相关论文: Bifidelity Karhunen-Lo\`eve Expansion Surrogate wi…

The Karhunen-Lo\`{e}ve (KL) expansion is a popular method for approximating random fields by transforming an infinite-dimensional stochastic domain into a finite-dimensional parameter space. Its numerical approximation is of central…

High-fidelity simulation models are widely used to analyze complex stochastic systems, but their high computational cost motivates the development of cheaper surrogate models that approximate the simulation model's input-output…

This work introduces a method to equip data-driven polynomial chaos expansion surrogate models with intervals that quantify the predictive uncertainty of the surrogate. To that end, jackknife-based conformal prediction is integrated into…

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.…

Image-based computational fluid dynamics (CFD) modeling enables derivation of hemodynamic information, which has become a paradigm in cardiovascular research and healthcare. Nonetheless, the predictive accuracy largely depends on precisely…

Simulating complex physical processes across a domain of input parameters can be very computationally expensive. Multi-fidelity surrogate modeling can resolve this issue by integrating cheaper simulations with the expensive ones in order to…

Gaussian random field is a ubiquitous model for spatial phenomena in diverse scientific disciplines. Its approximation is often crucial for computational feasibility in simulation, inference, and uncertainty quantification. The…

A multi-fidelity surrogate model for highly nonlinear multiscale problems is proposed. It is based on the introduction of two different surrogate models and an adaptive on-the-fly switching. The two concurrent surrogates are built…

This report examines numerical aspects of constructing Karhunen-Lo\`{e}ve expansions (KLEs) for second-order stochastic processes. The KLE relies on the spectral decomposition of the covariance operator via the Fredholm integral equation of…

Designing an inexpensive approximate surrogate model that captures the salient features of an expensive high-fidelity behavior is a prevalent approach in design optimization. In recent times, Deep Learning (DL) models are being used as a…

Reliability analysis typically relies on deterministic simulators, which yield repeatable outputs for identical inputs. However, many real-world systems display intrinsic randomness, requiring stochastic simulators whose outputs are random…

Surrogate modelling techniques have opened up new possibilities to overcome the limitations of computationally intensive numerical models in various areas of engineering and science. However, while fundamental in many engineering…

Data-driven surrogate models are widely used for applications such as design optimization and uncertainty quantification, where repeated evaluations of an expensive simulator are required. For most partial differential equation (PDE)…

The paper presents a novel methodology to build surrogate models of complicated functions by an active learning-based sequential decomposition of the input random space and construction of localized polynomial chaos expansions, referred to…

The active learning (AL) technique, one of the state-of-the-art methods for constructing surrogate models, has shown high accuracy and efficiency in forward uncertainty quantification (UQ) analysis. This paper provides a comprehensive study…

In the context of uncertainty quantification, computational models are required to be repeatedly evaluated. This task is intractable for costly numerical models. Such a problem turns out to be even more severe for stochastic simulators, the…

This paper is dedicated to enhancing the computational efficiency of traditional parallel-in-time methods for solving stochastic initial-value problems. The standard parareal algorithm often suffers from slow convergence when applied to…

High-fidelity numerical simulations of partial differential equations (PDEs) given a restricted computational budget can significantly limit the number of parameter configurations considered and/or time window evaluated for modeling a given…

Computational simulations with different fidelity have been widely used in engineering design. A high-fidelity (HF) model is generally more accurate but also more time-consuming than an low-fidelity (LF) model. To take advantages of both HF…

Numerically solving a large parametric nonlinear dynamical system is challenging due to its high complexity and the high computational costs. In recent years, machine-learning-aided surrogates are being actively researched. However, many…