Date:
Wed, 28/12/202212:00-13:30
Location:
Danciger B building – Seminars Room
Lecturer: Michael (Misha) Chertkov, UArizona
Abstract:
According to psychologist D. Kahneman (2002 Nobel prize winner in economics for the work on decision making under uncertainty) there are two modes/systems of thinking. System 1 operates automatically and quickly, like Deep Learning empowered by Differentiable Programming. System 2 allocates attention to the effortful mental activities, like building explainable heuristics in quantitative sciences.
In this talk we illustrate how applied mathematics is harnessing system 1 achievements of modern AI to build system 2 for quantitative sciences. Specifically, we discuss design, training and validation of the system 2 for Lagrangian Large Eddy Simulations (L-LES) of Turbulence.
We show how to design and validate equations, generalizing equations of the weakly compressible Smooth Particle Hydrodynamics, with extended parametric and functional freedom which is then resolved/fixed via training on Lagrangian data from a Direct Numerical Simulation of the Navier-Stokes equation. The L-LES framework includes parameters which are explainable in clear physical terms (system 2), e.g. parameters describing effects of eddy-diffusivity and smoothing kernels, and Neural Networks to represent effects of smaller (unresolved) scales and relations between velocity and pressure fields evaluated at the particle positions in a functional form. We utilize modern methodology of Differential Programming and Deep Neural Networks (system 2) to train the parametric and functional degrees of freedom. We show that the L-LES is capable to reproduce Lagrangian and Eulerian statistics of the flow at the resolved scales. This is a joint work of Los Alamos NL and UArizona teams (with Y. Tian, M. Woodward, M. Stepanov, C. Hyett, C. Fryer and D. Livescu).
Abstract:
According to psychologist D. Kahneman (2002 Nobel prize winner in economics for the work on decision making under uncertainty) there are two modes/systems of thinking. System 1 operates automatically and quickly, like Deep Learning empowered by Differentiable Programming. System 2 allocates attention to the effortful mental activities, like building explainable heuristics in quantitative sciences.
In this talk we illustrate how applied mathematics is harnessing system 1 achievements of modern AI to build system 2 for quantitative sciences. Specifically, we discuss design, training and validation of the system 2 for Lagrangian Large Eddy Simulations (L-LES) of Turbulence.
We show how to design and validate equations, generalizing equations of the weakly compressible Smooth Particle Hydrodynamics, with extended parametric and functional freedom which is then resolved/fixed via training on Lagrangian data from a Direct Numerical Simulation of the Navier-Stokes equation. The L-LES framework includes parameters which are explainable in clear physical terms (system 2), e.g. parameters describing effects of eddy-diffusivity and smoothing kernels, and Neural Networks to represent effects of smaller (unresolved) scales and relations between velocity and pressure fields evaluated at the particle positions in a functional form. We utilize modern methodology of Differential Programming and Deep Neural Networks (system 2) to train the parametric and functional degrees of freedom. We show that the L-LES is capable to reproduce Lagrangian and Eulerian statistics of the flow at the resolved scales. This is a joint work of Los Alamos NL and UArizona teams (with Y. Tian, M. Woodward, M. Stepanov, C. Hyett, C. Fryer and D. Livescu).