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Tissue dynamics play critical roles in many physiological functions and provide important metrics for clinical diagnosis. Capturing real-time high-resolution 3D images of tissue dynamics, however, remains a challenge. This study presents a hybrid physics-informed neural network algorithm that infers 3D flow-induced tissue dynamics and other physical quantities from sparse 2D images. The algorithm combines a recurrent neural network model of soft tissue with a differentiable fluid solver, leveraging prior knowledge in solid mechanics to project the governing equation on a discrete eigen space. The algorithm uses a Long-short-term memory-based recurrent encoder-decoder connected with a fully connected neural network to capture the temporal dependence of flow-structure-interaction. The effectiveness and merit of the proposed algorithm is demonstrated on synthetic data from a canine vocal fold model and experimental data from excised pigeon syringes. The results showed that the algorithm accurately reconstructs 3D vocal dynamics, aerodynamics, and acoustics from sparse 2D vibration profiles.

 

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. 

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. 

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.