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 - 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.
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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 -