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Probabilistic Methods for Systems Identification Under Uncertainty

Mohamed Aziz Bhouri, MIT

Paris Perdikaris, University of Pennsylvania

Dynamical systems discovery has recently received a lot of attention primarily thanks to the uninterrupted growth of accessible data across various scientific disciplines, including fluid dynamics, climate modeling, systems biology, bio-medical imaging, physical chemistry, etc. Identifying interpretable latent features that describe a dynamical system evolution is of utmost importance not only for physical phenomena understanding, but also for reliable future forecasts, which subsequently leads to effective intervention strategies for design and control of complex dynamical systems. The evolution of such systems can be typically characterized by differential equations, either with apriori unknown dynamics, or with a prescribed form of the dynamics but with a number of unknown parameters. Machine learning methods and data-driven modeling techniques have already proven their utility in solving high-dimensional problems in computer vision, natural language processing, etc; and various probabilistic approaches have also been developed for uncertainty quantification related to chaotic systems and stochastic processes for instance. Recently, several techniques have been proposed to build on machine learning methods and probabilistic frameworks in order to synergistically combine data and mechanistic prior knowledge, so as to develop scientific machine learning approaches capable of distilling dynamics from sparse, noisy, and/or irregularly sampled time-series data. Such methods are currently employed not only to infer parameters, but also to discover latent variables and unknown constitutive laws, as well as tackle forward and inverse problems in complex application domains including cardiovascular flow dynamics, metamaterials, cardiac electrophysiology, etc. Some of these techniques show great success by incorporating sparse regression methods and dictionary modeling, for instance. Others provide probabilistic parameters identification frameworks that can effectively accommodate noisy, sparse and irregularly sampled data to infer posterior distributions over plausible models, and subsequently yield robust future forecasts with quantified uncertainty. This mini-symposium aims to showcase current advances in data-driven methods for systems identification, including (but not limited to) topics in Bayesian inference, deep learning, dictionary learning, hybrid model- and data-driven approaches, model reduction, latent variable models for time-series data, and their application in computational mechanics.