Machine learning strategies for systems with invariance properties

Journal Article · Fri May 06 00:00:00 EDT 2016 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2016.05.003· OSTI ID:1247662

Ling, Julia ^[1]; Jones, Reese E. ^[1]; Templeton, Jeremy Alan ^[1]

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1. Sandia National Lab. (SNL-CA), Livermore, CA (United States)

Here, in many scientific fields, empirical models are employed to facilitate computational simulations of engineering systems. For example, in fluid mechanics, empirical Reynolds stress closures enable computationally-efficient Reynolds-Averaged Navier-Stokes simulations. Likewise, in solid mechanics, constitutive relations between the stress and strain in a material are required in deformation analysis. Traditional methods for developing and tuning empirical models usually combine physical intuition with simple regression techniques on limited data sets. The rise of high-performance computing has led to a growing availability of high-fidelity simulation data, which open up the possibility of using machine learning algorithms, such as random forests or neural networks, to develop more accurate and general empirical models. A key question when using data-driven algorithms to develop these models is how domain knowledge should be incorporated into the machine learning process. This paper will specifically address physical systems that possess symmetry or invariance properties. Two different methods for teaching a machine learning model an invariance property are compared. In the first , a basis of invariant inputs is constructed, and the machine learning model is trained upon this basis, thereby embedding the invariance into the model. In the second method, the algorithm is trained on multiple transformations of the raw input data until the model learns invariance to that transformation. Results are discussed for two case studies: one in turbulence modeling and one in crystal elasticity. It is shown that in both cases embedding the invariance property into the input features yields higher performance with significantly reduced computational training costs.

• Research Organization: Sandia National Laboratories (SNL-CA), Livermore, CA (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA)
• Grant/Contract Number: AC04-94AL85000
• OSTI ID: 1247662
• Alternate ID(s): OSTI ID: 1347630
• Report Number(s): SAND--2016-0249J; 618374
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: C Vol. 318; ISSN 0021-9991
• Publisher: Elsevier
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
constitutive models
machine learning
tensor invariants
turbulence models