Machine Learning for Science: Data-Driven Discovery Methods for Governing equations,Coordinates and Sensors
Machine learning and artificial intelligence algorithms are now being used to automate the discovery of governing physical equations and coordinate systems from measurement data alone. However, positing a universal physical law from data is challenging: (i) An appropriate coordinate system must also be advocated and (ii) simultaneously proposing an accompanying discrepancy model to account for the inevitable mismatch between theory and measurements must be considered. Using a combination of deep learning and sparse regression, specifically the sparse identification of nonlinear dynamics (SINDy) algorithm, we show how a robust mathematical infrastructure can be formulated for simultaneously learning physics models and their coordinate systems. This can be done with limited data and sensors. We demonstrate the methods on a diverse number of examples, showing how data can maximally be exploited for scientific and engineering applications. The work also highlights the fact that the naive application of ML/AI will generally be insufficient to extract universal physical laws without further modification.