the general goal of utilizing machine learning to enable expanded capability in the forecasting of large, complex, spatiotemporally chaotic systems for which an imperfect knowledge-based model exists

Summary

Introduction

The most impressive results have been obtained using artificial neural networks with many hidden neural states.3 These hidden layers form a “black box” model, where internal parameters are trained given a set of measured training data, but after which only the final model output is observed. This formulation using measured training data contrasts with how models used for forecasting physical spatiotemporally chaotic processes are formulated, which is typically done using the available scientific knowledge of the underlying mechanisms that govern the system’s evolution.

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