Cardiac digital twins provide a physics and physiology informed framework to
deliver predictive and personalized medicine. However, high-fidelity
multi-scale cardiac models remain a barrier to adoption due to their extensive
computational costs and the high number of model evaluations needed for
patient-specific personalization. Artificial Intelligence-based methods can
make the creation of fast and accurate whole-heart digital twins feasible. In
this work, we use Latent Neural Ordinary Differential Equations (LNODEs) to
learn the temporal pressure-volume dynamics of a heart failure patient. Our
surrogate model based on LNODEs is trained from 400 3D-0D whole-heart
closed-loop electromechanical simulations while accounting for 43 model
parameters, describing single cell through to whole organ and cardiovascular
hemodynamics. The trained LNODEs provides a compact and efficient
representation of the 3D-0D model in a latent space by means of a feedforward
fully-connected Artificial Neural Network that retains 3 hidden layers with 13
neurons per layer and allows for 300x real-time numerical simulations of the
cardiac function on a single processor of a standard laptop. This surrogate
model is employed to perform global sensitivity analysis and robust parameter
estimation with uncertainty quantification in 3 hours of computations, still on
a single processor. We match pressure and volume time traces unseen by the
LNODEs during the training phase and we calibrate 4 to 11 model parameters
while also providing their posterior distribution. This paper introduces the
most advanced surrogate model of cardiac function available in the literature
and opens new important venues for parameter calibration in cardiac digital
twins.

本文提出了一种基于 LNODEs 的心脏数字孪生代理模型，并且使用全局敏感度分析和鲁棒参数估计，实现了未知时间系列的模拟和参数校准。

使用潜变量神经常微分方程进行实时全心脏电机模拟

Real-time whole-heart electromechanical simulations using Latent Neural  Ordinary Differential Equations

Brittle optimization has been observed to adversely impact model likelihoods
for regression and VAEs when simultaneously fitting neural network mappings
from a (random) variable onto the mean and variance of a dependent Gaussian
variable. Previous works have bolstered optimization and improved likelihoods,
but fail other basic posterior predictive checks (PPCs). Under the PPC
framework, we propose critiques to test predictive mean and variance
calibration and the predictive distribution's ability to generate sensible
data. We find that our attractively simple solution, to treat heteroscedastic
variance variationally, sufficiently regularizes variance to pass these PPCs.
We consider a diverse gamut of existing and novel priors and find our methods
preserve or outperform existing model likelihoods while significantly improving
parameter calibration and sample quality for regression and VAEs.

本文使用后验预测检测框架，提出了一种简单但有效的解决方案，用于同时拟合神经网络映射从随机变量到一个服从高斯分布的变量的均值和方差。这种方法有效地规范了方差，保持或优于现有模型可能性，同时显著提高了回归和 VAEs 的参数校准和样本质量。