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Standard maximum likelihood or Bayesian approaches to parameter estimation for stochastic differential equations are not robust to perturbations in the continuous-in-time data. In this paper, we give a rather elementary explanation of this…
We consider the problem of transforming samples from one continuous source distribution into samples from another target distribution. We demonstrate with optimal transport theory that when the source distribution can be easily sampled from…
We study optimal stochastic control problem for non-Markovian stochastic differential equations (SDEs) where the drift, diffusion coefficients, and gain functionals are path-dependent, and importantly we do not make any ellipticity…
We introduce the Gaussian transform (GT), an optimal transport inspired iterative method for denoising and enhancing latent structures in datasets. Under the hood, GT generates a new distance function (GT distance) on a given dataset by…
In inverse problems, the parameters of a model are estimated based on observations of the model response. The Bayesian approach is powerful for solving such problems; one formulates a prior distribution for the parameter state that is…
Full-waveform inversion (FWI) is today a standard process for the inverse problem of seismic imaging. PDE-constrained optimization is used to determine unknown parameters in a wave equation that represent geophysical properties. The…
We consider stochastic optimal control of linear dynamical systems with additive non-Gaussian disturbance. We propose a novel, sampling-free approach, based on Fourier transformations and convex optimization, to cast the stochastic optimal…
In this article we study a variational problem providing a way to extend for all times minimizing geodesics connecting two given probability measures, in the Wasserstein space. This is simply obtained by allowing for negative coefficients…
Ensemble Kalman Inversion (EKI) has been a very popular algorithm used in Bayesian inverse problems. It samples particles from a prior distribution, and introduces a motion to move the particles around in pseudo-time. As the pseudo-time…
In this work, we explore the recent advances in equivariant filtering for inertial navigation systems to improve state estimation for uncrewed aerial vehicles (UAVs). Traditional state-of-the-art estimation methods, e.g., the multiplicative…
Optimal transport has gained significant attention in recent years due to its effectiveness in deep learning and computer vision. Its descendant metric, the Wasserstein distance, has been particularly successful in measuring distribution…
Replacing positivity constraints by an entropy barrier is popular to approximate solutions of linear programs. In the special case of the optimal transport problem, this technique dates back to the early work of Schr\"odinger. This approach…
In indirect measurements, the measurand is determined by solving an inverse problem which requires a model of the measurement process. Such models are often approximations and introduce systematic errors leading to a bias of the posterior…
Particle-based variational inference offers a flexible way of approximating complex posterior distributions with a set of particles. In this paper we introduce a new particle-based variational inference method based on the theory of…
We present an embedding of stochastic optimal control problems, of the so called path integral form, into reproducing kernel Hilbert spaces. Using consistent, sample based estimates of the embedding leads to a model free, non-parametric…
This work deals with the asymptotic distribution of both potentials and couplings of entropic regularized optimal transport for compactly supported probabilities in $\R^d$. We first provide the central limit theorem of the Sinkhorn…
This paper proposes new methodology for sequential state and parameter estimation within the ensemble Kalman filter. The method is fully Bayesian and propagates the joint posterior density of states and parameters over time. In order to…
The Optimal Transport (OT) problem with squared Euclidean cost consists in finding a coupling between two input measures that maximizes correlation. Consequently, the optimal coupling is often singular with respect to the Lebesgue measure.…
We present an optimal transport approach for mesh adaptivity and shock capturing of compressible flows. Shock capturing is based on a viscosity regularization of the governing equations by introducing an artificial viscosity field as…
Bayesian linear inverse problems aim to recover an unknown signal from noisy observations, incorporating prior knowledge. This paper analyses a data-dependent method to choose the scale parameter of a Gaussian prior. The method we study…