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The analysis of high-dimensional dynamical systems generally requires the integration of simulation data with experimental measurements. Experimental data often has substantial amounts of measurement noise that compromises the ability to…
With the rapid increase of valuable observational, experimental and simulating data for complex systems, great efforts are being devoted to discovering governing laws underlying the evolution of these systems. However, the existing…
This paper is devoted to filtering, smoothing, and prediction of polynomial processes that are partially observed. These problems are known to allow for an explicit solution in the simpler case of linear Gaussian state space models. The key…
Stochastic-gradient sampling methods are often used to perform Bayesian inference on neural networks. It has been observed that the methods in which notions of differential geometry are included tend to have better performances, with the…
In this paper we address the convergence of stochastic approximation when the functions to be minimized are not convex and nonsmooth. We show that the "mean-limit" approach to the convergence which leads, for smooth problems, to the ODE…
In applied sciences, we often deal with deterministic simulation models that are too slow for simulation-intensive tasks such as calibration or real-time control. In this paper, an emulator for a generic dynamic model, given by a system of…
We consider the inverse problem of reconstructing the posterior measure over the trajec- tories of a diffusion process from discrete time observations and continuous time constraints. We cast the problem in a Bayesian framework and derive…
This paper presents a probabilistic perspective on iterative methods for approximating the solution $\mathbf{x}_* \in \mathbb{R}^d$ of a nonsingular linear system $\mathbf{A} \mathbf{x}_* = \mathbf{b}$. In the approach a standard iterative…
Diffusion models for continuous state spaces based on Gaussian noising processes are now relatively well understood from both practical and theoretical perspectives. In contrast, results for diffusion models on discrete state spaces remain…
Stochastic differential equations (SDEs) provide a flexible framework for modeling temporal dynamics in partially observed systems. A central task is to calibrate such models from data, which requires inferring latent trajectories and…
The dynamic emulation of non-linear deterministic computer codes where the output is a time series, possibly multivariate, is examined. Such computer models simulate the evolution of some real-world phenomenon over time, for example models…
The augmented, iterated Kalman smoother is applied to system identification for inverse problems in evolutionary differential equations. In the augmented smoother, the unknown, time-dependent coefficients are included in the state vector,…
We analyze convergence rates of stochastic optimization procedures for non-smooth convex optimization problems. By combining randomized smoothing techniques with accelerated gradient methods, we obtain convergence rates of stochastic…
This paper considers the problem of steering the state distribution of a nonlinear stochastic system from an initial Gaussian to a terminal distribution with a specified mean and covariance, subject to probabilistic path constraints. An…
This paper is centered around the approximation of dynamical systems by means of Gaussian processes. To this end, trajectories of such systems must be collected to be used as training data. The measurements of these trajectories are…
In this paper, we consider a stochastic system described by a differential equation admitting a spatially varying random coefficient. The differential equation has been employed to model various static physics systems such as elastic…
We introduce a scalable approach to Gaussian process inference that combines spatio-temporal filtering with natural gradient variational inference, resulting in a non-conjugate GP method for multivariate data that scales linearly with…
We analyse and explain the increased generalisation performance of iterate averaging using a Gaussian process perturbation model between the true and batch risk surface on the high dimensional quadratic. We derive three phenomena…
We propose a stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs. Our approach is based on a bi-objective viewpoint of chance-constrained programs that seeks solutions on the…
A new algorithm is developed to tackle the issue of sampling non-Gaussian model parameter posterior probability distributions that arise from solutions to Bayesian inverse problems. The algorithm aims to mitigate some of the hurdles faced…