A Probabilistic Neural Twin for Treatment Planning in Peripheral Pulmonary Artery Stenosis

The substantial computational cost of high-fidelity models in numerical hemodynamics has, so far, relegated their use mainly to offline treatment planning. New breakthroughs in data-driven architectures and optimization techniques for fast surrogate modeling provide an exciting opportunity to overcome these limitations, enabling the use of such technology for time-critical decisions. We discuss an application to the repair of multiple stenosis in peripheral pulmonary artery disease through either transcatheter pulmonary artery rehabilitation or surgery, where it is of interest to achieve desired pressures and flows at specific locations in the pulmonary artery tree, while minimizing the risk for the patient. Since different degrees of success can be achieved in practice during treatment, we formulate the problem in probability, and solve it through a sample-based approach. We propose a new offline-online pipeline for probabilsitic real-time treatment planning which combines offline assimilation of boundary conditions, model reduction, and training dataset generation with online estimation of marginal probabilities, possibly conditioned on the degree of augmentation observed in already repaired lesions. Moreover, we propose a new approach for the parametrization of arbitrarily shaped vascular repairs through iterative corrections of a zero-dimensional approximant. We demonstrate this pipeline for a diseased model of the pulmonary artery tree available through the Vascular Model Repository.

InVAErt networks: a data-driven framework for emulation, inference and identifiability analysis

Use of generative models and deep learning for physics-based systems is currently dominated by the task of emulation. However, the remarkable flexibility offered by data-driven architectures would suggest to extend this representation to other aspects of system synthesis including model inversion and identifiability. We introduce inVAErt (pronounced \emph{invert}) networks, a comprehensive framework for data-driven analysis and synthesis of parametric physical systems which uses a deterministic encoder and decoder to represent the forward and inverse solution maps, normalizing flow to capture the probabilistic distribution of system outputs, and a variational encoder designed to learn a compact latent representation for the lack of bijectivity between inputs and outputs. We formally investigate the selection of penalty coefficients in the loss function and strategies for latent space sampling, since we find that these significantly affect both training and testing performance. We validate our framework through extensive numerical examples, including simple linear, nonlinear, and periodic maps, dynamical systems, and spatio-temporal PDEs.

LINFA: a Python library for variational inference with normalizing flow and annealing

Variational inference is an increasingly popular method in statistics and machine learning for approximating probability distributions. We developed LINFA (Library for Inference with Normalizing Flow and Annealing), a Python library for variational inference to accommodate computationally expensive models and difficult-to-sample distributions with dependent parameters. We discuss the theoretical background, capabilities, and performance of LINFA in various benchmarks. LINFA is publicly available on GitHub at https://github.com/desResLab/LINFA.

Differentially Private Normalizing Flows for Density Estimation, Data Synthesis, and Variational Inference with Application to Electronic Health Records

Electronic health records (EHR) often contain sensitive medical information about individual patients, posing significant limitations to sharing or releasing EHR data for downstream learning and inferential tasks. We use normalizing flows (NF), a family of deep generative models, to estimate the probability density of a dataset with differential privacy (DP) guarantees, from which privacy-preserving synthetic data are generated. We apply the technique to an EHR dataset containing patients with pulmonary hypertension. We assess the learning and inferential utility of the synthetic data by comparing the accuracy in the prediction of the hypertension status and variational posterior distribution of the parameters of a physics-based model. In addition, we use a simulated dataset from a nonlinear model to compare the results from variational inference (VI) based on privacy-preserving synthetic data, and privacy-preserving VI obtained from directly privatizing NFs for VI with DP guarantees given the original non-private dataset. The results suggest that synthetic data generated through differentially private density estimation with NF can yield good utility at a reasonable privacy cost. We also show that VI obtained from differentially private NF based on the free energy bound loss may produce variational approximations with significantly altered correlation structure, and loss formulations based on alternative dissimilarity metrics between two distributions might provide improved results.

Data-driven synchronization-avoiding algorithms in the explicit distributed structural analysis of soft tissue

We propose a data-driven framework to increase the computational efficiency of the explicit finite element method in the structural analysis of soft tissue. An encoder-decoder long short-term memory deep neural network is trained based on the data produced by an explicit, distributed finite element solver. We leverage this network to predict synchronized displacements at shared nodes, minimizing the amount of communication between processors. We perform extensive numerical experiments to quantify the accuracy and stability of the proposed synchronization-avoiding algorithm.

Multifidelity data fusion in convolutional encoder/decoder networks

We analyze the regression accuracy of convolutional neural networks assembled from encoders, decoders and skip connections and trained with multifidelity data. Besides requiring significantly less trainable parameters than equivalent fully connected networks, encoder, decoder, encoder-decoder or decoder-encoder architectures can learn the mapping between inputs to outputs of arbitrary dimensionality. We demonstrate their accuracy when trained on a few high-fidelity and many low-fidelity data generated from models ranging from one-dimensional functions to Poisson equation solvers in two-dimensions. We finally discuss a number of implementation choices that improve the reliability of the uncertainty estimates generated by Monte Carlo DropBlocks, and compare uncertainty estimates among low-, high- and multifidelity approaches.

AdaAnn: Adaptive Annealing Scheduler for Probability Density Approximation

Approximating probability distributions can be a challenging task, particularly when they are supported over regions of high geometrical complexity or exhibit multiple modes. Annealing can be used to facilitate this task which is often combined with constant a priori selected increments in inverse temperature. However, using constant increments limit the computational efficiency due to the inability to adapt to situations where smooth changes in the annealed density could be handled equally well with larger increments. We introduce AdaAnn, an adaptive annealing scheduler that automatically adjusts the temperature increments based on the expected change in the Kullback-Leibler divergence between two distributions with a sufficiently close annealing temperature. AdaAnn is easy to implement and can be integrated into existing sampling approaches such as normalizing flows for variational inference and Markov chain Monte Carlo. We demonstrate the computational efficiency of the AdaAnn scheduler for variational inference with normalizing flows on a number of examples, including density approximation and parameter estimation for dynamical systems.

An analysis of reconstruction noise from undersampled 4D flow MRI

Novel Magnetic Resonance (MR) imaging modalities can quantify hemodynamics but require long acquisition times, precluding its widespread use for early diagnosis of cardiovascular disease. To reduce the acquisition times, reconstruction methods from undersampled measurements are routinely used, that leverage representations designed to increase image compressibility. Reconstructed anatomical and hemodynamic images may present visual artifacts. Although some of these artifact are essentially reconstruction errors, and thus a consequence of undersampling, others may be due to measurement noise or the random choice of the sampled frequencies. Said otherwise, a reconstructed image becomes a random variable, and both its bias and its covariance can lead to visual artifacts; the latter leads to spatial correlations that may be misconstrued for visual information. Although the nature of the former has been studied in the literature, the latter has not received as much attention. In this study, we investigate the theoretical properties of the random perturbations arising from the reconstruction process, and perform a number of numerical experiments on simulated and MR aortic flow. Our results show that the correlation length remains limited to two to three pixels when a Gaussian undersampling pattern is combined with recovery algorithms based on $\ell_1$-norm minimization. However, the correlation length may increase significantly for other undersampling patterns, higher undersampling factors (i.e., 8x or 16x compression), and different reconstruction methods.