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  1. Abstract Phonon Boltzmann transport equation (BTE) is a key tool for modeling multiscale phonon transport, which is critical to the thermal management of miniaturized integrated circuits, but assumptions about the system temperatures (i.e., small temperature gradients) are usually made to ensure that it is computationally tractable. To include the effects of large temperature non-equilibrium, we demonstrate a data-free deep learning scheme, physics-informed neural network (PINN), for solving stationary, mode-resolved phonon BTE with arbitrary temperature gradients. This scheme uses the temperature-dependent phonon relaxation times and learns the solutions in parameterized spaces with both length scale and temperature gradient treated as input variables. Numerical experiments suggest that the proposed PINN can accurately predict phonon transport (from 1D to 3D) under arbitrary temperature gradients. Moreover, the proposed scheme shows great promise in simulating device-level phonon heat conduction efficiently and can be potentially used for thermal design. 
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  2. Abstract Computational hemodynamic modeling has been widely used in cardiovascular research and healthcare. However, the reliability of model predictions is largely dependent on the uncertainties of modeling parameters and boundary conditions, which should be carefully quantified and further reduced with available measurements. In this work, we focus on propagating and reducing the uncertainty of vascular geometries within a Bayesian framework. A novel deep learning (DL)-assisted parallel Markov chain Monte Carlo (MCMC) method is presented to enable efficient Bayesian posterior sampling and geometric uncertainty reduction. A DL model is built to approximate the geometry-to-hemodynamic map, which is trained actively using online data collected from parallel MCMC chains and utilized for early rejection of unlikely proposals to facilitate convergence with less expensive full-order model evaluations. Numerical studies on two-dimensional aortic flows are conducted to demonstrate the effectiveness and merit of the proposed method. 
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  3. Determination of abdominal aortic aneurysm (AAA) rupture risk involves the accurate prediction of mechanical stresses acting on the arterial tissue, as well as the wall strength which has a correlation with oxygen supply within the aneurysmal wall. Our laboratory has previously reported the significance of an intraluminal thrombus (ILT) presence and morphology on localized oxygen deprivation by assuming a uniform consistency of ILT. The aim of this work is to investigate the effects of ILT structural composition on oxygen flow by adopting a multilayered porous framework and comparing a two-layer ILT model with one-layer models. Three-dimensional idealized and patient-specific AAA geometries are generated. Numerical simulations of coupled fluid flow and oxygen transport between blood, arterial wall, and ILT are performed, and spatial variations of oxygen concentrations within the AAA are obtained. A parametric study is conducted, and ILT permeability and oxygen diffusivity parameters are individually varied within a physiological range. A gradient of permeability is also defined to represent the heterogenous structure of ILT. Results for oxygen measures as well as filtration velocities are obtained, and it is found that the presence of any ILT reduces and redistributes the concentrations in the aortic wall markedly. Moreover, it is found that the integration of a porous ILT significantly affects the oxygen transport in AAA and the concentrations are linked to ILT’s permeability values. Regardless of the ILT stratification, maximum variation in wall oxygen concentrations is higher in models with lower permeability, while the concentrations are not sensitive to the value of the diffusion coefficient. Based on the observations, we infer that average one-layer parameters for ILT material characteristics can be used to reasonably estimate the wall oxygen concentrations in aneurysm models. 
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  4. Optimization and uncertainty quantification have been playing an increasingly important role in computational hemodynamics. However, existing methods based on principled modeling and classic numerical techniques have faced significant challenges, particularly when it comes to complex three-dimensional (3D) patient-specific shapes in the real world. First, it is notoriously challenging to parameterize the input space of arbitrary complex 3D geometries. Second, the process often involves massive forward simulations, which are extremely computationally demanding or even infeasible. We propose a novel deep learning surrogate modeling solution to address these challenges and enable rapid hemodynamic predictions. Specifically, a statistical generative model for 3D patient-specific shapes is developed based on a small set of baseline patient-specific geometries. An unsupervised shape correspondence solution is used to enable geometric morphing and scalable shape synthesis statistically. Moreover, a simulation routine is developed for automatic data generation by automatic meshing, boundary setting, simulation, and post-processing. An efficient supervised learning solution is proposed to map the geometric inputs to the hemodynamics predictions in latent spaces. Numerical studies on aortic flows are conducted to demonstrate the effectiveness and merit of the proposed techniques. 
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