Related papers: Deep Adaptive Arbitrary Polynomial Chaos Expansion…

Data-driven surrogate modeling has emerged as a promising approach for reducing computational expenses of multiscale simulations. Recurrent Neural Network (RNN) is a common choice for modeling of path-dependent behavior. However, previous…

Recently, contrastive learning has risen to be a promising approach for large-scale self-supervised learning. However, theoretical understanding of how it works is still unclear. In this paper, we propose a new guarantee on the downstream…

Sequential generative models conditioned on uncertain rewards are central to AI-driven scientific discovery, yet the epistemic uncertainty they inherit from imperfect reward estimates remains unquantified. We propagate this uncertainty…

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…

Deep neural networks (DNNs) are vulnerable to adversarial examples obtained by adding small perturbations to original examples. The added perturbations in existing attacks are mainly determined by the gradient of the loss function with…

Physical models with uncertain inputs are commonly represented as parametric partial differential equations (PDEs). That is, PDEs with inputs that are expressed as functions of parameters with an associated probability distribution.…

A surrogate model approximates a computationally expensive solver. Polynomial Chaos is a method to construct surrogate models by summing combinations of carefully chosen polynomials. The polynomials are chosen to respect the probability…

Deep surrogate models for parametric partial differential equations (PDEs) can deliver high-fidelity approximations but remain prohibitively data-hungry: training often requires thousands of fine-grid simulations, each incurring substantial…

We derive an adaptive hierarchical method of estimating high dimensional probability density functions. We call this method of density estimation the "adaptive cluster expansion" or ACE for short. We present an application of this approach,…

Human exposure induced by wireless communication systems increasingly draws the public attention. Here, an indoor down-link scenario is concerned and the exposure level is statistically analyzed. The electromagnetic field (EMF) emitted by a…

We propose an efficient surrogate modeling technique for uncertainty quantification. The method is based on a well-known dimension-adaptive collocation scheme. We improve the scheme by enhancing sparse polynomial surrogates with conformal…

Data-driven discovery of partial differential equations (PDEs) has attracted increasing attention in recent years. Although significant progress has been made, certain unresolved issues remain. For example, for PDEs with high-order…

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…

Computational models support high-stakes decisions across engineering and science, and practitioners increasingly seek probabilistic predictions to quantify uncertainty in such models. Existing approaches generate predictions either by…

With the mass construction of Gen III nuclear reactors, it is a popular trend to use deep learning (DL) techniques for fast and effective diagnosis of possible accidents. To overcome the common problems of previous work in diagnosing…

State-of-the-art computer codes for simulating real physical systems are often characterized by a vast number of input parameters. Performing uncertainty quantification (UQ) tasks with Monte Carlo (MC) methods is almost always infeasible…

Derivation of the probability density evolution provides invaluable insight into the behavior of many stochastic systems and their performance. However, for most real-time applica-tions, numerical determination of the probability density…

In this work, an adaptive predictive control scheme for linear systems with unknown parameters and bounded additive disturbances is proposed. In contrast to related adaptive control approaches that robustly consider the parametric…

Simulating the time evolution of Partial Differential Equations (PDEs) of large-scale systems is crucial in many scientific and engineering domains such as fluid dynamics, weather forecasting and their inverse optimization problems.…

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…