The DOI matches its Crossref record; 36 of the 36 references it cites were found in a registry or an index.
Learning data-driven discretizations for partial differential equations
Open accessAbstract
The numerical solution of partial differential equations (PDEs) is challenging because of the need to resolve spatiotemporal features over wide length- and timescales. Often, it is computationally intractable to resolve the finest features in the solution. The only recourse is to use approximate coarse-grained representations, which aim to accurately represent long-wavelength dynamics while properly accounting for unresolved small-scale physics. Deriving such coarse-grained equations is notoriously difficult and often ad hoc. Here we introduce data-driven discretization, a method for learning optimized approximations to PDEs based on actual solutions to the known underlying equations. Our approach uses neural networks to estimate spatial derivatives, which are optimized end to end to best satisfy the equations on a low-resolution grid. The resulting numerical methods are remarkably accurate, allowing us to integrate in time a collection of nonlinear equations in 1 spatial dimension at resolutions 4× to 8× coarser than is possible with standard finite-difference methods.
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Discovering governing equations from data by sparse identification of nonlinear dynamical systems
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Machine learning–accelerated computational fluid dynamics
Kochkov, D., Smith, J. A., Alieva, A., Wang, Q., Brenner, M. P., & Hoyer, S. (2021) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2101784118 · Cited by 1,042
Self-citationData-driven discovery of coordinates and governing equations
Champion, K., Lusch, B., Kutz, J. N., & Brunton, S. L. (2019) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1906995116 · Cited by 909
WeatherBench: A Benchmark Data Set for Data‐Driven Weather Forecasting
Rasp, S., Dueben, P. D., Scher, S., Weyn, J. A., Mouatadid, S., & Thuerey, N. (2020) · Journal of Advances in Modeling Earth Systems · doi:10.1029/2020ms002203 · Cited by 663
Enforcing Analytic Constraints in Neural Networks Emulating Physical Systems
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Metadata
- Authors
- Bar-Sinai, Y., Hoyer, S., Hickey, J., & Brenner, M. P.
- Venue
- Proceedings of the National Academy of Sciences
- Published
- 2019-07-16
- Volume
- 116
- Issue
- 31
- Pages
- 15344-15349
- ISSN
- 0027-8424 (ISSN-L)
- 1091-6490
- OpenAlex
- W2891039272
- Cited by
- 543
- References
- 36
- FWCI
- 26.50
- Type
- journal article
- Language
- en
- Open access
- hybrid
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