Related papers: A Mechanistic Dynamic Emulator
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…
A computational tool for coarse-graining nonlinear systems of ordinary differential equations in time is discussed. Three illustrative model examples are worked out that demonstrate the range of capability of the method. This includes the…
Stochastic simulators are ubiquitous in many fields of applied sciences and engineering. In the context of uncertainty quantification and optimization, a large number of simulations is usually necessary, which becomes intractable for…
We present a deep learning emulator for stochastic and chaotic spatio-temporal systems, explicitly conditioned on the parameter values of the underlying partial differential equations (PDEs). Our approach involves pre-training the model on…
The dynamics of a linear system embedded in a heat bath environment and subject to non- Gaussian noise is studied. Higher order cumulants in coordinate space are derived and their impact on the dynamics and on asymptotic steady state…
Molecular dynamics simulations use statistical mechanics at the atomistic scale to enable both the elucidation of fundamental mechanisms and the engineering of matter for desired tasks. The behavior of molecular systems at the microscale is…
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…
Dynamical systems theory has long provided a foundation for understanding evolving phenomena across scientific domains. Yet, the application of this theory to complex real-world systems remains challenging due to issues in mathematical…
Fitting a theoretical model to experimental data in a Bayesian manner using Markov chain Monte Carlo typically requires one to evaluate the model thousands (or millions) of times. When the model is a slow-to-compute physics simulation,…
Nonlinear stochastic motion presents significant challenges for Bayesian particle tracking. To address this challenge, this paper proposes a framework to construct an invertible transformation that maps the nonlinear state-space model (SSM)…
The problem of determining the mathematical model of the dynamics of multi-dimensional control systems in the presence of noise under the condition that the correlation functions cannot be found. Known statistical dynamics of linear systems…
Reliability analysis is a sub-field of uncertainty quantification that assesses the probability of a system performing as intended under various uncertainties. Traditionally, this analysis relies on deterministic models, where experiments…
We study the problem of modeling a non-linear dynamical system when given a time series by deriving equations directly from the data. Despite the fact that time series data are given as input, models for dynamics and estimation algorithms…
A Gaussian operator basis provides a means to formulate phase-space simulations of the real- and imaginary-time evolution of quantum systems. Such simulations are guaranteed to be exact while the underlying distribution remains…
This paper explores learning emulators for parameter estimation with uncertainty estimation of high-dimensional dynamical systems. We assume access to a computationally complex simulator that inputs a candidate parameter and outputs a…
We consider the effect of replacing in stochastic differential equations leading to the dynamical collapse of the statevector, white noise stochastic processes with non white ones. We prove that such a modification can be consistently…
We present a method of parameter estimation for large class of nonlinear systems, namely those in which the state consists of output derivatives and the flow is linear in the parameter. The method, which solves for the unknown parameter by…
Calibration of expensive simulation models involves an emulator based on simulation outputs generated across various parameter settings to replace the actual model. Noisy outputs of stochastic simulation models require many simulation…
Stochastic averaging allows for the reduction of the dimension and complexity of stochastic dynamical systems with multiple time scales, replacing fast variables with statistically equivalent stochastic processes in order to analyze…
The recent accelerated growth in the computing power has generated popularization of experimentation with dynamic computer models in various physical and engineering applications. Despite the extensive statistical research in computer…