Thanks to IT industry push, Machine Learning (ML) capabilities are in a phase of tremendous growth, and there is great opportunity to point these practically powerful tools toward modeling specific to applications, e.g. in natural and engineering sciences. The challenge is to incorporate domain expertise from traditional physical and engineering discipline scientific discovery into next-generation ML models. We propose to develop novel applied & theoretical mathematics and statistics, computational and algorithmic, that extends cutting-edge ML tools and merge them with application-specific knowledge stated in the form of constraints, symmetries, conservation laws, phenomenological assumptions and other examples of domain expertise regarding relevant degrees of freedom. The emerging Physics Informed Machine Learning (PIML) methodology will bridge the two complementary poles -- application agnostic modern machine learning (in particular deep learning), computationally efficient but lacking interpretability, and science based tuning, highly interpretable but lacking automatization and implementation efficiency. Different aspects of the PIML methodology, such as model selection through neural networks and (generally) graphical models and underlying optimization, inference and learning, will be discussed in this colloquium on examples of applications from fluid mechanics (turbulence) and energy systems.
Michael (Misha) Chertkov's areas of interest include mathematics and statistics applied to physical, engineering and data sciences. He received Ph.D. in physics from the Weizmann Institute of Science in 1996, and his M.Sc. in physics from Novosibirsk State University in 1990. Spent three years at Princeton University as a R.H. Dicke Fellow in the Department of Physics. Joined Los Alamos National Lab in 1999, initially as a J.R. Oppenheimer Fellow in the Theoretical Division, and continued as a Technical Staff Member leading projects in physics of algorithms, energy grid systems, physics and engineering informed data science and machine learning for turbulence. In 2019 M. Chertkov moved to Tucson to lead Interdisciplinary Graduate Program in Applied Mathematics at the University of Arizona. He published more than 200 papers and is a fellow of the American Physical Society (APS) and a senior member of IEEE.