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Stochastic mathematical models are essential tools for understanding and predicting complex phenomena. The purpose of this work is to study the exit times of a stochastic dynamical system-specifically, the mean exit time and the…
The recently developed generalized Fourier-Galerkin method is complemented by a numerical continuation with respect to the kinetic energy, which extends the framework to the investigation of modal interactions resulting in folds of the…
An old problem in multivariate statistics is that linear Gaussian models are often unidentifiable, i.e. some parameters cannot be uniquely estimated. In factor (component) analysis, an orthogonal rotation of the factors is unidentifiable,…
This paper addresses the consensus of a class of uncertain nonlinear fractional-order multi-agent systems (FOMAS). First a fractional non-fragile dynamic output feedback controller is put forward via the output measurements of neighboring…
This paper proposes an integration of surrogate modeling and topology to significantly reduce the amount of data required to describe the underlying global dynamics of robot controllers, including closed-box ones. A Gaussian Process (GP),…
The probabilistic characterization of non-Markovian responses to nonlinear dynamical systems under colored excitation is an important issue, arising in many applications. Extending the Fokker-Planck-Kolmogorov equation, governing the…
Uncertainty quantification (UQ) tasks, such as sensitivity analysis and parameter estimation, entail a huge computational complexity when dealing with input-output maps involving the solution of nonlinear differential problems, because of…
Understanding the computational complexity of quantum states is a central challenge in quantum many-body physics. In qubit systems, fermionic Gaussian states can be efficiently simulated on classical computers and hence can be employed as a…
The motion of a colloidal probe in a complex fluid, such as a micellar solution, is usually described by the generalized Langevin equation, which is linear. However, recent numerical simulations and experiments have shown that this linear…
Extreme response assessment is important in the design and operation of engineering structures, and is a crucial part of structural risk and reliability analyses. Structures should be designed in a way that enables them to withstand the…
Bayesian learning using Gaussian processes provides a foundational framework for making decisions in a manner that balances what is known with what could be learned by gathering data. In this dissertation, we develop techniques for…
The paper addresses the problem of passivation of a class of nonlinear systems where the dynamics are unknown. For this purpose, we use the highly flexible, data-driven Gaussian process regression for the identification of the unknown…
We develop a moment equation closure minimization method for the inexpensive approximation of the steady state statistical structure of nonlinear systems whose potential functions have bimodal shapes and which are subjected to correlated…
We develop an approach for Bayesian learning of spatiotemporal dynamical mechanistic models. Such learning consists of statistical emulation of the mechanistic system that can efficiently interpolate the output of the system from arbitrary…
In recent decades, the main focus of computer modeling has been on supporting the design and development of engineering prototyes, but it is now ubiquitous in non-traditional areas such as medical rehabilitation. Conventional modeling…
The purpose of this paper is to provide a discussion, with illustrating examples, on Bayesian forecasting for dynamic generalized linear models (DGLMs). Adopting approximate Bayesian analysis, based on conjugate forms and on Bayes linear…
Continuous-time state estimation is gaining in popularity due to its abilities to provide smooth solutions, handle asynchronous sensors, and interpolate between data points. While there are two main paradigms, parametric (e.g., temporal…
We propose a new method to numerically calculate higher-order correlation functions of primordial fluctuations generated from any early-universe scenario. Our key-starting point is the realization that the tree-level In-In formalism is…
The generalized Langevin equation (GLE) is a useful framework for analyzing and modeling the dynamics of many-body systems in terms of low-dimensional reaction coordinates, with its specific form determined by the choice of projection…
We present a quantum algorithm based on repeated measurement to solve initial-value problems for nonlinear ordinary differential equations (ODEs), which may be generated from partial differential equations in plasma physics. We map a…