Related papers: Inference for Delay Differential Equations Using M…
In this work, a Gaussian process regression(GPR) model incorporated with given physical information in partial differential equations(PDEs) is developed: physics-assisted Gaussian processes(PAGP). The targets of this model can be divided…
We present a method for time series analysis of both, scalar and nonscalar time-delay systems. If the dynamics of the system investigated is governed by a time-delay induced instability, the method allows to determine the delay time. In a…
Recent advances in learning techniques have enabled the modelling of dynamical systems for scientific and engineering applications directly from data. However, in many contexts explicit data collection is expensive and learning algorithms…
This work is concerned with the use of Gaussian surrogate models for Bayesian inverse problems associated with linear partial differential equations. A particular focus is on the regime where only a small amount of training data is…
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…
The application of Stochastic Differential Equations (SDEs) to the analysis of temporal data has attracted increasing attention, due to their ability to describe complex dynamics with physically interpretable equations. In this paper, we…
We develop a novel multi-layer predictor-feedback to achieve exact compensation of state-dependent input delay of general nonlinear integro-differential equations. The system of interest is an unconventional mixed Partial Differential…
We present a new approach for constructing a data-driven surrogate model and using it for Bayesian parameter estimation in partial differential equation (PDE) models. We first use parameter observations and Gaussian Process regression to…
Physical phenomena are observed in many fields (sciences and engineering) and are often studied by time-consuming computer codes. These codes are analyzed with statistical models, often called emulators. In many situations, the physical…
In many areas of science and engineering, discovering the governing differential equations from the noisy experimental data is an essential challenge. It is also a critical step in understanding the physical phenomena and prediction of the…
Large-scale Gaussian process inference has long faced practical challenges due to time and space complexity that is superlinear in dataset size. While sparse variational Gaussian process models are capable of learning from large-scale data,…
Gaussian processes are a powerful framework for uncertainty-aware function approximation and sequential decision-making. Unfortunately, their classical formulation does not scale gracefully to large amounts of data and modern hardware for…
Computer models are used as a way to explore complex physical systems. Stationary Gaussian process emulators, with their accompanying uncertainty quantification, are popular surrogates for computer models. However, many computer models are…
Deep Gaussian Processes learn probabilistic data representations for supervised learning by cascading multiple Gaussian Processes. While this model family promises flexible predictive distributions, exact inference is not tractable.…
Effectively modeling phenomena present in highly nonlinear dynamical systems whilst also accurately quantifying uncertainty is a challenging task, which often requires problem-specific techniques. We present a novel, domain-agnostic…
Time-delay dynamical systems inherently embody infinite-dimensional dynamics, thereby amplifying their complexity. This aspect is especially notable in nonlinear dynamical systems, which frequently defy analytical solutions and necessitate…
Besides parametric uncertainties and disturbances, the unmodeled dynamics and time delay at the input are often present in practical systems, which cannot be ignored in some cases. This paper aims to solve output feedback tracking control…
In this work we develop a Bayesian setting to infer unknown parameters in initial-boundary value problems related to linear parabolic partial differential equations. We realistically assume that the boundary data are noisy, for a given…
We consider the statistical linear inverse problem of making inference on an unknown source function in an elliptic partial differential equation from noisy observations of its solution. We employ nonparametric Bayesian procedures based on…
Pseudospectral approximation provides a means to approximate the dynamics of delay differential equations (DDE) by ordinary differential equations (ODE). This article develops a computer-aided algorithm to determine the distance between the…