相关论文: A survey of unsupervised learning methods for high…

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…

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…

The surrogate model-based uncertainty quantification method has drawn much attention in many engineering fields. Polynomial chaos expansion (PCE) and deep learning (DL) are powerful methods for building a surrogate model. However, PCE needs…

Learning data representations under uncertainty is an important task that emerges in numerous scientific computing and data analysis applications. However, uncertainty quantification techniques are computationally intensive and become…

Deep learning-based surrogate models have demonstrated remarkable advantages over classical solvers in terms of speed, often achieving speedups of 10 to 1000 times over traditional partial differential equation (PDE) solvers. However, a…

We introduce a method to construct a stochastic surrogate model from the results of dimensionality reduction in forward uncertainty quantification. The hypothesis is that the high-dimensional input augmented by the output of a computational…

We present a novel physics-constrained polynomial chaos expansion as a surrogate modeling method capable of performing both scientific machine learning (SciML) and uncertainty quantification (UQ) tasks. The proposed method possesses a…

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…

Parameter identification is crucial in virtual engineering processes, yet determining appropriate system excitations for identifying specific parameters remains challenging. In practice, extensive experimental programs often fail to…

Machine learning (ML) surrogate models are increasingly used in engineering analysis and design to replace computationally expensive simulation models, significantly reducing computational cost and accelerating decision-making processes.…

Partial differential equations (PDEs) are fundamental for theoretically describing numerous physical processes that are based on some input fields in spatial configurations. Understanding the physical process, in general, requires…

Due to the importance of uncertainty quantification (UQ), Bayesian approach to inverse problems has recently gained popularity in applied mathematics, physics, and engineering. However, traditional Bayesian inference methods based on Markov…

Uncertainty quantification (UQ) has received much attention in the literature in the past decade. In this context, Sparse Polynomial chaos expansions (PCE) have been shown to be among the most promising methods because of their ability to…

Predictive estimation, which comprises model calibration, model prediction, and validation, is a common objective when performing inverse uncertainty quantification (UQ) in diverse scientific applications. These techniques typically require…

The accessibility of spatially distributed data, enabled by affordable sensors, field, and numerical experiments, has facilitated the development of data-driven solutions for scientific problems, including climate change, weather…

We propose a non-intrusive reduced-order modeling method based on proper orthogonal decomposition (POD) and polynomial chaos expansion (PCE) for stochastic representations in uncertainty quantification (UQ) analysis. Firstly, POD provides…

Thanks to their versatility, ease of deployment and high-performance, surrogate models have become staple tools in the arsenal of uncertainty quantification (UQ). From local interpolants to global spectral decompositions, surrogates are…

The present work addresses the issue of accurate stochastic approximations in high-dimensional parametric space using tools from uncertainty quantification (UQ). The basis adaptation method and its accelerated algorithm in polynomial chaos…

Surrogate modeling and uncertainty quantification tasks for PDE systems are most often considered as supervised learning problems where input and output data pairs are used for training. The construction of such emulators is by definition a…

Many problems in engineering and sciences require the solution of large scale optimization constrained by partial differential equations (PDEs). Though PDE-constrained optimization is itself challenging, most applications pose additional…