Abstract
Machine learning (ML) is redefining what is possible in data-intensive fields of science and engineering. However, applying ML to problems in the physical sciences comes with a unique set of challenges: scientists want physically interpretable models that can (i) generalize to predict previously unobserved behaviors, (ii) provide effective forecasting predictions (extrapolation), and (iii) be certifiable. Autonomous systems will necessarily interact with changing and uncertain environments, motivating the need for models that can accurately extrapolate based on physical principles (e.g. Newton's universal second law for classical mechanics, F = ma). Standard ML approaches have shown impressive performance for predicting dynamics in an interpolatory regime, but the resulting models often lack interpretability and fail to generalize. We build on a sparse regression framework that discovers governing dynamical systems models from data, selecting relevant terms in the dynamics from a library of possible functions. Our critically enabling innovation introduces a relaxed version of a sparse optimization framework that allows the use of non-convex sparsity promoting regularization functions and addresses three open challenges in scientific problems and data sets: (i) robust handling of outliers and corrupt data within noisy sensor measurements, (ii) parametric dependencies in candidate library functions, and (iii) the imposition of physical constraints. By explicitly addressing these open challenges, the integrated and unified algorithm developed provides a significant advancement over current state-of-the-art sparse model discovery methods. We show that the approach discovers parsimonious dynamical models on several example systems. This flexible approach can be tailored to the unique challenges associated with a wide range of applications and data sets, providing a powerful ML-based framework for learning governing models for physical systems from data.
Highlights
With abundant data being generated across scientific fields, researchers are increasingly turning to machine learning (ML) methods to aid scientific inquiry
This is in contrast to neural networks (NNs), which are defined by exceedingly large parametrizations which typically lack interpretability or generalizability
We develop a unified sparse optimization framework for dynamical system discovery that provides significant advancement to current sparsity promotion algorithms by providing a unified and integrated framework which accounts for three critical and practical innovations that include the discovery of models with (i) corrupt/missing training data, (ii) partially known physics and/or physical constraints, and (iii) parametric dependencies in the candidate functions representing the dynamics
Summary
With abundant data being generated across scientific fields, researchers are increasingly turning to machine learning (ML) methods to aid scientific inquiry. We develop a unified sparse optimization framework for dynamical system discovery that provides significant advancement to current sparsity promotion algorithms by providing a unified and integrated framework which accounts for three critical and practical innovations that include the discovery of models with (i) corrupt/missing training data, (ii) partially known physics and/or physical constraints, and (iii) parametric dependencies in the candidate functions representing the dynamics. The SR3 optimization framework allows for critically enabling extensions of the SINDy model discovery framework As already highlighted, these extensions handle the important practical considerations of (i) robust handling of outliers and corrupt data within noisy sensor measurements, (ii) parametric dependencies in candidate library functions, and (iii) the imposition of physical constraints.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
