There is a growing demand for performing larger-scale Bayesian inference tasks, arising from greater data availability and higher-dimensional model parameter spaces. In this work we present parallelization strategies for the methodology of integrated nested Laplace approximations (INLA), a popular framework for performing approximate Bayesian inference on the class of Latent Gaussian models. Our approach makes use of nested thread-level parallelism, a parallel line search procedure using robust regression in INLA's optimization phase and the state-of-the-art sparse linear solver PARDISO. We leverage mutually independent function evaluations in the algorithm as well as advanced sparse linear algebra techniques. This way we can flexibly utilize the power of today's multi-core architectures. We demonstrate the performance of our new parallelization scheme on a number of different real-world applications. The introduction of parallelism leads to speedups of a factor 10 and more for all larger models. Our work is already integrated in the current version of the open-source R-INLA package, making its improved performance conveniently available to all users.

Aims This work aims at presenting a fully coupled approach for the numerical solution of contact problems between multiple elastic structures immersed in a fluid flow. The key features of the computational model are (i) a fully coupled fluid–structure interaction with contact, (ii) the use of a fibre-reinforced material for the leaflets, (iii) a stent, and (iv) a compliant aortic root. Methods and results The computational model takes inspiration from the immersed boundary techniques and allows the numerical simulation of the blood–tissue interaction of bioprosthetic heart valves (BHVs) as well as the contact among the leaflets. First, we present pure mechanical simulations, where blood is neglected, to assess the performance of different material properties and valve designs. Secondly, fully coupled fluid–structure interaction simulations are employed to analyse the combination of haemodynamic and mechanical characteristics. The isotropic leaflet tissue experiences high-stress values compared to the fibre-reinforced material model. Moreover, elongated leaflets show a stress concentration close to the base of the stent. We observe a fully developed flow at the systolic stage of the heartbeat. On the other hand, flow recirculation appears along the aortic wall during diastole. Conclusion The presented FSI approach can be used for analysing the mechanical and haemodynamic performance of a BHV. Our study suggests that stresses concentrate in the regions where leaflets are attached to the stent and in the portion of the aortic root where the BHV is placed. The results from this study may inspire new BHV designs that can provide a better stress distribution.

We present a new multilevel minimization framework for the training of deep residual networks (ResNets), which has the potential to significantly reduce training time and effort. Our framework is based on the dynamical system’s viewpoint, which formulates a ResNet as the discretization of an initial value problem. The training process is then formulated as a time-dependent optimal control problem, which we discretize using different time-discretization parameters, eventually generating multilevel-hierarchy of auxiliary networks with different resolutions. The training of the original ResNet is then enhanced by training the auxiliary networks with reduced resolutions. By design, our framework is conveniently independent of the choice of the training strategy chosen on each level of the multilevel hierarchy. By means of numerical examples, we analyze the convergence behavior of the proposed method and demonstrate its robustness. For our examples we employ a multilevel gradient-based methods. Comparisons with standard single level methods show a speedup of more than factor three while achieving the same validation accuracy.

No abstract

There is a growing demand for performing larger-scale Bayesian inference tasks, arising from greater data availability and higher-dimensional model parameter spaces. In this work we present parallelization strategies for the methodology of integrated nested Laplace approximations (INLA), a popular framework for performing approximate Bayesian inference on the class of Latent Gaussian models. Our approach makes use of nested OpenMP parallelism, a parallel line search procedure using robust regression in INLA's optimization phase and the state-of-the-art sparse linear solver PAR-DISO. We leverage mutually independent function evaluations in the algorithm as well as advanced sparse linear algebra techniques. This way we can flexibly utilize the power of today's multi-core architectures. We demonstrate the performance of our new parallelization scheme on a number of different real-world applications. The introduction of parallelism leads to speedups of a factor 10 and more for all larger models. Our work is already integrated in the current version of the open-source R-INLA package, making its improved performance conveniently available to all users.