Related papers: Physics-Informed Polynomial Chaos Expansions
A spline chaos expansion, referred to as SCE, is introduced for uncertainty quantification analysis. The expansion provides a means for representing an output random variable of interest with respect to multivariate orthonormal basis…
Data-based discovery of effective, coarse-grained (CG) models of high-dimensional dynamical systems presents a unique challenge in computational physics and particularly in the context of multiscale problems. The present paper offers a…
Simulating complex physical systems is crucial for understanding and predicting phenomena across diverse fields, such as fluid dynamics and heat transfer, as well as plasma physics and structural mechanics. Traditional approaches rely on…
In this contribution, we discuss the construction of Polynomial Chaos surrogates for Monte Carlo radiation transport applications via non-intrusive spectral projection. This contribution focuses on improvements with respect to the approach…
Methods based on polynomial chaos expansion allow to approximate the behavior of systems with uncertain parameters by deterministic dynamics. These methods are used in a wide range of applications, spanning from simulation of uncertain…
To date, the analysis of high-dimensional, computationally expensive engineering models remains a difficult challenge in risk and reliability engineering. We use a combination of dimensionality reduction and surrogate modelling termed…
The challenges for non-intrusive methods for Polynomial Chaos modeling lie in the computational efficiency and accuracy under a limited number of model simulations. These challenges can be addressed by enforcing sparsity in the series…
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…
We present a new approach for constructing a data-driven surrogate model and using it for Bayesian parameter estimation in partial differential equation (PDE) models. We first use parameter observations and Gaussian Process regression to…
Incorporating probabilistic terms in mathematical models is crucial for capturing and quantifying uncertainties in real-world systems, especially when the solution is not unique or exhibits sudden qualitative changes as parameters vary.…
This paper presents an approach for the modelling of dependent random variables using generalised polynomial chaos. This allows to write chance-constrained optimization problems with respect to a joint distribution modelling dependencies…
This paper deals with some of the methodologies used to construct polynomial surrogate models based on generalized polynomial chaos (gPC) expansions for applications to uncertainty quantification (UQ) in aerodynamic computations. A core…
Polynomial chaos based methods enable the efficient computation of output variability in the presence of input uncertainty in complex models. Consequently, they have been used extensively for propagating uncertainty through a wide variety…
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…
Partial differential equations (PDEs) serve as the cornerstone of mathematical physics. In recent years, Physics-Informed Neural Networks (PINNs) have significantly reduced the dependence on large datasets by embedding physical laws…
Partial differential equations (PDEs) that fit scientific data can represent physical laws with explainable mechanisms for various mathematically-oriented subjects, such as physics and finance. The data-driven discovery of PDEs from…
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…
This work introduces a method to equip data-driven polynomial chaos expansion surrogate models with intervals that quantify the predictive uncertainty of the surrogate. To that end, jackknife-based conformal prediction is integrated into…
A probabilistic performance-oriented controller design approach based on polynomial chaos expansion and optimization is proposed for flight dynamic systems. Unlike robust control techniques where uncertainties are conservatively handled,…
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…