Related papers: Inference of dynamic systems from noisy and sparse…

The use of Gaussian process models is typically limited to datasets with a few tens of thousands of observations due to their complexity and memory footprint. The two most commonly used methods to overcome this limitation are 1) the…

A key task in the field of modeling and analyzing nonlinear dynamical systems is the recovery of unknown governing equations from measurement data only. There is a wide range of application areas for this important instance of system…

In this paper we propose the first non-parametric Bayesian model using Gaussian Processes to make inference on Poisson Point Processes without resorting to gridding the domain or to introducing latent thinning points. Unlike competing…

Nonparametric Bayesian models are used routinely as flexible and powerful models of complex data. Many times, a statistician may have additional informative beliefs about data distribution of interest, e.g., its mean or subset components,…

Leveraging autonomous systems in safety-critical scenarios requires verifying their behaviors in the presence of uncertainties and black-box components that influence the system dynamics. In this work, we develop a framework for verifying…

An efficient technique is introduced for model inference of complex nonlinear dynamical systems driven by noise. The technique does not require extensive global optimization, provides optimal compensation for noise-induced errors and is…

Recently, a novel linear model predictive control algorithm based on a physics-informed Gaussian Process has been introduced, whose realizations strictly follow a system of underlying linear ordinary differential equations with constant…

This paper introduces an active learning framework for manifold Gaussian Process (GP) regression, combining manifold learning with strategic data selection to improve accuracy in high-dimensional spaces. Our method jointly optimizes a…

Gaussian processes are widely employed as versatile modelling and predictive tools in spatial statistics, functional data analysis, computer modelling and diverse applications of machine learning. They have been widely studied over…

Statistical regression models whose mean functions are represented by ordinary differential equations (ODEs) can be used to describe phenomenons dynamical in nature, which are abundant in areas such as biology, climatology and genetics. The…

This paper introduces a computationally efficient algorithm in system theory for solving inverse problems governed by linear partial differential equations (PDEs). We model solutions of linear PDEs using Gaussian processes with priors…

We propose practical deep Gaussian process models on Riemannian manifolds, similar in spirit to residual neural networks. With manifold-to-manifold hidden layers and an arbitrary last layer, they can model manifold- and scalar-valued…

We present a conditional diffusion model - ConDiSim, for simulation-based inference of complex systems with intractable likelihoods. ConDiSim leverages denoising diffusion probabilistic models to approximate posterior distributions,…

Ordinary differential equation models are used to describe dynamic processes across biology. To perform likelihood-based parameter inference on these models, it is necessary to specify a statistical process representing the contribution of…

Gaussian Processes (GPs) are Bayesian models that provide uncertainty estimates associated to the predictions made. They are also very flexible due to their non-parametric nature. Nevertheless, GPs suffer from poor scalability as the number…

We focus on variational inference in dynamical systems where the discrete time transition function (or evolution rule) is modelled by a Gaussian process. The dominant approach so far has been to use a factorised posterior distribution,…

Mathematical models implemented on a computer have become the driving force behind the acceleration of the cycle of scientific processes. This is because computer models are typically much faster and economical to run than physical…

We present a data-driven nonintrusive model order reduction method for dynamical systems with moving boundaries. The proposed method draws on the proper orthogonal decomposition, Gaussian process regression, and moving least squares…

Off-the-shelf Gaussian Process (GP) covariance functions encode smoothness assumptions on the structure of the function to be modeled. To model complex and non-differentiable functions, these smoothness assumptions are often too…

This work presents a data-driven method for learning low-dimensional time-dependent physics-based surrogate models whose predictions are endowed with uncertainty estimates. We use the operator inference approach to model reduction that…