29 research outputs found
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
Uncertainty quantification in virtual surgery hemodynamics predictions for single ventricle palliation.
International audienceThe adoption of simulation tools to predict surgical outcomes is increasingly leading to questions about the variability of these predictions in the presence of uncertainty associated with the input clinical data. In the present study, we propose a methodology for full propagation of uncertainty from clinical data to model results that, unlike deterministic simulation, enables estimation of the confidence associated with model predictions.We illustrate this problem in a virtual stage II single ventricle palliation surgery example. First, probability density functions (PDFs) of right pulmonary artery (PA) flow split ratio and average pulmonary pressure are determined from clinical measurements, complemented by literature data. Starting from a zero dimensional semi-empirical approximation, Bayesian parameter estimation is used to find the distributions of boundary conditions that produce the expected PA flow split and average pressure PDFs as pre-operative model results. To reduce computational cost, this inverse problem is solved using a Kriging approximant. Second, uncertainties in the boundary conditions are propagated to simulation predictions. Sparse grid stochastic collocation is employed to statistically characterize model predictions of post-operative hemodynamics in models with and without PA stenosis. The results quantify the statistical variability in virtual surgery predictions, allowing for placement of confidence intervals on simulation outputs
Uncertainty quantification in virtual surgery hemodynamics predictions for single ventricle palliation.
International audienceThe adoption of simulation tools to predict surgical outcomes is increasingly leading to questions about the variability of these predictions in the presence of uncertainty associated with the input clinical data. In the present study, we propose a methodology for full propagation of uncertainty from clinical data to model results that, unlike deterministic simulation, enables estimation of the confidence associated with model predictions.We illustrate this problem in a virtual stage II single ventricle palliation surgery example. First, probability density functions (PDFs) of right pulmonary artery (PA) flow split ratio and average pulmonary pressure are determined from clinical measurements, complemented by literature data. Starting from a zero dimensional semi-empirical approximation, Bayesian parameter estimation is used to find the distributions of boundary conditions that produce the expected PA flow split and average pressure PDFs as pre-operative model results. To reduce computational cost, this inverse problem is solved using a Kriging approximant. Second, uncertainties in the boundary conditions are propagated to simulation predictions. Sparse grid stochastic collocation is employed to statistically characterize model predictions of post-operative hemodynamics in models with and without PA stenosis. The results quantify the statistical variability in virtual surgery predictions, allowing for placement of confidence intervals on simulation outputs