Physics-Informed Machine Learning

Data-driven methods for model discovery in computational physics

Project Overview

Recent advances in computational power have allowed researchers to augment traditional modeling methods in physical science and engineering with machine-led discovery autonomous methodologies that can greatly speed up the pace of research in determining hidden underlying relationships in physical models.

Project Summary

Using classical algebraic methods to represent a functional relationship between the turbulent stresses and ordinary variables namely velocity, pressure and their gradients, the autonomic closure could train machines to accurately and efficiently determine complex nonlinear, nonlocal and nonequlibrium effects in turbulent flow fields.

Autonomic Closure for Turbulent Flows in LES

Aerospace Engineering Research Associate

Apr 2015 - May 2019

Autonomic closure for large eddy simulations (LES) replaces traditional prescribed subgrid models with an adaptive self-optimizing closure that solves a local, nonlinear, non-parametric system identification problem for each subgrid term at every point and time. Here we maximize the balance between accuracy and efficiency in the autonomic approach, with a particular focus on capturing the spatial structure of subgrid production fields, including the scale-dependent support-density fields on which large values of subgrid production are concentrated. A relatively local, second-order, velocity-only, collocated implementation is found to produce subgrid stress and production fields that closely match not only statistics but also most details of the spatial structure in the exact fields at essentially all resolved scales, at a computational cost that is 1000x lower than previous autonomic closure implementations. This is sufficient to enable implementation of autonomic closure in aposteriori tests, and we show that the most accurate and efficient implementation identified here is stable in an LES of forced homogeneous isotropic turbulence. We also show that this implementation provides accurate results in tests on homogeneous shear turbulence, demonstrating the wide applicability of the autonomic closure methodology.

Research in turbulence seeks to achieve the primary objective of accurately representing forward and backward momentum and energy exchanges at all length and time scales. Although most of simulations can provide meaningful results in general applications, while not accurately representing small-scale exchanges, simulating complex flows found in multi-physics applications (combustion, particle-laden flow) require closure at the finest scales to accurately represent the process.

While scale-similarity methods "read" the flowfield at coarser scales to determine subgrid stresses at finer scales, they are severely restricted in representing the stress tensor in the number of degrees of freedom. Autonomic closure frees up the limit placed on the number of degrees of freedom by first building a representation that consider every possible term, followed by selecting the dominant terms that contribute to the stress tensor at a given point in space and time. The selection process is primarily driven by optimization methods, some of which find applications in general machine learning algorithms. The result is determining the most accurate representation that accounts for non-linear, non-local, and non-equilibrium effects in a turbulent flowfield.

The image shown above compares predicted stress tensor fields with autonomic closure (right) with the true DNS stress fields (left). The pdfs below (panel a, b) compare statistics between true DNS stress and production fields with the one determined by autonomic closure, while metrics M1, M2 in panel (c) reveal that errors between the two fields diminish as they are measured from finer scales to coarser scales for homogeneous isotropic turbulence and homogenous shear turbulence.