Related papers: Surrogate modelling for stochastic dynamical syste…

In this paper we propose an algorithm for recovering sparse orthogonal polynomials using stochastic collocation. Our approach is motivated by the desire to use generalized polynomial chaos expansions (PCE) to quantify uncertainty in models…

This work addresses integrating probabilistic propositional logic constraints into the distribution encoded by a probabilistic circuit (PC). PCs are a class of tractable models that allow efficient computations (such as conditional and…

The intermittent nature of renewable power availability is one of the major sources of uncertainty in power systems. While markets can guarantee that the demand is covered by the available generation, transmission system operators have to…

Traditional deterministic subgrid-scale (SGS) models are often dissipative and unstable, especially in regions of chaotic and turbulent flow. Ongoing work in climate science and ocean modeling motivates the use of stochastic SGS models for…

In the field of uncertainty quantification, sparse polynomial chaos (PC) expansions are commonly used by researchers for a variety of purposes, such as surrogate modeling. Ideas from compressed sensing may be employed to exploit this…

Numerical simulation of stochastic differential equations over long time intervals poses significant computational challenges. In this paper, we propose a novel recursive polynomial chaos evolution method that achieves model reduction…

The polynomial NARMAX (Nonlinear AutoRegressive Moving Average model with eXogenous input) is a model that represents the dynamics of physical systems. This polynomial contains information from the past of the inputs and outputs of the…

In this work, a modified neural architecture search method (NAS) based physics-informed deep learning model is presented for stochastic analysis in heterogeneous porous material. Monte Carlo method based on a randomized spectral…

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…

Multi-model ensembles provide a pragmatic approach to the representation of model uncertainty in climate prediction. However, such representations are inherently ad hoc, and, as shown, probability distributions of climate variables based on…

A surrogate model approximates a computationally expensive solver. Polynomial Chaos is a method to construct surrogate models by summing combinations of carefully chosen polynomials. The polynomials are chosen to respect the probability…

Operator learning (OL) has emerged as a powerful tool in scientific machine learning (SciML) for approximating mappings between infinite-dimensional functional spaces. One of its main applications is learning the solution operator of…

Mesh-based simulations play a key role when modeling complex physical systems that, in many disciplines across science and engineering, require the solution of parametrized time-dependent nonlinear partial differential equations (PDEs). In…

Bayesian analysis enables combining prior knowledge with measurement data to learn model parameters. Commonly, one resorts to computing the maximum a posteriori (MAP) estimate, when only a point estimate of the parameters is of interest. We…

The requirement for identifying accurate system representations has not only been a challenge to fulfill, but it has compromised the scalability of formal methods, as the resulting models are often too complex for effective decision making…

Driven by increased complexity of dynamical systems, the solution of system of differential equations through numerical simulation in optimization problems has become computationally expensive. This paper provides a smart data driven…

Polynomial chaos methods have been extensively used to analyze systems in uncertainty quantification. Furthermore, several approaches exist to determine a low-dimensional approximation (or sparse approximation) for some quantity of interest…

In this paper, a new polynomial chaos based framework for analyzing linear systems with probabilistic parameters is presented. Stability analysis and synthesis of optimal quadratically stabilizing controllers for such systems are presented…

Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph with non-trivial topological features. Data-driven approximations of…

This paper analyzes the effects of input uncertainties on the outputs of a three dimensional natural convection problem in a differentially heated cubical enclosure. Two different cases are considered for parameter uncertainty propagation…