Non-Markovian Optimal Prediction
Alexandre J. Chorin, Ole H. Hald, Raz Kupferman
Abstract
Optimal prediction methods compensate for a lack of resolution in the numerical solution of complex problems through the use of prior statistical information. We know from previous work that in the presence of strong underresolution a good approximation needs a non-Markovian "memory", determined by an equation for the "orthogonal", i.e., unresolved, dynamics. We present a simple approximation of the orthogonal dynamics, which involves an ansatz and a Monte-Carlo evaluation of autocorrelations. The analysis provides a new understanding of the fluctuation-dissipation formulas of statistical physics. An example is given.
Create a lesson
Related papers
Sensitivity Calculus and its Numerical Implementation for Multi-D Hyperbolic Balance Laws
Olivia Dreßen, Michael Herty, Adrian Kolb et al.
A Unified Framework for Wasserstein Convergence of ULMC Methods beyond Log-Concavity: Old and New
Wanjie Lyu, Xiaojie Wang, Bin Yang
Beyond PINNs: A Unified Gauss--Newton and Petrov--Galerkin Framework for Neural and Hybrid PDE Solvers
Nilo Schwencke, Roland Maier
Incremental Column Subset Selection via Conditional Determinantal Point Processes
Laura Grigori, Zhipeng Xue
A Hybrid High-Order Method for the Elasticity Problem with Linear Slip Interface
Erik Burman, Peiqi Huang
Adaptive Sparse-grid Discontinuous Galerkin Approximations the Bhatnagar--Gross--Krook Model
Stefan Schnake, Miroslav Stoyanov, Eirik Endeve et al.