Physics constrained nonlinear regression models for time series

By Andrew J. Majda, John Harlim. 2012

153 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Control and Systems Engineering

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Citations in the corpus

Theory-Guided Data Science: A New Paradigm for Scientific Discovery from Data (2016, background): “driven PDEs can be found in a recent work in climate science [55], [56], where physically constrained time-series regression models were developed to incorporate memory”
Data-Driven Sparse Sensor Placement for Reconstruction: Demonstrating the Benefits of Exploiting Known Patterns (2017, methodology): “ Recently, compressed sensing, sparsity-promoting algorithms such as the lasso regression [33,34,35], and machine learning have been increasingly applied to characterize and control dynamical systems [36,37,38,39,40,31,41, 42,43,44,45,46,47]. These techniques have been effective in modeling high dim”
Inferring Biological Networks by Sparse Identification of Nonlinear Dynamics (2016, background): “Recent nonlinear regression techniques have produced nonlinear dynamic models that preserve physical constraints, such as conservation of energy [51].”
Chaos as an intermittently forced linear system (2016, background): “The motion of planets [76], weather and climate [63, 65, 66, 38, 83, 67], population dynamics [9, 94, 102], epidemiology [93], financial markets, earthquakes, solar flares, and turbulence [53, 51, 52, 95, 12], all provide compelling examples of chaos.”
Constrained sparse Galerkin regression (2016, methodology): “A notable exception is the physics-constrained multi-level quadratic regression used to identify models in climate and turbulence (Majda & Harlim 2012).”
Data-driven non-Markovian closure models (2014, methodology): “The work of [28, 29] proposed multi-level regression (MLR) models that did allow for quadratic interactions between the observed and some of the hidden variables and showed that these interactions — given quadratic energy invariants in the flow models to which they were applied — result in a stable,”
A Big Data Guide to Understanding Climate Change: The Case for Theory-Guided Data Science (2014, unknown): “Finally, within predictive models, it has been shown both theoretically 35 and in practice 36 that theory-agnostic models generalize poorly to unseen data despite being highly accurate on observed data.”
Stochastic climate theory and modeling (2015, unknown): “Recent studies use these physical constraints to successfully derive physically consistent stochastic climate models 57,97,126 .”