Related papers: Bayesian learning with Gaussian processes for low-…

Two non-intrusive uncertainty propagation approaches are proposed for the performance analysis of engineering systems described by expensive-to-evaluate deterministic computer models with parameters defined as interval variables. These…

Reduced-order modeling has a long tradition in computational fluid dynamics. The ever-increasing significance of data for the synthesis of low-order models is well reflected in the recent successes of data-driven approaches such as Dynamic…

Supervised machine learning describes the practice of fitting a parameterized model to labeled input-output data. Supervised machine learning methods have demonstrated promise in learning efficient surrogate models that can (partially)…

This paper considers a stochastic control framework, in which the residual model uncertainty of the dynamical system is learned using a Gaussian Process (GP). In the proposed formulation, the residual model uncertainty consists of a…

Biological systems commonly exhibit complex spatiotemporal patterns whose underlying generative mechanisms pose a significant analytical challenge. Traditional approaches to spatiodynamic inference rely on dimensionality reduction through…

This study proposes a new discrete neural operator for surrogate modeling of transient Darcy flow fields in heterogeneous porous media with random parameters. The new method integrates temporal encoding, operator learning and UNet to…

Non-intrusive reduced-order models (ROMs) have recently generated considerable interest for constructing computationally efficient counterparts of nonlinear dynamical systems emerging from various domain sciences. They provide a…

The ability to predict future states is crucial to informed decision-making while interacting with dynamic environments. With cameras providing a prevalent and information-rich sensing modality, the problem of predicting future states from…

Bayesian inverse problems use observed data to update a prior probability distribution for an unknown state or parameter of a scientific system to a posterior distribution conditioned on the data. In many applications, the unknown parameter…

This paper deals with surrogate modelling of a computer code output in a hierarchical multi-fidelity context, i.e., when the output can be evaluated at different levels of accuracy and computational cost. Using observations of the output at…

This paper presents a novel methodology for tractably solving optimal control and offline reinforcement learning problems for high-dimensional systems. This work is motivated by the ongoing challenges of safety, computation, and optimality…

We study time uncertainty-aware modeling of continuous-time dynamics of interacting objects. We introduce a new model that decomposes independent dynamics of single objects accurately from their interactions. By employing latent Gaussian…

Data assimilation (DA) has increasingly emerged as a critical tool for state estimation across a wide range of applications. It is significantly challenging when the governing equations of the underlying dynamics are unknown. To this end,…

A variational inference-based framework for training a multi-output Gaussian process latent variable model, specifically tailored to the tails-up spatio-temporal stream network, is developed. Training, given a censored observational data…

Safety-critical technical systems operating in unknown environments require the ability to quickly adapt their behavior, which can be achieved in control by inferring a model online from the data stream generated during operation. Gaussian…

Dynamic systems described by differential equations often involve feedback among system components. When there are time delays for components to sense and respond to feedback, delay differential equation (DDE) models are commonly used. This…

Non-Bayesian social learning theory provides a framework for distributed inference of a group of agents interacting over a social network by sequentially communicating and updating beliefs about the unknown state of the world through…

This paper presents an approach for constrained Gaussian Process (GP) regression where we assume that a set of linear transformations of the process are bounded. It is motivated by machine learning applications for high-consequence…

The identification of the constrained dynamics of mechanical systems is often challenging. Learning methods promise to ease an analytical analysis, but require considerable amounts of data for training. We propose to combine insights from…

While there is currently a lot of enthusiasm about "big data", useful data is usually "small" and expensive to acquire. In this paper, we present a new paradigm of learning partial differential equations from {\em small} data. In…