Related papers: Direct Interval Propagation Methods using Neural-N…

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…

Surrogate models - also called emulators - are widely used to facilitate Bayesian inference in settings where computational costs preclude the use of standard posterior inference algorithms. Their deployment is now standard practice across…

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…

We consider the point evaluation of the solution to interface problems with geometric uncertainties, where the uncertainty in the obstacle is described by a high-dimensional parameter $\boldsymbol{y}\in[-1,1]^d$, $d\in\mathbb{N}$. We focus…

We propose a novel \textit{capsule} based deep encoder-decoder model for surrogate modeling and uncertainty quantification of systems in mechanics from sparse data. The proposed framework is developed by adapting Capsule Network (CapsNet)…

Recently, several optimization methods have been successfully applied to the hyperparameter optimization of deep neural networks (DNNs). The methods work by modeling the joint distribution of hyperparameter values and corresponding error.…

For computational efficiency, surrogate models have been used to emulate mathematical simulators for physical or biological processes. High-speed simulation is crucial for conducting uncertainty quantification (UQ) when the simulation is…

Uncertainty estimation, which provides a means of building explainable neural networks for medical imaging applications, have mostly been studied for single deep learning models that focus on a specific task. In this paper, we propose a…

Surrogate modeling is a viable solution for applications involving repetitive evaluations of expensive computational fluid dynamics models, such as uncertainty quantification and inverse problems. This study proposes a multi-layer…

We present a deep learning framework for quantifying and propagating uncertainty in systems governed by non-linear differential equations using physics-informed neural networks. Specifically, we employ latent variable models to construct…

High-performance scientific simulations, important for comprehension of complex systems, encounter computational challenges especially when exploring extensive parameter spaces. There has been an increasing interest in developing deep…

Large-scale numerical simulations are used across many scientific disciplines to facilitate experimental development and provide insights into underlying physical processes, but they come with a significant computational cost. Deep neural…

This paper proposes a novel robust Model Predictive Control (MPC) scheme for linear discrete-time systems affected by model uncertainty described by interval matrices. The key feature of the proposed method is a bound on the uncertainty…

This chapter deals with kernel methods as a special class of techniques for surrogate modeling. Kernel methods have proven to be efficient in machine learning, pattern recognition and signal analysis due to their flexibility, excellent…

The success of deep learning, a brain-inspired form of AI, has sparked interest in understanding how the brain could similarly learn across multiple layers of neurons. However, the majority of biologically-plausible learning algorithms have…

Statistical learning algorithms provide a generally-applicable framework to sidestep time-consuming experiments, or accurate physics-based modeling, but they introduce a further source of error on top of the intrinsic limitations of the…

Surrogate Neural Networks are nowadays routinely used in industry as substitutes for computationally demanding engineering simulations (e.g., in structural analysis). They allow to generate faster predictions and thus analyses in industrial…

Arithmetic constraints on integer intervals are supported in many constraint programming systems. We study here a number of approaches to implement constraint propagation for these constraints. To describe them we introduce integer interval…

We integrate neural operators with diffusion models to address the spectral limitations of neural operators in surrogate modeling of turbulent flows. While neural operators offer computational efficiency, they exhibit deficiencies in…

The quantification of uncertainties of computer simulations due to input parameter uncertainties is paramount to assess a model's credibility. For computationally expensive simulations, this is often feasible only via surrogate models that…