Optimal prediction with memory

By Alexandre J. Chorin, Ole H. Hald, Raz Kupferman. 2002

279 citations recorded by the source corpus.

Subfields: Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/9c5d9e539e10d5afe6faa179a63ad9ddf8e26826

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In Statistical and Nonlinear Physics

Citations in the corpus

Data-driven non-Markovian closure models (2014, methodology): “Leading up to this task, let us first note that, since L and Ut commute, LUt = UtL [42], we can rewrite (4.7) as ∂ ∂t Utv = UtLv; this, in turn, can be rewritten as: (4.15) ∂ ∂t Utv = UtE[Lv|v] + Ut(Lv − E[Lv|v]).”
Mathematical and physical ideas for climate science (2013, methodology): “There are the short and long memory approximations made in the method of optimal prediction (Bernstein, 2007; Chorin and Stinis, 2006; Chorin and Hald , 2013; Chorin et al., 1998, 2000, 2002, 2006; Defrasne, 2004; Hald and Kupferman, 2001; Park et al., 2007).”
The physics of climate variability and climate change (2019, methodology): “s. In the remainder of this subsection, we give two examples of this success and further references to many more. Alternative approaches to ecient solutions of the GLE can be found, for instance, in Chorin et al. (2002). d. EMR applications. We choose here an EMR model to simulate Northern Hemispher”
Heterogeneous Multiscale Methods: A Review (2007, result): “applied to this problem gives the same result [41, 42].”
On closures for reduced order models—A spectrum of first-principle to machine-learned avenues (2021, unknown): “The estimation of the closure term as a function of the time history of the resolved scales has roots in the Mori–Zwanzig formalism, 325,376 and the memory embedding of LSTM implementation for closure modeling is supported by the Takens embedding theorem.”
Constructive methods of invariant manifolds for kinetic problems (2003, unknown): “[217].”
Nonintrusive and Structure Preserving Multiscale Integration of Stiff ODEs, SDEs, and Hamiltonian Systems with Hidden Slow Dynamics via Flow Averaging (2009, methodology): “Another idea is to treat fast variables by conditioning; here, we refer the reader to optimal prediction [28, 27, 29] that has also been used for model reduction.”
Stochastic climate theory and modeling (2015, unknown): “These include multi-159 level regression 70,74 , ﬁtting the parameters via the Fokker-Planck equation 3,146 , stochastic averaging 23,103 , optimal prediction 18,154 or Markov Chains 21 .”
Invariant Manifolds for Physical and Chemical Kinetics (2005, background): “The authors claim [282] that result of the computations is close to the best possible estimate that can be obtained given the partial data.”