Related papers: Learning Koopman eigenfunctions of stochastic diff…
In this paper, we introduce a new algorithm for rare event estimation based on adaptive importance sampling. We consider a smoothed version of the optimal importance sampling density, which is approximated by an ensemble of interacting…
Koopman operators and transfer operators represent nonlinear dynamics in state space through its induced action on linear spaces of observables and measures, respectively. This framework enables the use of linear operator theory for…
Stochastic optimal control, which has the goal of driving the behavior of noisy systems, is broadly applicable in science, engineering and artificial intelligence. Our work introduces Stochastic Optimal Control Matching (SOCM), a novel…
The Koopman operator provides an infinite-dimensional linear description of nonlinear dynamical systems that can be leveraged in the context of stability analysis. In particular, Lyapunov functions can be obtained in a systematic way via…
We study stochastic optimal control problems for (possibly degenerate) McKean-Vlasov controlled diffusions and obtain discrete-time as well as finite interacting particle approximations. (i) Under mild assumptions, we first prove the…
We consider systems of slow--fast diffusions with small noise in the slow component. We construct provably logarithmic asymptotically optimal importance schemes for the estimation of rare events based on the moderate deviations principle.…
Importance Sampling (IS) is a widely used variance reduction technique for enhancing the efficiency of Monte Carlo methods, particularly in rare-event simulation and related applications. Despite its effectiveness, the performance of IS is…
\emph{Koopman Regularization} is a constrained optimization-based method to learn the governing equations from sparse and corrupted samples of the vector field. \emph{Koopman Regularization} extracts a functionally independent set of…
In this paper, we develop an efficient numerical solver for unsteady diffusion-type partial differential equations with random coefficients. A major computational challenge in such problems lies in repeatedly handling large-scale linear…
This work collects some methodological insights for numerical solution of a "minimum-dispersion" control problem for nonlinear stochastic differential equations, a particular relaxation of the covariance steering task. The main ingredient…
We present a method for the approximate propagation of mean and covariance of a probability distribution through ordinary differential equations (ODE) with discontinous right-hand side. For piecewise affine systems, a normalization of the…
The solution to a stochastic optimal control problem can be determined by computing the value function from a discretization of the associated Hamilton-Jacobi-Bellman equation. Alternatively, the problem can be reformulated in terms of a…
We rigorously derive novel error bounds for extended dynamic mode decomposition (EDMD) to approximate the Koopman operator for discrete- and continuous time (stochastic) systems; both for i.i.d. and ergodic sampling under non-restrictive…
Diffusion models have achieved impressive success in high-fidelity image generation but suffer from slow sampling due to their inherently iterative denoising process. While recent one-step methods accelerate inference by learning direct…
We investigate in this paper an alternative method to simulation based recursive importance sampling procedure to estimate the optimal change of measure for Monte Carlo simulations. We propose an algorithm which combines (vector and…
We consider the problem of learning time-varying functions in a distributed fashion, where agents collect local information to collaboratively achieve a shared estimate. This task is particularly relevant in control applications, whenever…
The aim of this paper is to introduce a new Monte Carlo method based on importance sampling techniques for the simulation of stochastic differential equations. The main idea is to combine random walk on squares or rectangles methods with…
Optimal sensor placement is an important yet unsolved problem in control theory. In biological organisms, genetic activity is often highly nonlinear, making it difficult to design libraries of promoters to act as reporters of the cell…
The Koopman operator provides a principled framework for analyzing nonlinear dynamical systems through linear operator theory. Recent advances in dynamic mode decomposition (DMD) have shown that trajectory data can be used to identify…
Kalman filtering is a cornerstone of estimation theory, yet learning the optimal filter under unknown and potentially singular noise covariances remains a fundamental challenge. In this paper, we revisit this problem through the lens of…