Normal forms for reduced stochastic climate models

By Andrew J. Majda, Christian L. E. Franzke, Daan Crommelin. 2009

153 citations recorded by the source corpus.

Subfields: Atmospheric Science, Global and Planetary Change

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atmospheric Science

In Global and Planetary Change

Citations in the corpus

Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations (2018, methodology): “identification in climate (Majda et al., 2009), nonlinear Laplacian spectral analysis (Giannakis and Majda, 2012), modeling emergent behavior (Roberts, 2014), Koopman analysis (Mezić, 2005; Budǐsić et al.”
Hidden physics models: Machine learning of nonlinear partial differential equations (2017, background): “The literature on data-driven discovery of dynamical systems [3] is vast and encompasses equation-free modeling [4], artificial neural networks [5], nonlinear regression [6], empirical dynamic modeling [7,8], modeling emergent behavior [9], automated inference of dynamics [10–12], normal form identi”
Physics constrained nonlinear regression models for time series (2012, methodology): “The approach developed here builds on earlier work for single level models without memory effects which uses physical analytic properties [16, 17, 18, 19] to constrain data driven methods [9, 20, 21, 22].”
FUNDAMENTAL LIMITATIONS OF AD HOC LINEAR AND QUADRATIC MULTI-LEVEL REGRESSION MODELS FOR PHYSICAL SYSTEMS (2012, unknown): “9) might create non-physical blow-up and instability of statistical solutions of the multi-level regression model in contrast to the correct physical behavior of the underlying system [8, 9, 21, 24].”
Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control (2021, methodology): “A wide range of data-driven model discovery methods exist, including equation-free modeling [1], normal form identiﬁcation [2–4], nonlinear Laplacian spectral analysis [5], Koop-man analysis [6, 7] and dynamic mode decomposition (DMD) [8–10], symbolic regression [11–15], sparse regression [16, 17],…”
Nonlinear Trends, Long-Range Dependence, and Climate Noise Properties of Surface Temperature (2012, background): “This suggests that either multivariate (von Storch and Zwiers 1999), higher-order autoregressive (von Storch and Zwiers 1999), or other models that combine shortand long-range dependence like ARFIMA(p, d, q) or nonlinear stochastic models (e.g., Majda et al. 2008, 2009) are needed.”
Sparse Identification of Nonlinear Dynamics with Control (SINDYc) (2016, methodology): “, 2014), and methods for uncertainty quantification and subspace analysis in turbulent flows and the climate (Majda and Harlim, 2007; Majda et al., 2009; Sapsis and Majda, 2013).”
Stochastic climate theory and modeling (2015, unknown): “Majda et al. 96 developed the nonlinear normal form of stochastic climate models and also physical constraints for parameter estimation.”
Challenges in Climate Science and Contemporary Applied Mathematics (2012, methodology): “The imperfect models in (4) range from comprehensive AOS climate models with billions of variables [21, 111, 113, 117], to lower dimensional statistical-stochastic models for suitable low-frequency teleconnections ([90, 94] and references therein) to purely data driven regression models with varying”
Low‐frequency nonlinearity and regime behavior in the Northern Hemisphere extratropical atmosphere (2017, background): “Systematically derived nonlinear dynamic-stochastic models contain the necessary damping in physically meaningful form as nonlinear damping [Majda et al., 1999, 2008, 2009; Franzke et al., 2005, 2015b; Franzke and Majda, 2006; Peavoy et al., 2015].”