TY - JOUR
T1 - Differentiable physics-enabled closure modeling for Burgers’ turbulence
AU - Shankar, Varun
AU - Puri, Vedant
AU - Balakrishnan, Ramesh
AU - Maulik, Romit
AU - Viswanathan, Venkatasubramanian
N1 - Funding Information:
This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE 1745016 awarded to VS. The authors from CMU acknowledge the support from the Technologies for Safe and Efficient Transportation University Transportation Center, and Mobility21, A United States Department of Transportation National University Transportation Center. This work was supported in part by Oracle Cloud credits and related resources provided by the Oracle for Research program. RM is supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, under Contract DE-AC02-06CH11357.
Publisher Copyright:
© 2023 The Author(s). Published by IOP Publishing Ltd.
PY - 2023/3/1
Y1 - 2023/3/1
N2 - Data-driven turbulence modeling is experiencing a surge in interest following algorithmic and hardware developments in the data sciences. We discuss an approach using the differentiable physics paradigm that combines known physics with machine learning to develop closure models for Burgers’ turbulence. We consider the one-dimensional Burgers system as a prototypical test problem for modeling the unresolved terms in advection-dominated turbulence problems. We train a series of models that incorporate varying degrees of physical assumptions on an a posteriori loss function to test the efficacy of models across a range of system parameters, including viscosity, time, and grid resolution. We find that constraining models with inductive biases in the form of partial differential equations that contain known physics or existing closure approaches produces highly data-efficient, accurate, and generalizable models, outperforming state-of-the-art baselines. Addition of structure in the form of physics information also brings a level of interpretability to the models, potentially offering a stepping stone to the future of closure modeling.
AB - Data-driven turbulence modeling is experiencing a surge in interest following algorithmic and hardware developments in the data sciences. We discuss an approach using the differentiable physics paradigm that combines known physics with machine learning to develop closure models for Burgers’ turbulence. We consider the one-dimensional Burgers system as a prototypical test problem for modeling the unresolved terms in advection-dominated turbulence problems. We train a series of models that incorporate varying degrees of physical assumptions on an a posteriori loss function to test the efficacy of models across a range of system parameters, including viscosity, time, and grid resolution. We find that constraining models with inductive biases in the form of partial differential equations that contain known physics or existing closure approaches produces highly data-efficient, accurate, and generalizable models, outperforming state-of-the-art baselines. Addition of structure in the form of physics information also brings a level of interpretability to the models, potentially offering a stepping stone to the future of closure modeling.
UR - http://www.scopus.com/inward/record.url?scp=85148205271&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85148205271&partnerID=8YFLogxK
U2 - 10.1088/2632-2153/acb19c
DO - 10.1088/2632-2153/acb19c
M3 - Article
AN - SCOPUS:85148205271
SN - 2632-2153
VL - 4
JO - Machine Learning: Science and Technology
JF - Machine Learning: Science and Technology
IS - 1
M1 - 015017
ER -