Identification of physical processes via combined data-driven and data-assimilation methods

Abstract

With the advent of modern data collection and storage technologies, data-driven approaches have been developed for discovering the governing partial differential equations (PDE) of physical problems. However, in the extant works the model parameters in the equations are either assumed to be known or have a linear dependency. Therefore, most of the realistic physical processes cannot be identified with the current data-driven PDE discovery approaches. In this study, an innovative framework is developed that combines data-driven and data-assimilation methods for simultaneously identifying physical processes and inferring model parameters. Spatiotemporal measurement data are first divided into a training data set and a testing data set. Using the training data set, a data-driven method is developed to learn the governing equation of the considered physical problem by identifying the occurred (or dominated) processes and selecting the proper empirical model. Through introducing a prediction error of the learned governing equation for the testing data set, a data-assimilation method is devised to estimate the uncertain model parameters of the selected empirical model. For the contaminant transport problem investigated, the results demonstrate that the proposed method can adequately identify the considered physical processes via concurrently discovering the corresponding governing equations and inferring uncertain parameters of nonlinear models, even in the presence of measurement errors. This work helps to broaden the applicable area of the research of data driven discovery of governing equations of physical problems.

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• Deep-learning of Parametric Partial Differential Equations from Sparse and Noisy Data
• Coercing Machine Learning to Output Physically Accurate Results
• Deep-learning based discovery of partial differential equations in integral form from sparse and noisy data
• Model selection of chaotic systems from data with hidden variables using sparse data assimilation
• Data-driven Identification of 2D Partial Differential Equations using extracted physical features
• Machine Learning of Partial Differential Equations from Noise Data
• Identification of Physical Processes and Unknown Parameters of 3D Groundwater Contaminant Problems via Theory-guided U-net