Implementation and Calibration of a Deep Neural Network to Predict Parameters of Left Ventricular Systolic Function Based on Pulmonary and Systemic Arterial Pressure Signals

The evaluation of cardiac contractility by the assessment of the ventricular systolic elastance function is clinically challenging and cannot be easily obtained at the bedside. In this work, we present a framework characterizing left ventricular systolic function from clinically readily available data, including systemic and pulmonary arterial pressure signals. We implemented and calibrated a deep neural network (DNN) consisting of a multi-layer perceptron with 4 fully connected hidden layers and with 16 neurons per layer, which was trained with data obtained from a lumped model of the cardiovascular system modeling different levels of cardiac function. The lumped model included a function of circulatory autoregulation from carotid baroreceptors in pulsatile conditions. Inputs for the DNN were systemic and pulmonary arterial pressure curves. Outputs from the DNN were parameters of the lumped model characterizing left ventricular systolic function, especially end-systolic elastance. The DNN adequately performed and accurately recovered the relevant hemodynamic parameters with a mean relative error of less than 2%.Therefore, our framework can easily provide complex physiological parameters of cardiac contractility, which could lead to the development of invaluable tools for the clinical evaluation of patients with severe cardiac dysfunction.

Adaptive Mitigation: Identification of the Dynamic Drivers of Effective Policy during the COVID-19 Pandemic

Thierry Bossy

Introduction: The unprecedented speed and scale of the COVID-19 pandemic necessitated the rapid implementation of untested public health measures to mitigate the consequences of viral spread. In the 8 months that have passed since the first recognized case, an enormous amount of research has been published evaluating the efficacy of the various policies implemented by different countries, however the majority of these studies focus on a specific region or time, over-representing high-income countries during periods of extreme transmission or “peak events”. The aim of this study is to provide a more general analysis that considers a global scope of the pandemic and the dynamic drivers that build effective policies to mitigate human interactions and slow the spread of disease. Methods: We collected a range of information regarding epidemic trends, weather, demographics, government response and mobility reports across the globe. We then built an hybrid Neural Network that combined an LSTM layer with a multilayer perceptron to infer the reproduction number from various non-epidemiological factors. The model was designed to predict the reproduction number (R-value) on 93 countries with available data and compare it to our ground truth estimate obtained from officially reported epidemiological data. Finally, we used an alternative model to assess the impact of public health measures on the epidemic. Findings: From the available features, we obtained the best performances using demographics combined with mobility features. The sanitary indices (beds/thousand, diabetes prevalence, ...) did not help the prediction and, more interestingly, the pressure indicator of historical weather forecast improved the prediction of the reproduction number by about 4.5%. This optimized model predicted the reproduction number with a mean absolute error of 0.254 across the 93 countries over the time of the epidemic. For many countries (Switzerland, United Kingdom, South Africa, ...) this error passed below 0.17. An alternative version of the model allowed us to estimate the impact of policies in terms of average reduction in reproduction number, and more importantly, allowed us to compare these trends between countries. For instance, we observe that the model showed that no policy had a positive impact in India as opposed to Switzerland, where most of them are associated to improved epidemic control. Conclusion: Understanding these complex interactions may allow individuals and policy makers to better adapt mitigation strategies to optimize the efficacy of the implemented policies.

2020

Inverse Modelling and Predictive Inference in Continuum Mechanics: a Data-Driven Approach

Claire Marianne Charlotte Capelo

The explosive growth of machine learning in the age of data has led to a new probabilistic and data-driven approach to solving very different types of problems. In this paper we study the feasibility of using such data-driven algorithms to solve classic physical and mathematical problems. In particular, we try to model the solution of an inverse continuum mechanics problem in the context of linear elasticity using deep neural networks. To better address the inverse function, we start first by studying the simplest related task,consisting of a building block of the actual composite problem. By empirically proving the learnability of simpler functions, we aim to draw conclusions with respect to the initial problem.The basic inverse problem that motivates this paper is that of a 2D plate with inclusion under specific loading and boundary conditions. From measurements at static equilibrium,we wish to recover the position of the hole. Although some analytical solutions have been formulated for 3D-infinite solids - most notably Eshelby’s inclusion problems - finite problems with particular geometries, material inhomogeneities, loading and boundary conditions require the use of numerical methods which are most often efficient solutions to the forward problem, the mapping from the parameter space to the measurement/signal space, i.e. in our case computing displacements and stresses knowing the size and position of the inclusion. Using numerical data generated from the well-defined forward problem,we train a neural network to approximate the inverse function relating displacements and stresses to the position of the inclusion. The preliminary results on the 2D-finite problem are promising, but the black-box nature of neural networks is a huge issue when it comes to understanding the solution.For this reason, we study a 3D-infinite continuous isotropic medium with unique concentrated load, for which the Green’s function gives an analytical mathematical expression relating relative position of the point force and the displacements in the solid. After de-riving the expression of the inverse, namely recovering the relative position of the force from the Green’s matrix computed at a given point in the medium, we are able to study the sensitivity of the inverse function. From both the expression of the Green’s function and its inverse, we highlight what issues might arise when training neural networks to solve the inverse problem. As the Green’s function is not bijective, bijection must been forced when training for regression. Moreover, due to displacements growing to infinity as we approach the singularity at zero, the training domain must be constrained to be some distance away from the singularity. As we train a neural network to fit the inverse of the Green’s function, we show that the input parameters should include the least possible redundant information to ensure the most efficient training.We then extend our analysis to two point forces. As more loads are added, bijection is harder to enforce as permutations of forces must be taken into account and more collisions may arise, i.e. multiple specific combinations of forces might yield the same measurements.One obvious solution is to increase the number of nodes where displacements are measured to limit the possibility of collision. Through new experiments, we show again that the best training is achieved for the least possible amount of nodes, as long as the training data generated is indeed bijective. As the medium is elastic, we propose a neural network architecture that matches the composite nature of the inverse problem. We also present another formulation of the problem which is invariant to permutations of the forces,namely multilabel classification, and yields good performance in the two-load case.Finally, we study the composite inverse function for 2, 3, 4 and 5 forces. By comparing training and accuracy for different neural network architectures, we expose the model easiest to train. Moreover, the evolution of the final accuracy as more loads are added indicates that deep-neural networks (DNNs) are not well suited to fit a non-linear mapping from and to a high-dimensional space. The results are more convincing for multilabel classification.

2020

POSEIDON: Privacy-Preserving Federated Neural Network Learning

Jean-Philippe Léonard Bossuat, David Jules Froelicher, Joao André Gomes de Sá E Sousa, Jean-Pierre Hubaux, Apostolos Pyrgelis, Sinem Sav, Juan Ramón Troncoso-Pastoriza

In this paper, we address the problem of privacy-preserving training and evaluation of neural networks in an N-party, federated learning setting. We propose a novel system, POSEIDON, the first of its kind in the regime of privacy-preserving neural network training. It employs multiparty lattice-based cryptography to preserve the confidentiality of the training data, the model, and the evaluation data, under a passive-adversary model and collusions between up to N - 1 parties. To efficiently execute the secure backpropagation algorithm for training neural networks, we provide a generic packing approach that enables Single Instruction, Multiple Data (SIMD) operations on encrypted data. We also introduce arbitrary linear transformations within the cryptographic bootstrapping operation, optimizing the costly cryptographic computations over the parties, and we define a constrained optimization problem for choosing the cryptographic parameters. Our experimental results show that POSEIDON achieves accuracy similar to centralized or decentralized non-private approaches and that its computation and communication overhead scales linearly with the number of parties. POSEIDON trains a 3-layer neural network on the MNIST dataset with 784 features and 60K samples distributed among 10 parties in less than 2 hours.

INTERNET SOC2021

Inverse Modelling and Predictive Inference in Continuum Mechanics: a Data-Driven Approach

Claire Marianne Charlotte Capelo

2020

Adaptive Mitigation: Identification of the Dynamic Drivers of Effective Policy during the COVID-19 Pandemic

Thierry Bossy

2020