Related papers: Consistency regularization-based Deep Polynomial C…
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…
Deep neural networks have been shown to be highly miscalibrated. often they tend to be overconfident in their predictions. It poses a significant challenge for safety-critical systems to utilise deep neural networks (DNNs), reliably. Many…
The polynomial chaos (PC) expansion has been widely used as a surrogate model in the Bayesian inference to speed up the Markov chain Monte Carlo (MCMC) calculations. However, the use of a PC surrogate introduces the modeling error, that may…
Compressive sampling has been widely used for sparse polynomial chaos (PC) approximation of stochastic functions. The recovery accuracy of compressive sampling highly depends on the incoherence properties of the measurement matrix. In this…
Confidence calibration - the process to calibrate the output probability distribution of neural networks - is essential for safety-critical applications of such networks. Recent works verify the link between mis-calibration and overfitting.…
In recent years we have witnessed a growing interest in various non-equilibrium systems described in terms of stochastic non-linear field theories. In some of those systems like the KPZ and related models, the interesting behavior is in the…
Backpropagation (BP) is the standard algorithm for training the deep neural networks that power modern artificial intelligence including large language models. However, BP is energy inefficient and unlikely to be implemented by the brain.…
This work is directed to uncertainty quantification of homogenized effective properties for composite materials with complex, three dimensional microstructure. The uncertainties arise in the material parameters of the single constituents as…
Counterfactual explanations (CEs) offer interpretable insights into machine learning predictions by answering ``what if?" questions. However, in real-world settings where models are frequently updated, existing counterfactual explanations…
The Cluster Expansion (CE) Method encounters significant computational challenges in multicomponent systems due to the computational expense of generating training data through density functional theory (DFT) calculations. This work aims to…
A novel approach to approximate solutions of Stochastic Differential Equations (SDEs) by Deep Neural Networks is derived and analysed. The architecture is inspired by the notion of Deep Operator Networks (DeepONets), which is based on…
Many parametric statistical models are not properly normalised and only specified up to an intractable partition function, which renders parameter estimation difficult. Examples of unnormalised models are Gibbs distributions, Markov random…
This paper addresses the Bayesian calibration of dynamic models with parametric and structural uncertainties, in particular where the uncertain parameters are unknown/poorly known spatio-temporally varying subsystem models. Independent…
Constructing surrogate models for uncertainty quantification (UQ) on complex partial differential equations (PDEs) having inherently high-dimensional $\mathcal{O}(10^{\ge 2})$ stochastic inputs (e.g., forcing terms, boundary conditions,…
Recent research has highlighted a critical issue known as ``robust fairness", where robust accuracy varies significantly across different classes, undermining the reliability of deep neural networks (DNNs). A common approach to address this…
Sequential propagation of chaos (SPoC) is a recently developed tool to solve mean-field stochastic differential equations and their related nonlinear Fokker-Planck equations. Based on the theory of SPoC, we present a new method (deepSPoC)…
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…
Polynomial chaos expansion is a popular way to develop surrogate models for stochastic systems with arbitrary random variables. Standard techniques such as Galerkin projection, stochastic collocation, and least squares approximation, are…
Counterfactual Explanations (CEs) have received increasing interest as a major methodology for explaining neural network classifiers. Usually, CEs for an input-output pair are defined as data points with minimum distance to the input that…
Presence of a high-dimensional stochastic parameter space with discontinuities poses major computational challenges in analyzing and quantifying the effects of the uncertainties in a physical system. In this paper, we propose a stochastic…