Information theory and stochastics for multiscale nonlinear systems

By Andrew J. Majda, Rafail V. Abramov, Marcus J. Grote. 2005

226 citations recorded by the source corpus.

Subfields: Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/decf87f8fcb7d48dcb6c80c16f5b7e0e4c1022a5

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In Statistical and Nonlinear Physics

Citations in the corpus

Data-driven non-Markovian closure models (2014, methodology): “Numerical results for a conceptual stochastic climate model proposed in [45] are presented in Sec.”
Filtering Complex Turbulent Systems (2012, methodology): “In order to quantify and compare the different types of turbulent chaotic dynamics in the L-96 model as F is varied, it is convenient to rescale the system to have unit energy for statistical fluctuations around the constant mean statistical state, ū [96]; thus, the transformation uj = ū + E 1/2 p ũ”
Stochastic climate theory and modeling (2015, unknown): “[93] Majda, A.”
Challenges in Climate Science and Contemporary Applied Mathematics (2012, background): “The explicit form of the PDF, p eq (x), allows one to calculate explicit forms of the ideal response operator to perturbations in forcing, F , or the dissipation parameter , a, as well as explicit analytic expressions for the FDT linear response operator and various approximations [102].”
Data-driven forecasting of high-dimensional chaotic systems with long short-term memory networks (2018, methodology): “Following [35,56], we apply a shifting and scaling to standardize the Lorenz 96 states Xj.”
A review of numerical methods for nonlinear partial differential equations (2012, unknown): “Instead, there is a growing role for nonlinear stochastic PDEs [112, 146, 42] with a wide range of applications, from ﬁnancial models and data assimilation in atmospheric sciences to material sciences and biological models; see [118, 185, 116, 121, 154, 169, 166] and the references therein.”
Physics constrained nonlinear regression models for time series (2012, methodology): “The TBH model [19, 24, 25] is described by the following quadratically nonlinear equation for complex Fourier coefficients, uk, 1 ≤ |k| ≤ 50 with u−k = uk, duk dt = − ik 2 ∑”
An update on the nonequilibrium linear response (2012, background): “rmula (13) repeats Kubo’s original derivation while stopping short before specifying ρ. Also others have re-found the Agarwal formula, such as in Theorem 2, formulæ (2.22) and (2.23), of Chapter 2 in [12]. Weidlich gives a quantum version: his equation (2.17) replaces L1ρ → i ~ [ρ,H1] with the commu”
Decadal climate prediction: an update from the trenches (2014, methodology): “Some investigators have used relative entropy from information theory (Kleeman 2002; Majda et al. 2005; DelSole 2004) as a comprehensive measure of predictability, though this method works best with large ensembles or large numbers of hindcasts.”
Climate Response Using a Three-Dimensional Operator Based on the Fluctuation–Dissipation Theorem (2007, methodology): “Similar fluctuation–response relations can be obtained not just for the mean response but for any arbitrary system characteristic and for time-dependent forcing (Risken (1984)).”
Two Limits of Initial-Value Decadal Predictability in a CGCM (2010, background): “…to GHG changes are so weak at this range as to have no discernable effect on our results. c. Relative entropy As described by Kleeman (2002) and Majda et al. (2005), relative entropy is a means of comparing a distribution to a baseline distribution and thus can be employed in predictability…”
Polynomial nonlinear spatio‐temporal integro‐difference equation models (2011, background): “2011, 32 339–350 3 4 8 processes, polynomial interactions in spectral space are an important mechanism for energy transfer, and thus the formulation of polynomial models in this context is scientifically appealing (e.g. Majda et al. 2005, 2006, 2010).”