Related papers: Polynomial Chaos Surrogate Construction for Random…

Numerical solutions of partial differential equations (PDEs) require expensive simulations, limiting their application in design optimization, model-based control, and large-scale inverse problems. Surrogate modeling techniques seek to…

Chaotic systems pose fundamental challenges for data-driven dynamics discovery, as small modeling errors lead to exponentially growing trajectory discrepancies. Since exact long-term prediction is unattainable, it is natural to ask what a…

We propose a methodology for improving the accuracy of surrogate models of the observable response of physical systems as a function of the systems' spatially heterogeneous parameter fields with applications to uncertainty quantification…

Poroelasticity -- coupled fluid flow and elastic deformation in porous media -- often involves spatially variable permeability, especially in subsurface systems. In such cases, simulations with random permeability fields are widely used for…

Polynomial chaos is a powerful technique for propagating uncertainty through ordinary and partial differential equations. Random variables are expanded in terms of orthogonal polynomials and differential equations are derived for 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…

The paper addresses Bayesian inferences in inverse problems with uncertainty quantification involving a computationally expensive forward map associated with solving a partial differential equations. To mitigate the computational cost, the…

This work presents a novel framework for physically consistent model error characterization and operator learning for reduced-order models of non-equilibrium chemical kinetics. By leveraging the Bayesian framework, we identify and infer…

Generative modeling has evolved to a notable field of machine learning. Deep polynomial neural networks (PNNs) have demonstrated impressive results in unsupervised image generation, where the task is to map an input vector (i.e., noise) to…

Neural networks for LHC physics have to be accurate, reliable, and controlled. Using neural surrogates for the prediction of loop amplitudes as a use case, we first show how activation functions are systematically tested with…

Standard Bayesian inference schemes are infeasible for inverse problems with computationally expensive forward models. A common solution is to replace the model with a cheaper surrogate. To avoid overconfident conclusions, it is essential…

Surrogate models provide compact relations between user-defined input parameters and output quantities of interest, enabling the efficient evaluation of complex parametric systems in many-query settings. Such capabilities are essential in a…

In an ever-increasing interest for Machine Learning (ML) and a favorable data development context, we here propose an original methodology for data-based prediction of two-dimensional physical fields. Polynomial Chaos Expansion (PCE),…

We apply the Tensor Train (TT) approximation to construct the Polynomial Chaos Expansion (PCE) of a random field, and solve the stochastic elliptic diffusion PDE with the stochastic Galerkin discretization. We compare two strategies of the…

In this work we introduce a manifold learning-based method for uncertainty quantification (UQ) in systems describing complex spatiotemporal processes. Our first objective is to identify the embedding of a set of high-dimensional data…

The work presented here investigates the application of polynomial chaos expansion toward input shaper design in order to maintain robustness in dynamical systems subject to uncertainty. Furthermore, this work intends to specifically…

Solving complex problems requires continuous effort in developing theory and practice to cope with larger, more difficult scenarios. Working with surrogates is normal for creating a proxy that realistically models the problem into the…

This paper proposes a novel computationally efficient dynamic bi-orthogonality based approach for calibration of a computer simulator with high dimensional parametric and model structure uncertainty. The proposed method is based on a…

Computational modeling of the structural behavior of continuous fiber composite materials often takes into account the periodicity of the underlying micro-structure. A well established method dealing with the structural behavior of periodic…

This paper is dedicated to enhancing the computational efficiency of traditional parallel-in-time methods for solving stochastic initial-value problems. The standard parareal algorithm often suffers from slow convergence when applied to…