Related papers: Ensemble Kalman Diffusion Guidance: A Derivative-f…

Inverse problems are ubiquitous because they formalize the integration of data with mathematical models. In many scientific applications the forward model is expensive to evaluate, and adjoint computations are difficult to employ; in this…

The standard probabilistic perspective on machine learning gives rise to empirical risk-minimization tasks that are frequently solved by stochastic gradient descent (SGD) and variants thereof. We present a formulation of these tasks as…

Solving inverse problems without the use of derivatives or adjoints of the forward model is highly desirable in many applications arising in science and engineering. In this paper, we propose a new version of such a methodology, a framework…

In inverse problems, the goal is to estimate unknown model parameters from noisy observational data. Traditionally, inverse problems are solved under the assumption of a fixed forward operator describing the observation model. In this…

The Ensemble Kalman filter (EnKF) was introduced by Evensen in 1994 [10] as a novel method for data assimilation: state estimation for noisily observed time-dependent problems. Since that time it has had enormous impact in many application…

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,…

In this work, we present a new derivative-free optimization method and investigate its use for training neural networks. Our method is motivated by the Ensemble Kalman Filter (EnKF), which has been used successfully for solving optimization…

The ensemble Kalman inversion (EKI) is a particle based method which has been introduced as the application of the ensemble Kalman filter to inverse problems. In practice it has been widely used as derivative-free optimization method in…

Solving inverse problems without any training involves using a pretrained generative model and making appropriate modifications to the generation process to avoid finetuning of the generative model. While recent methods have explored the…

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…

Diffusion models have become increasingly popular for generative modeling due to their ability to generate high-quality samples. This has unlocked exciting new possibilities for solving inverse problems, especially in image restoration and…

Derivative-free Bayesian inversion is an important task in many science and engineering applications, particularly when computing the forward model derivative is computationally and practically challenging. In this paper, we introduce…

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…

Diffusion models have emerged as the new state-of-the-art generative model with high quality samples, with intriguing properties such as mode coverage and high flexibility. They have also been shown to be effective inverse problem solvers,…

We study the use of novel techniques arising in machine learning for inverse problems. Our approach replaces the complex forward model by a neural network, which is trained simultaneously in a one-shot sense when estimating the unknown…

The ensemble Kalman filter (EnKF) is a widely used methodology for state estimation in partial, noisily observed dynamical systems, and for parameter estimation in inverse problems. Despite its widespread use in the geophysical sciences,…

The Ensemble Kalman Inversion (EKI) method is widely used for solving inverse problems, leveraging ensemble-based techniques to iteratively refine parameter estimates. Despite its versatility, the accuracy of EKI is constrained by the…

This work presents new results and understanding of the Ensemble Kalman filter (EnKF) for inverse problems. In particular, using a Lagrangian dual perspective we show that EnKF can be derived from the sample average approximation (SAA) of…

Inverse design problems are common in engineering and materials science. The forward direction, i.e., computing output quantities from design parameters, typically requires running a numerical simulation, such as a FEM, as an intermediate…

Among the class of nonlinear particle filtering methods, the Ensemble Kalman Filter (EnKF) has gained recent attention for its use in solving inverse problems. We review the original method and discuss recent developments in particular in…