Search

A numerical approach based on the hidden physics model to estimate the model parameters of elastic wave equations with the sparse and noisy data is presented in this paper. Through discretizing the time derivatives of elastic wave equations and placing the priors of the state variables as Gaussian process, the model parameters and structure of elastic wave equations are encoded in the kernel function of a multi-output Gaussian process. In the learning stage, a parameter bound constraint condition is incorporated to enforce the physical bound of the model parameters. The numerical results from several benchmark problems, including homogeneous media, layer media, anisotropic media, and homogeneous model with an inclusion, demonstrate the feasibility and performance of the hidden physics model. • A hidden physics model is developed for parameter estimation of elastic wave equations. • A Physics-informed kernel is derived to encode the structure and model parameters of elastic wave equations. • An active learning strategy is suggested to improve the efficiency. • The performance of the hidden physics model is demonstrated by several benchmark problems. [ABSTRACT FROM AUTHOR]

Image-based computational fluid dynamics (CFD) modeling enables derivation of hemodynamic information (e.g., flow field, wall shear stress, and pressure distribution), which has become a paradigm in cardiovascular research and healthcare. Nonetheless, the predictive accuracy largely depends on precisely specified boundary conditions and model parameters, which, however, are usually uncertain (or unknown) in most patient-specific cases. Quantifying the uncertainties in model predictions due to input randomness can provide predictive confidence and is critical to promote the transition of CFD modeling in clinical applications. In the meantime, forward propagation of input uncertainties often involves numerous expensive CFD simulations, which is computationally prohibitive in most practical scenarios. This paper presents an efficient bi-fidelity surrogate modeling framework for uncertainty quantification (UQ) in cardiovascular simulations, by leveraging the accuracy of high-fidelity models and efficiency of low-fidelity models. Contrary to most data-fit surrogate models with several scalar quantities of interest, this work aims to provide high-resolution, full-field predictions (e.g., velocity and pressure fields). Moreover, a novel empirical error bound estimation approach is introduced to evaluate the performance of the surrogate a priori. The proposed framework is tested on a number of vascular flows with both standardized and patient-specific vessel geometries, and different combinations of high- and low-fidelity models are investigated. The results show that the bi-fidelity approach can achieve high predictive accuracy with a significant reduction of computational cost, exhibiting its merit and effectiveness. Particularly, the uncertainties from a high-dimensional input space can be accurately propagated to clinically relevant quantities of interest (e.g., wall shear stress) in the patient-specific case using only a limited number of high-fidelity simulations, suggesting a good potential in practical clinical applications. • Presented a bi-fidelity surrogate modeling framework for hemodynamic simulations. • Proposed a novel error estimation method to assess bi-fidelity surrogate a priori. • Demonstrated effectiveness of the approach on idealized/patient-specific cases. [ABSTRACT FROM AUTHOR]

Abstract: We study nontrivial applications of the reduced basis method (RBM) for electromagnetic applications with an emphasis on scattering and the estimation of radar cross section (RCS). The method and several extensions are explained with two examples with different characteristics. Parameters that are allowed to vary within the model include frequency, incident angle and measurement angle as well as the geometry of the scatterers. With appropriate applications of the empirical interpolation method (EIM), transformation of the domain, configuration of perfectly matched layer, exponential convergence of the reduced basis solution over the entire parameter domain is achieved. Moreover, we demonstrate that this approach allows for the effective capture of the critical behavior, in this case through shapes that minimize scattering. This further highlights the robustness and quality of the greedy approximation and the reduced basis method approach. [Copyright &y& Elsevier]