Data-driven learning of nonlocal physics from high-fidelity synthetic data
- Lehigh Univ., Bethlehem, PA (United States)
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Sandia National Lab. (SNL-CA), Livermore, CA (United States)
A key challenge to nonlocal models is the analytical complexity of deriving them from first principles, and frequently their use is justified a posteriori. Here, we extract nonlocal models from data, circumventing these challenges and providing data-driven justification for the resulting model form. Extracting data-driven surrogates is a major challenge for machine learning (ML) approaches, due to nonlinearities and lack of convexity — it is particularly challenging to extract surrogates which are provably well-posed and numerically stable. Our scheme not only yields a convex optimization problem, but also allows extraction of nonlocal models whose kernels may be partially negative while maintaining well-posedness even in small-data regimes. To achieve this, based on established nonlocal theory, we embed in our algorithm sufficient conditions on the non-positive part of the kernel that guarantee well-posedness of the learnt operator. These conditions are imposed as inequality constraints to meet the requisite conditions of the nonlocal theory. We demonstrate this workflow for a range of applications, including reproduction of manufactured nonlocal kernels; numerical homogenization of Darcy flow associated with a heterogeneous periodic microstructure; nonlocal approximation to high-order local transport phenomena; and approximation of globally supported fractional diffusion operators by truncated kernels.
- Research Organization:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Sandia National Lab. (SNL-CA), Livermore, CA (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE National Nuclear Security Administration (NNSA)
- Grant/Contract Number:
- AC04-94AL85000; NA0003525
- OSTI ID:
- 1765754
- Alternate ID(s):
- OSTI ID: 1809475
- Report Number(s):
- SAND-2020-5158J; 686140
- Journal Information:
- Computer Methods in Applied Mechanics and Engineering, Vol. 374; ISSN 0045-7825
- Publisher:
- ElsevierCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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