118 citations · 697 across the 32 of their papers we have counts for
33 papers
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…
Sampling, feasibility, and priors in Bayesian estimation
Alexandre J. Chorin, Fei Lu, Robert N. Miller +2
Importance sampling algorithms are discussed in detail, with an emphasis on implicit sampling, and applied to data assimilation via particle filters. Implicit sampling makes it pos…
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…
Path integral formulation of stochastic optimal control with generalized costs
Insoon Yang, Matthias Morzfeld, Claire J. Tomlin +1
Path integral control solves a class of stochastic optimal control problems with a Monte Carlo (MC) method for an associated Hamilton-Jacobi-Bellman (HJB) equation. The MC approach…
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…
Conditions for successful data assimilation
Alexandre J. Chorin, Matthias Morzfeld
We show, using idealized models, that numerical data assimilation can be successful only if an effective dimension of the problem is not excessive. This effective dimension depends…
Implicit particle methods and their connection with variational data assimilation
Ethan Atkins, Matthias Morzfeld, Alexandre J. Chorin
The implicit particle filter is a sequential Monte Carlo method for data assimilation that guides the particles to the high-probability regions via a sequence of steps that include…
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…
On the existence and scaling of structure functions in turbulence according to the data
Alex Arenas, Alexandre Chorin
We sample a velocity field that has an inertial spectrum and a skewness that matches experimental data. In particular, we compute a self-consistent correction to the Kolmogorov exp…
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…
Conditional Expectations and Renormalization
Alexandre J. Chorin
In optimal prediction methods one estimates the future behavior of underresolved systems by solving reduced systems of equations for expectations conditioned by partial data; renor…
A Model of a Turbulent Boundary Layer With a Non-Zero Pressure Gradient
G. I. Barenblatt, A. J. Chorin, V. M. Prostokishin
According to a model of the turbulent boundary layer proposed by the authors, in the absence of external turbulence the intermediate region between the viscous sublayer and the ext…
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…
A Note Concerning the Turbulent Boundary Layer Drag at Large Reynolds Numbers
G. I. Barenblatt, A. J. Chorin, V. M. Prostokishin
A correlation is obtained for the drag coefficient of the turbulent boundary layer as a function of the effective boundary layer Reynolds number that we previously int…
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…