118 citations · 697 across the 32 of their papers we have counts for
23 papers · 1 filter
Comparison of continuous and discrete-time data-based modeling for hypoelliptic systems
Fei Lu, Kevin K. Lin, Alexandre J. Chorin
We compare two approaches to the predictive modeling of dynamical systems from partial observations at discrete times. The first is continuous in time, where one uses data to infer…
Data-based stochastic model reduction for the Kuramoto--Sivashinsky equation
Fei Lu, Kevin Lin, Alexandre J. Chorin
The problem of constructing data-based, predictive, reduced models for the Kuramoto-Sivashinsky equation is considered, under circumstances where one has observation data only for…
A discrete approach to stochastic parametrization and dimensional reduction in nonlinear dynamics
Alexandre J. Chorin, Fei Lu
Many physical systems are described by nonlinear differential equations that are too complicated to solve in full. A natural way to proceed is to divide the variables into those th…
Limitations of polynomial chaos expansions in the Bayesian solution of inverse problems
Fei Lu, Matthias Morzfeld, Xuemin Tu +1
Polynomial chaos expansions are used to reduce the computational cost in the Bayesian solutions of inverse problems by creating a surrogate posterior that can be evaluated inexpens…
Parameter estimation by implicit sampling
Matthias Morzfeld, Xuemin Tu, Jon Wilkening +1
Implicit sampling is a weighted sampling method that is used in data assimilation, where one sequentially updates estimates of the state of a stochastic model based on a stream of…
Estimating the uncertainty in underresolved nonlinear dynamics
Alexandre J. Chorin, Ole H. Hald
The Mori-Zwanzig formalism of statistical mechanics is used to estimate the uncertainty caused by underresolution in the solution of a nonlinear dynamical system. A general approac…
Implicit particle filtering for models with partial noise, and an application to geomagnetic data assimilation
Matthias Morzfeld, Alexandre J. Chorin
Implicit particle filtering is a sequential Monte Carlo method for data assim- ilation, designed to keep the number of particles manageable by focussing attention on regions of lar…
A random map implementation of implicit filters
Matthias Morzfeld, Xuemin Tu, Ethan Atkins +1
Implicit particle filters for data assimilation generate high-probability samples by representing each particle location as a separate function of a common reference variable. This…
Implicit particle filters for data assimilation
Alexandre J. Chorin, Matthias Morzfeld, Xuemin Tu
Implicit particle filters for data assimilation update the particles by first choosing probabilities and then looking for particle locations that assume them, guiding the particles…
Interpolation and Iteration for Nonlinear Filters
Alexandre J. Chorin, Xuemin Tu
We present a general form of the iteration and interpolation process used in implicit particle filters. Implicit filters are based on a pseudo-Gaussian representation of posterior…
Non-Bayesian particle filters
Alexandre J. Chorin, Xuemin Tu
Particle filters for data assimilation in nonlinear problems use "particles" (replicas of the underlying system) to generate a sequence of probability density functions (pdfs) thro…
Monte Carlo without Chains
Alexandre Chorin
A sampling method for spin systems is presented. The spin lattice is written as the union of a nested sequence of sublattices, all but the last with conditionally independent spins…
Numerical scaling analysis of the small-scale structure in turbulence
Panagiotis Stinis, Alexandre J. Chorin
We show how to use numerical methods within the framework of successive scaling to analyse the microstructure of turbulence, in particular to find inertial range exponents and stru…
Problem reduction, renormalization, and memory
Alexandre J. Chorin, Panagiotis Stinis
Methods for the reduction of the complexity of computational problems are presented, as well as their connections to renormalization, scaling, and irreversible statistical mechanic…
Non-Markovian Optimal Prediction
Alexandre J. Chorin, Ole H. Hald, Raz Kupferman
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…
Stochastic Optimal Prediction with Application to Averaged Euler Equations
John Bell, Alexandre J. Chorin, William Crutchfield
Optimal prediction (OP) methods compensate for a lack of resolution in the numerical solution of complex problems through the use of an invariant measure as a prior measure in the…
The Characteristic Length Scale of the Intermediate Structure in Zero-Pressure-Gradient Boundary Layer Flow
G. I. Barenblatt, A. J. Chorin, V. M. Prostokishin
In a turbulent boundary layer over a smooth flat plate with zero pressure gradient, the intermediate structure between the viscous sublayer and the free stream consists of two laye…
Optimal Prediction for Hamiltonian partial differential equations
A. J. Chorin, R. Kupferman, D. Levy
Optimal prediction methods compensate for a lack of resolution in the numerical solution of time-dependent differential equations through the use of prior statistical information.…
The Kolmogorov-Obukhov Exponent in the Inertial Range of Turbulence: A Reexamination of Experimental Data
G. I. Barenblatt, A. J. Chorin, V. M. Prostokishin
In recent papers Benzi et al. presented experimental data and an analysis to the effect that the well-known "2/3" Kolmogorov-Obukhov exponent in the inertial range of local structu…
The influence of the flow of the reacting gas on the conditions for a Thermal Explosion
G. I. Barenblatt, A. J. Chorin, A. Kast
The classical problem of thermal explosion is modified so that the chemically active gas is not at rest but is flowing in a long cylindrical pipe. Up to a certain section the heat-…
Prediction of large-scale dynamics using unresolved computations
A. J. Chorin, A. Kast, R. Kupferman
We present a theoretical framework and numerical methods for predicting the large-scale properties of solutions of partial differential equations that are too complex to be properl…
A new formulation of the near-equilibrium theory of turbulence
G. I. Barenblatt, A. J. Chorin
We present a status report on a discrete approach to the the near-equilibrium statistical theory of three-dimensional turbulence, which generalizes earlier work by no longer requir…
Self-Similar Intermediate Structures in Turbulent Boundary Layers At Large Reynolds Numbers
Grigory I. Barenblatt, Alexandre J. Chorin, V. M. Prostokishin
Processing the data from a large variety of zero-pressure-gradient boundary layer flows shows that the Reynolds-number-dependent scaling law, which the present authors obtained ear…