Related papers: Global sensitivity analysis for models described b…
In a model of the form $Y=h(X_1,\ldots,X_d)$ where the goal is to estimate a parameter of the probability distribution of $Y$, we define new sensitivity indices which quantify the importance of each variable $X_i$ with respect to this…
Many systems in physics, engineering, and biology exhibit multiscale stochastic dynamics, where low-dimensional slow variables evolve under the influence of high-dimensional fast processes. In practice, observations are often limited to a…
Many real-world processes and phenomena are modeled using systems of ordinary differential equations with parameters. Given such a system, we say that a parameter is globally identifiable if it can be uniquely recovered from input and…
The method of derivative based global sensitivity measures (DGSM) has recently become popular among practitioners. It has a strong link with the Morris screening method and Sobol' sensitivity indices and has several advantages over them.…
We develop an approach to learn an interpretable semi-parametric model of a latent continuous-time stochastic dynamical system, assuming noisy high-dimensional outputs sampled at uneven times. The dynamics are described by a nonlinear…
We consider a non-linear parabolic partial differential equation (PDE) on $\mathbb R^d$ with a distributional coefficient in the non-linear term. The distribution is an element of a Besov space with negative regularity and the non-linearity…
Parameter estimation for a parabolic linear stochastic partial differential equation in one space dimension is studied observing the solution field on a discrete grid in a fixed bounded domain. Considering an infill asymptotic regime in…
Stochastic partial differential equations (SPDEs) are the mathematical tool of choice for modelling spatiotemporal PDE-dynamics under the influence of randomness. Based on the notion of mild solution of an SPDE, we introduce a novel neural…
We consider parametric estimation for a parabolic linear second order stochastic partial differential equation (SPDE) from high frequency data which are observed in time and space. By using thinned data obtained from the high frequency…
This work introduces the use of multivariate global sensitivity analysis for assessing the impact of uncertain electric machine design parameters on efficiency maps and profiles. Contrary to the common approach of applying variance-based…
This paper is concerned with the numerical approximation of quantities of interest associated with solutions to parametric elliptic partial differential equations (PDEs). The key novelty of this work is in its focus on the quantities of…
Stochastic differential equation mixed-effects models (SDEMEMs) are flexible hierarchical models that are able to account for random variability inherent in the underlying time-dynamics, as well as the variability between experimental units…
Using mathematical models to assist in the interpretation of experiments is becoming increasingly important in research across applied mathematics, and in particular in biology and ecology. In this context, accurate parameter estimation is…
Models with high-dimensional parameter spaces are common in many applications. Global sensitivity analyses can provide insights on how uncertain inputs and interactions influence the outputs. Many sensitivity analysis methods face…
In this paper, a local-global model reduction method is presented to solve stochastic optimal control problems governed by partial differential equations (PDEs). If the optimal control problems involve uncertainty, we need to use a few…
Global sensitivity analysis (GSA) can provide rich information for controlling output uncertainty. In practical applications, segmented models are commonly used to describe an abrupt model change. For segmented models, the complicated…
Differential Equation (DE) is a commonly used modeling method in various scientific subjects such as finance and biology. The parameters in DE models often have interesting scientific interpretations, but their values are often unknown and…
Graph Neural Networks have achieved impressive results across diverse network modeling tasks, but accurately estimating uncertainty on graphs remains difficult, especially under distributional shifts. Unlike traditional uncertainty…
In global sensitivity analysis, the well known Sobol' sensitivity indices aim to quantify how the variance in the output of a mathematical model can be apportioned to the different variances of its input random variables. These indices are…
The PAWN index is gaining traction among the modelling community as a sensitivity measure. However, the robustness to its design parameters has not yet been scrutinized: the size ($N$) and sampling ($\varepsilon$) of the model output, the…