Survey of multifidelity methods in uncertainty propagation, inference, and optimization
B Peherstorfer, K Willcox, M Gunzburger - Siam Review, 2018 - SIAM
In many situations across computational science and engineering, multiple computational
models are available that describe a system of interest. These different models have varying …
models are available that describe a system of interest. These different models have varying …
The cardiovascular system: mathematical modelling, numerical algorithms and clinical applications
Mathematical and numerical modelling of the cardiovascular system is a research topic that
has attracted remarkable interest from the mathematical community because of its intrinsic …
has attracted remarkable interest from the mathematical community because of its intrinsic …
Review of multi-fidelity models
MG Fernández-Godino - arXiv preprint arXiv:1609.07196, 2016 - arxiv.org
This article provides an overview of multi-fidelity modeling trends. Fidelity in modeling refers
to the level of detail and accuracy provided by a predictive model or simulation. Generally …
to the level of detail and accuracy provided by a predictive model or simulation. Generally …
[图书][B] Mathematical modelling of the human cardiovascular system: data, numerical approximation, clinical applications
Mathematical and numerical modelling of the human cardiovascular system has attracted
remarkable research interest due to its intrinsic mathematical difficulty and the increasing …
remarkable research interest due to its intrinsic mathematical difficulty and the increasing …
Multifidelity approaches for optimization under uncertainty
LWT Ng, KE Willcox - International Journal for numerical …, 2014 - Wiley Online Library
It is important to design robust and reliable systems by accounting for uncertainty and
variability in the design process. However, performing optimization in this setting can be …
variability in the design process. However, performing optimization in this setting can be …
A guide to uncertainty quantification and sensitivity analysis for cardiovascular applications
VG Eck, WP Donders, J Sturdy… - … journal for numerical …, 2016 - Wiley Online Library
As we shift from population‐based medicine towards a more precise patient‐specific regime
guided by predictions of verified and well‐established cardiovascular models, an urgent …
guided by predictions of verified and well‐established cardiovascular models, an urgent …
On transfer learning of neural networks using bi-fidelity data for uncertainty propagation
Due to their high degree of expressiveness, neural networks have recently been used as
surrogate models for mapping inputs of an engineering system to outputs of interest. Once …
surrogate models for mapping inputs of an engineering system to outputs of interest. Once …
Generative learning of the solution of parametric partial differential equations using guided diffusion models and virtual observations
We introduce a generative learning framework to model high-dimensional parametric
systems using gradient guidance and virtual observations. We consider systems described …
systems using gradient guidance and virtual observations. We consider systems described …
Towards efficient uncertainty quantification in complex and large-scale biomechanical problems based on a Bayesian multi-fidelity scheme
In simulation of cardiovascular processes and diseases patient-specific model parameters,
such as constitutive properties, are usually not easy to obtain. Instead of using population …
such as constitutive properties, are usually not easy to obtain. Instead of using population …
Multilevel sequential2 Monte Carlo for Bayesian inverse problems
The identification of parameters in mathematical models using noisy observations is a
common task in uncertainty quantification. We employ the framework of Bayesian inversion …
common task in uncertainty quantification. We employ the framework of Bayesian inversion …