Related papers: Surrogate modelling for stochastic dynamical syste…
Generalized Polynomial Chaos (gPC) expansions are well established for forward uncertainty propagation in many application areas. Although the associated computational effort may be reduced in comparison to Monte Carlo techniques, for…
We focus on improving the accuracy of an approximate model of a multiscale dynamical system that uses a set of parameter-dependent terms to account for the effects of unresolved or neglected dynamics on resolved scales. We start by…
Computational inverse problems for biomedical simulators suffer from limited data and relatively high parameter dimensionality. This often requires sensitivity analysis, where parameters of the model are ranked based on their influence on…
In the presence of system-environment coupling, classical complex systems undergo stochastic dynamics, where rich phenomena can emerge at large spatio-temporal scales. To investigate these phenomena, numerical approaches for simulating…
Inferring parameter distributions of complex industrial systems from noisy time series data requires methods to deal with the uncertainty of the underlying data and the used simulation model. Bayesian inference is well suited for these…
Polynomial chaos expansions are used to reduce the computational cost in the Bayesian solutions of inverse problems by creating a surrogate posterior that can be evaluated inexpensively. We show, by analysis and example, that when the data…
For a large class of orthogonal basis functions, there has been a recent identification of expansion methods for computing accurate, stable approximations of a quantity of interest. This paper presents, within the context of uncertainty…
In this work, we consider the Biot problem with uncertain poroelastic coefficients. The uncertainty is modelled using a finite set of parameters with prescribed probability distribution. We present the variational formulation of the…
Addressing the uncertainty introduced by increasing renewable integration is crucial for secure power system operation, yet capturing it while preserving the full nonlinear physics of the grid remains a significant challenge. This paper…
Many physical systems are described by nonlinear differential equations that are too complicated to solve in full. A natural way to proceed is to divide the variables into those that are of direct interest and those that are not, formulate…
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…
This paper presents a surrogate modelling technique based on domain partitioning for Bayesian parameter inference of highly nonlinear engineering models. In order to alleviate the computational burden typically involved in Bayesian…
We propose a statistical-stochastic surrogate modeling approach to predict the response of the mean and variance statistics under various initial conditions and external forcing perturbations. The proposed modeling framework extends the…
Many real-world systems are modelled using complex ordinary differential equations (ODEs). However, the dimensionality of these systems can make them challenging to analyze. Dimensionality reduction techniques like Proper Orthogonal…
This work proposes and analyzes a generalized acceleration technique for decreasing the computational complexity of using stochastic collocation (SC) methods to solve partial differential equations (PDEs) with random input data. The SC…
We present polynomial-augmented neural networks (PANNs), a novel machine learning architecture that combines deep neural networks (DNNs) with a polynomial approximant. PANNs combine the strengths of DNNs (flexibility and efficiency in…
In this paper, we show that the common approach for simulation non-linear stochastic models, commonly used in system identification, via setting the noise contributions to zero results in a biased response. We also demonstrate that to…
This work introduces a new approach for accelerating the numerical analysis of time-domain partial differential equations (PDEs) governing complex physical systems. The methodology is based on a combination of a classical reduced-order…
In this paper we present a basis selection method that can be used with $\ell_1$-minimization to adaptively determine the large coefficients of polynomial chaos expansions (PCE). The adaptive construction produces anisotropic basis sets…
This project introduces the GNAR-HARX model, which combines Generalised Network Autoregressive (GNAR) structure with Heterogeneous Autoregressive (HAR) dynamics and exogenous predictors such as implied volatility. The model is designed for…