Huanhuan Yang

Huanhuan Yang, Max Gunzburger, Lili Ju

Centroidal Voronoi tessellation (CVT)-based mesh generation is a very effective technique for creating high-quality Voronoi meshes and their dual Delaunay triangulations that often play a crucial role in applications, including ocean and atmospheric simulations using finite volume schemes. In the next generation climate models, the spacing scales change dramatically across the whole sphere and require ultra-high resolution and smooth transitions from coarse to fine grid regions. Thus fast and robust spherical CVT (SCVT) meshing algorithms become highly desirable. In this paper, we first propose a Lloyd-preconditioned limited-memory BFGS method for constructing SCVTs that is also applicable to the construction of CVTs of general domains. This method is then parallelized based on overlapping domain decomposition, enabling excellent scalability on distributed systems. Results of several computational experiments show that the new method could incur computational time costs one order of magnitude smaller compared with some existing methods for generating large-scale highly variable-resolution meshes, while also providing significantly improvements in mesh quality.

Huanhuan Yang, Alessandro Veneziani

Clinical oriented applications of computational electrocardiology require efficient and reliable identification of patient-specific parameters of mathematical models based on available measures. In particular, the estimation of cardiac conductivities in models of potential propagation is crucial, since they have major quantitative impact on the solution. Available estimates of cardiac conductivities are significantly diverse in the literature and the definition of experimental/mathematical estimation techniques is an open problem with important practical implications in clinics. We have recently proposed a methodology based on a variational procedure, where the reliability is confirmed by numerical experiments. In this paper we explore model-order-reduction techniques to fit the estimation procedure into timelines of clinical interest. Specifically we consider the Monodomain model and resort to Proper Orthogonal Decomposition (POD) techniques to take advantage of an off-line step when solving iteratively the electrocardiological forward model online. In addition, we perform the Discrete Empirical Interpolation Method (DEIM) to tackle the nonlinearity of the model. While standard POD techniques usually fail in this kind of problems, due to the wave-front propagation dynamics, an educated novel sampling of the parameter space based on the concept of Domain of Effectiveness introduced here dramatically reduces the computational cost of the inverse solver by at least 95%.

Chenran Zhao, Dianxi Shi, Mengzhu Wang et al.

Current Hierarchical Reinforcement Learning (HRL) algorithms excel in long-horizon sequential decision-making tasks but still face two challenges: delay effects and spurious correlations. To address them, we propose a causal HRL approach called D3HRL. First, D3HRL models delayed effects as causal relationships across different time spans and employs distributed causal discovery to learn these relationships. Second, it employs conditional independence testing to eliminate spurious correlations. Finally, D3HRL constructs and trains hierarchical policies based on the identified true causal relationships. These three steps are iteratively executed, gradually exploring the complete causal chain of the task. Experiments conducted in 2D-MineCraft and MiniGrid show that D3HRL demonstrates superior sensitivity to delay effects and accurately identifies causal relationships, leading to reliable decision-making in complex environments.