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The Ensemble Kalman Filter (EnKF) belongs to the class of iterative particle filtering methods and can be used for solving control--to--observable inverse problems. In this context, the EnKF is known as Ensemble Kalman Inversion (EKI). In…

Ensemble Kalman inversion is a parallelizable derivative-free method to solve inverse problems. The method uses an ensemble that follows the Kalman update formula iteratively to solve an optimization problem. The ensemble size is crucial to…

The fundamental computational issues in Bayesian inverse problems (BIP) governed by partial differential equations (PDEs) stem from the requirement of repeated forward model evaluations. A popular strategy to reduce such costs is to replace…

Equivariant imaging (EI) enables training signal reconstruction models without requiring ground truth data by leveraging signal symmetries. Deep equilibrium models (DEQs) are a powerful class of neural networks where the output is a fixed…

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…

In this study, an efficient stochastic gradient-free method, the ensemble neural networks (ENN), is developed. In the ENN, the optimization process relies on covariance matrices rather than derivatives. The covariance matrices are…

Variational Autoencoders (VAEs) are a powerful framework for learning latent representations of reduced dimensionality, while Neural ODEs excel in learning transient system dynamics. This work combines the strengths of both to generate fast…

When solving inverse problems, one increasingly popular approach is to use pre-trained diffusion models as plug-and-play priors. This framework can accommodate different forward models without re-training while preserving the generative…

We introduce a practical method for incorporating equality and inequality constraints in global optimization methods based on stochastic interacting particle systems, specifically consensus-based optimization (CBO) and ensemble Kalman…

Equivariant Imaging (EI) regularization has become the de-facto technique for unsupervised training of deep imaging networks, without any need of ground-truth data. Observing that the EI-based unsupervised training paradigm currently has…

This work proposes ensemble Kalman randomized maximum likelihood estimation, a new derivative-free method for performing randomized maximum likelihood estimation, which is a method that can be used to generate approximate samples from…

Many parameter estimation problems arising in applications are best cast in the framework of Bayesian inversion. This allows not only for an estimate of the parameters, but also for the quantification of uncertainties in the estimates.…

Numerical models of geothermal reservoirs typically depend on hundreds or thousands of unknown parameters, which must be estimated using sparse, noisy data. However, these models capture complex physical processes, which frequently results…

We propose an approach based on function evaluations and Bayesian inference to extract higher-order differential information of objective functions {from a given ensemble of particles}. Pointwise evaluation $\{V(x^i)\}_i$ of some potential…

Black-Box Optimization (BBO) methods can find optimal policies for systems that interact with complex environments with no analytical representation. As such, they are of interest in many Artificial Intelligence (AI) domains. Yet classical…

In recent years, uncertainty-aware full waveform inversion (FWI) has received increasing attention, with a growing emphasis on producing informative uncertainty estimates alongside inversion results. Bayesian inference methods--particularly…

This work presents a novel approach for the optimization of dynamic systems on finite-dimensional Lie groups. We rephrase dynamic systems as so-called neural ordinary differential equations (neural ODEs), and formulate the optimization…

In stochastic systems, informative approaches select key measurement or decision variables that maximize information gain to enhance the efficacy of model-related inferences. Neural Learning also embodies stochastic dynamics, but…

We consider the Ensemble Kalman Inversion which has been recently introduced as an efficient, gradient-free optimisation method to estimate unknown parameters in an inverse setting. In the case of large data sets, the Ensemble Kalman…

Inverse problems are common and important in many applications in computational physics but are inherently ill-posed with many possible model parameters resulting in satisfactory results in the observation space. When solving the inverse…