Sandip V. George

Gevik Grigorian, Sandip V. George, Simon Arridge

Data-driven modelling and scientific machine learning have been responsible for significant advances in determining suitable models to describe data. Within dynamical systems, neural ordinary differential equations (ODEs), where the system equations are set to be governed by a neural network, have become a popular tool for this challenge in recent years. However, less emphasis has been placed on systems that are only partially-observed. In this work, we employ a hybrid neural ODE structure, where the system equations are governed by a combination of a neural network and domain-specific knowledge, together with symbolic regression (SR), to learn governing equations of partially-observed dynamical systems. We test this approach on two case studies: A 3-dimensional model of the Lotka-Volterra system and a 5-dimensional model of the Lorenz system. We demonstrate that the method is capable of successfully learning the true underlying governing equations of unobserved states within these systems, with robustness to measurement noise.

Camilo Quiceno Quintero, Sandip Varkey George

The complex dynamics of the heart are reflected in its electrical activity, captured through electrocardiograms (ECGs). In this study we use nonlinear time series analysis to understand how ECG complexity varies with cardiac pathology. Using the large PTB-XL dataset, we extracted nonlinear measures from lead II ECGs, and cross-channel metrics (leads II, V2, AVL) using Spearman correlations and mutual information. Significant differences between diseased and healthy individuals were found in almost all measures between healthy and diseased classes, and between 5 diagnostic superclasses ($p<.001$). Moreover, incorporating these complexity quantifiers into machine learning models substantially improved classification accuracy measured using area under the ROC curve (AUC) from 0.86 (baseline) to 0.87 (nonlinear measures) and 0.90 (including cross-time series metrics).