Related papers: Interacting Langevin Diffusions: Gradient Structur…
Langevin dynamics has found a large number of applications in sampling, optimization and estimation. Preconditioning the gradient in the dynamics with the covariance - an idea that originated in literature related to solving estimation and…
The unscented Kalman inversion (UKI) method presented in [1] is a general derivative-free approach for the inverse problem. UKI is particularly suitable for inverse problems where the forward model is given as a black box and may not be…
The Bayesian approach to inverse problems is widely used in practice to infer unknown parameters from noisy observations. In this framework, the ensemble Kalman inversion has been successfully applied for the quantification of uncertainties…
We consider an infinite lattice system of interacting spins living on a smooth compact manifold, with short- but not necessarily finite-range pairwise interactions. We construct the gradient flow of the infinite-volume free energy on the…
We propose a novel method for sampling from unnormalized Boltzmann densities based on a probability flow ordinary differential equation (ODE) derived from linear stochastic interpolants. The key innovation of our approach is the use of a…
We investigate the application of ensemble transform approaches to Bayesian inference of logistic regression problems. Our approach relies on appropriate extensions of the popular ensemble Kalman filter and the feedback particle filter to…
Many data-science problems can be formulated as an inverse problem, where the parameters are estimated by minimizing a proper loss function. When complicated black-box models are involved, derivative-free optimization tools are often…
Ensemble Kalman Inversion (EKI) methods are a family of iterative methods for solving weighted least-squares problems, especially those arising in scientific and engineering inverse problems in which unknown parameters or states are…
Vision-Language Latent Diffusion Models (LDMs) (Rombach et al., 2022) provide powerful generative priors for inverse problems. However, existing LDM-based inverse solvers typically require a large number of neural function evaluations…
Biomolecular systems are often modeled with partially known nonlinear stochastic dynamics, making state and parameter estimation a central challenge. While Kalman filtering techniques are widely used in this setting, their performance…
Bayesian inference in complex generative models is often obstructed by the absence of tractable likelihoods and the infeasibility of computing gradients of high-dimensional simulators. Existing likelihood-free methods for generalized…
We consider Bayesian inference for large scale inverse problems, where computational challenges arise from the need for repeated evaluations of an expensive forward model. This renders most Markov chain Monte Carlo approaches infeasible,…
This paper presents a computationally fast algorithm for estimating, both, the system and observation noise covariances of nonlinear dynamics, that can be used in an ensemble Kalman filtering framework. The new method is a modification of…
The ensemble Kalman inversion is widely used in practice to estimate unknown parameters from noisy measurement data. Its low computational costs, straightforward implementation, and non-intrusive nature makes the method appealing in various…
Ensemble Kalman Sampler (EKS) is a method to find approximately $i.i.d.$ samples from a target distribution. As of today, why the algorithm works and how it converges is mostly unknown. The continuous version of the algorithm is a set of…
Recent developments in generative modeling have utilized score-based methods coupled with stochastic differential equations to sample from complex probability distributions. However, these and other performant sampling methods generally…
Drawing from the theory of stochastic differential equations, we introduce a novel sampling method for known distributions and a new algorithm for diffusion generative models with unknown distributions. Our approach is inspired by the…
This paper studies the problem of distributed state estimation (DSE) over sensor networks on matrix Lie groups, which is crucial for applications where system states evolve on Lie groups rather than vector spaces. We propose a…
A new Langevin equation with a field-dependent kernel is proposed to deal with bottomless systems within the framework of the stochastic quantization of Parisi and Wu. The corresponding Fokker-Planck equation is shown to be a diffusion-type…
The interaction between the foundation structures and the soil has been developed for many engineering applications. For the determination of the stress in foundation structure it is needed to determine the influence of the stiffness of…