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Robust learning from noisy, incomplete, high-dimensional experimental data via physically constrained symbolic regression

https://doi.org/10.1038/s41467-021-23479-0

Reinbold, Patrick_A_K ; Kageorge, Logan_M ; Schatz, Michael_F ; Grigoriev, Roman_O ( May 2021 , Nature Communications)

Abstract
Machine learning offers an intriguing alternative to first-principle analysis for discovering new physics from experimental data. However, to date, purely data-driven methods have only proven successful in uncovering physical laws describing simple, low-dimensional systems with low levels of noise. Here we demonstrate that combining a data-driven methodology with some general physical principles enables discovery of a quantitatively accurate model of a non-equilibrium spatially extended system from high-dimensional data that is both noisy and incomplete. We illustrate this using an experimental weakly turbulent fluid flow where only the velocity field is accessible. We also show that this hybrid approach allows reconstruction of the inaccessible variables – the pressure and forcing field driving the flow.

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Capturing Turbulent Dynamics and Statistics in Experiments with Unstable Periodic Orbits

https://doi.org/10.1103/PhysRevLett.125.064501

Suri, Balachandra ; Kageorge, Logan ; Grigoriev, Roman O. ; Schatz, Michael F. ( August 2020 , Physical Review Letters)

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Using noisy or incomplete data to discover models of spatiotemporal dynamics

https://doi.org/10.1103/PhysRevE.101.010203

Reinbold, Patrick A. ; Gurevich, Daniel R. ; Grigoriev, Roman O. ( January 2020 , Physical Review E)

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Robust and optimal sparse regression for nonlinear PDE models

https://doi.org/10.1063/1.5120861

Gurevich, Daniel R. ; Reinbold, Patrick A. K. ; Grigoriev, Roman O. ( October 2019 , Chaos: An Interdisciplinary Journal of Nonlinear Science)
Data-driven discovery of partial differential equation models with latent variables

https://doi.org/10.1103/PhysRevE.100.022219

Reinbold, Patrick A. ; Grigoriev, Roman O. ( August 2019 , Physical Review E)

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Heteroclinic and homoclinic connections in a Kolmogorov-like flow

https://doi.org/10.1103/PhysRevE.100.013112

Suri, Balachandra ; Pallantla, Ravi Kumar ; Schatz, Michael F. ; Grigoriev, Roman O. ( July 2019 , Physical Review E)
Unstable equilibria and invariant manifolds in quasi-two-dimensional Kolmogorov-like flow

https://doi.org/10.1103/PhysRevE.98.023105

Suri, Balachandra ; Tithof, Jeffrey ; Grigoriev, Roman O. ; Schatz, Michael F. ( August 2018 , Physical Review E)