Machine learning based surrogate models offer researchers powerful tools for accelerating simulation-based workflows. However, as standard datasets in this space often cover small classes of physical behavior, it can be difficult to evaluate the efficacy of new approaches. To address this gap, we introduce the Well: a large-scale collection of datasets containing numerical simulations of a wide variety of spatiotemporal physical systems. The Well draws from domain experts and numerical software developers to provide 15TB of data across 16 datasets covering diverse domains such as biological systems, fluid dynamics, acoustic scattering, as well as magneto-hydrodynamic simulations of extra-galactic fluids or supernova explosions. These datasets can be used individually or as part of a broader benchmark suite. To facilitate usage of the Well, we provide a unified PyTorch interface for training and evaluating models. We demonstrate the function of this library by introducing example baselines that highlight the new challenges posed by the complex dynamics of the Well. The code and data is available at https://github.com/PolymathicAI/the_well.

Spatial patterns of elevated wall shear stress and pressure due to blood flow past aortic stenosis (AS) are studied using GPU-accelerated patient-specific computational fluid dynamics. Three cases of moderate to severe AS, one with a dilated ascending aorta and two within the normal range (root diameter less than 4cm) are simulated for physiological waveforms obtained from echocardiography. The computational framework is built based on sharp-interface Immersed Boundary Method, where aortic geometries segmented from CT angiograms are integrated into a high-order incompressible Navier-Stokes solver. The key question addressed here is, given the presence of turbulence due to AS which increases wall shear stress (WSS) levels, why some AS patients undergo much less aortic dilation. Recent case studies of AS have linked the existence of an elevated WSS hotspot (due to impingement of AS on the aortic wall) to the dilation process. Herein we further investigate the WSS distribution for cases with and without dilation to understand the possible hemodynamics which may impact the dilation process. We show that the spatial distribution of elevated WSS is significantly more focused for the case with dilation than those without dilation. We further show that this focal area accommodates a persistent pocket of high pressure, which may have contributed to the dilation process through an increased wall-normal forcing. The cases without dilation, on the contrary, showed a rather oscillatory pressure behaviour, with no persistent pressure "buildup" effect. We further argue that a more proximal branching of the aortic arch could explain the lack of a focal area of elevated WSS and pressure, because it interferes with the impingement process due to fluid suction effects. These phenomena are further illustrated using an idealized aortic geometry. We finally show that a restored inflow eliminates the focal area of elevated WSS and pressure zone from the ascending aorta.