publications

2023

1. Convolutional Echo State Networks for Forecasting Complex Spatiotemporal Dynamics

   Shahi, Shahrokh, Fenton, Flavio H., and Cherry, Elizabeth M.

   Preprint 2023

2022

1. Robust Reservoir Computing Approaches for Predicting Cardiac Electrical Dynamics

   Shahi, Shahrokh

   Georgia Institute of Technology, SMARTech, PhD Dissertations 2022

   Abs HTML

   Computational modeling of cardiac electrophysiological signaling is of vital importance in understanding, preventing, and treating life-threatening arrhythmias. Traditionally, mathematical models incorporating physical principles have been used to study cardiac dynamical systems and can generate mechanistic insights, but their predictions are often quantitatively inaccurate due to model complexity, the lack of observability in the system, and variability within individuals and across the population. In contrast, machine-learning techniques can learn directly from training data, which in this context are time series of observed state variables, without prior knowledge of the system dynamics. The reservoir computing framework, a learning paradigm derived from recurrent neural network concepts and most commonly realized as an echo state network (ESN), offers a streamlined training process and holds promise to deliver more accurate predictions than mechanistic models. Accordingly, this research aims to develop robust ESN-based forecasting approaches for nonlinear cardiac electrodynamics, and thus presents the first application of machine-learning, and deep-learning techniques in particular, for modeling the complex electrical dynamics of cardiac cells and tissue. To accomplish this goal, we completed a set of three projects. (i) We compared the performance of available mainstream techniques for prediction with that of the baseline ESN approach along with several new ESN variants we proposed, including a physics-informed hybrid ESN. (ii) We proposed a novel integrated approach, the autoencoder echo state network (AE-ESN), that can accurately forecast the long-term future dynamics of cardiac electrical activity. This technique takes advantage of the best characteristics of both gated recurrent neural networks and ESNs by integrating a long short-term memory (LSTM) autoencoder into the ESN framework to improve reliability and robustness. (iii) We extended the long-term prediction of cardiac electrodynamics from a single cardiac cell to the tissue level, where, in addition to the temporal information, the data includes spatial dimensions and diffusive coupling. Building on the main design idea of the AE-ESN, a convolutional autoencoder was equipped with an ESN to create the Conv-ESN technique, which can process the spatiotemporal data and effectively capture the temporal dependencies between samples of data. Using these techniques, we forecast cardiac electrodynamics for a variety of datasets obtained in both in silico and in vitro experiments. We found that the proposed integrated approaches provide robust and computationally efficient techniques that can successfully predict the dynamics of electrical activity in cardiac cells and tissue with higher prediction accuracy than mainstream deep-learning approaches commonly used for predicting temporal data. On the application side, our approaches provide accurate forecasts over clinically useful time periods that could allow prediction of electrical problems with sufficient time for intervention and thus may support new types of treatments for some kinds of heart disease.

2. A Machine-learning Approach for Long-term Prediction of Experimental Cardiac Action Potential Time Series Using an Autoencoder and Echo State Networks (Selected as Featured Article by the Editors 🎖)

   Shahi, Shahrokh, Fenton, Flavio H., and Cherry, Elizabeth M.

   Chaos: An Interdisciplinary Journal of Nonlinear Science. 2022

   Abs HTML PDF Blog

   Computational modeling and experimental/clinical prediction of the complex signals during cardiac arrhythmias have the potential to lead to new approaches for prevention and treatment. Machine-learning (ML) and deep-learning approaches can be used for time-series forecasting and have recently been applied to cardiac electrophysiology. While the high spatiotemporal nonlinearity of cardiac electrical dynamics has hindered application of these approaches, the fact that cardiac voltage time series are not random suggests that reliable and efficient ML methods have the potential to predict future action potentials. This work introduces and evaluates an integrated architecture in which a long short-term memory autoencoder (AE) is integrated into the echo state network (ESN) framework. In this approach, the AE learns a compressed representation of the input nonlinear time series. Then, the trained encoder serves as a feature-extraction component, feeding the learned features into the recurrent ESN reservoir. The proposed AE-ESN approach is evaluated using synthetic and experimental voltage time series from cardiac cells, which exhibit nonlinear and chaotic behavior. Compared to the baseline and physics-informed ESN approaches, the AE-ESN yields mean absolute errors in predicted voltage 6–14 times smaller when forecasting approximately 20 future action potentials for the datasets considered. The AE-ESN also demonstrates less sensitivity to algorithmic parameter settings. Furthermore, the representation provided by the feature-extraction component removes the requirement in previous work for explicitly introducing external stimulus currents, which may not be easily extracted from real-world datasets, as additional time series, thereby making the AE-ESN easier to apply to clinical data.

3. Prediction of Chaotic Time Series Using Recurrent Neural Networks and Reservoir Computing Techniques: A Comparative Study

   Shahi, Shahrokh, Fenton, Flavio H., and Cherry, Elizabeth M.

   Machine Learning with Applications, Elsevier 2022

   Abs HTML PDF

   In recent years, machine-learning techniques, particularly deep learning, have outperformed traditional time-series forecasting approaches in many contexts, including univariate and multivariate predictions. This study aims to investigate the capability of (i) gated recurrent neural networks, including long short-term memory (LSTM) and gated recurrent unit (GRU) networks, (ii) reservoir computing (RC) techniques, such as echo state networks (ESNs) and hybrid physics-informed ESNs, and (iii) the nonlinear vector autoregression (NVAR) approach, which has recently been introduced as the next generation RC, for the prediction of chaotic time series and to compare their performance in terms of accuracy, efficiency, and robustness. We apply the methods to predict time series obtained from two widely used chaotic benchmarks, the Mackey-Glass and Lorenz-63 models, as well as two other chaotic datasets representing a bursting neuron and the dynamics of the El Nino Southern Oscillation, and to one experimental dataset representing a time series of cardiac voltage with complex dynamics. We find that even though gated RNN techniques have been successful in forecasting time series generally, they can fall short in predicting chaotic time series for the methods, datasets, and ranges of hyperparameter values considered here . In contrast, for the chaotic datasets studied, we found that reservoir computing and NVAR techniques are more computationally efficient and offer more promise in long-term prediction of chaotic time series.

2021

1. Long-Time Prediction of Arrhythmic Cardiac Action Potentials Using Recurrent Neural Networks and Reservoir Computing

   Shahi, Shahrokh, Marcotte, Christopher, Herndon, Conner, Fenton, Flavio H., Shiferaw, Yohannes, and Cherry, Elizabeth M.

   Frontiers in Physiology, Nonlinear Analysis and Machine Learning in Cardiology 2021

   Abs HTML PDF Blog

   The electrical signals triggering the heart's contraction are governed by nonlinear processes that can produce complex irregular activity, especially during or preceding the onset of cardiac arrhythmias. Forecasts of cardiac voltage time series in such conditions could allow new opportunities for intervention and control but would require efficient computation of highly accurate predictions. Although machine-learning (ML) approaches hold promise for delivering such results, nonlinear time-series forecasting poses significant challenges. In this manuscript, we study the performance of two recurrent neural network (RNN) approaches along with echo state networks (ESNs) from the reservoir computing (RC) paradigm in predicting cardiac voltage data in terms of accuracy, efficiency, and robustness. We show that these ML time-series prediction methods can forecast synthetic and experimental cardiac action potentials for around 15 beats with a high degree of accuracy, with ESNs typically two orders of magnitude faster than RNN approaches for the same network size.

2. Robust Reservoir Computing Approaches for Predicting Cardiac Wave Dynamics

   Shahi, Shahrokh, Marcotte, Christopher, Shiferaw, Yohannes, and Cherry, Elizabeth M.

   In SIAM Conference on Computational Science and Engineering (CSE21) 2021

   Abs

   Computational modeling of cardiac electrophysiological signaling is of great importance in understanding, preventing, and treating life-threatening arrhythmias. To address fundamental limitations in conventional modeling approaches such as mathematical models and data-assimilation techniques, and to leverage the potential of machine-learning techniques in providing new insights from highly spatiotemporal cardiac data, a novel robust computational machine-learning approach is presented in which knowledge-based models are integrated with a reservoir-computing framework to build a reliable predictive model for reconstructing and analyzing the complex dynamics of cardiac electrical waves. In this hybrid approach, the input layer of an echo state network (ESN) is driven by (i) the measured data obtained through experiments and (ii) well-established knowledge-based PDE models describing non-measurable quantities. The input signals are fed, together with a set of weights, into a sub-population of the reservoir nodes. By construction, the reservoir provides a discrete-time dynamical system generated by a randomized basis expansion. The outputs of a subset of the reservoir nodes are fed into the output layer, which observes the state of the reservoir. We present a set of examples to illustrate and verify the accuracy and applicability of the proposed approach for cardiac electrical wave dynamics.

3. Time Series Prediction Using Recurrent Neural Networks and Reservoir Computing Techniques: A Comparative Study

   Shahi, Shahrokh, Fenton, Flavio, Shiferaw, Yohannes, and Cherry, Elizabeth M.

   In SIAM Conference on Applications of Dynamical Systems, 2021 (DS21) 2021

   Abs Slides

   Reservoir computing (RC) approaches have been developed to overcome the inherent limitations of conventional recurrent neural networks (RNNs), which are notoriously difficult and computationally expensive to train in complex dynamical domains, such as time-series forecasting. Echo state networks (ESNs) are a popular realization of the RC paradigm where a reservoir of randomly connected neurons provides a discrete-time nonlinear dynamical system, and the training efforts remain limited to obtaining the output layer weights. Despite their success in providing an efficient approach for processing nonlinear temporal data, the ESN performance depends heavily on the network parameters and the hyperparameter values used for building the network. Therefore, some complex and expensive RNNs, such as long short-term memory (LSTM) networks, may still be preferred over ESNs in time-series prediction tasks. This work compares RNN and RC techniques by evaluating the performance of ESNs and LSTMs in forecasting cardiac action potential dynamics in terms of prediction accuracy, computational cost, and robustness. We highlight the circumstances in which one approach is preferred over another and provide a reference for choosing the right model for forecasting time series like action potentials that, to the best of our knowledge, is missing in the literature.

2020

1. An Integrated Interval Neural Network for Uncertainty Modeling in Inhomogeneous Materials

   Shahi, Shahrokh, Muhanna, Rafi L, and Fedele, Francesco

   In Reliable Engineering Computing, Risk and Uncertainty in Engineering Computation 2020

   Abs

   Engineering fields rely heavily on the Finite Element Method (FEM) as a modeling tool in deterministic systems where no uncertainty is introduced. The effects of uncertainty are of growing concern in the analysis and design of engineering structures and need to be studied to improve the predictability of mathematical models. Recently, in addition to others, Interval Finite Element Method (IFEM) has been introduced to account for uncertainties by incorporating interval arithmetic into the conventional FEM formulation, in which all uncertain parameters are defined as intervals. Nonetheless, in combination with complexity of structures and inhomogeneous materials, the computational and experimental cost remains an inevitable issue in such simulations. This work aims at integrating Artificial Neural Networks (ANN) and IFEM techniques to establish a flexible and efficient approach for modeling uncertainties in general inhomogeneous structures, in which an Interval Neural Network (INN) is employed as a substitution for the conventional constitutive material model to establish a homogenized representation of structures regardless of material complexity. In this approach, at first, the required dataset is generated by creating and running a set of IFEM simulations. The INN will then be trained to predict the homogenized mechanical behavior of the structure as a function of independent parameters. Afterwards, the trained INN will be integrated in the IFEM procedure to obtain the system’s response under uncertainty. The proposed approach is applied to a set of engineering problems to illustrate and verify the capabilities of the methodology.

2. Uncertainty in Boundary Conditions—An Interval Finite Element Approach (The best student paper award 🎖)

   Muhanna, Rafi L, and Shahi, Shahrokh

   In Decision Making under Constraints 2020

   HTML Blog

2016

1. Algorithms for Graph Partitioning

   Shahi, Shahrokh

   MSc degree in Computer Science, Graduated with Distinction, Imperial College London 2016

   Abs PDF Blog

   Graph partitioning is a fundamental algorithmic problem in combinatorics moti- vated by applications such as clustering and community detection in social networks as well as theoretical importance in particular in spectral methods and the Unique Games Conjecture in computational complexity. The main theme in this problem is the following: Given a graph consisting of a collection of loosely connected dense subgraphs, design an efficient algorithm to detect, either exactly or approximately, the underlying dense subgraphs. There are many variations of the problem, ranging from information theoretic possibility of discovering the communities to efficient algorithms for doing so as well as local walk and distributed models for the algorithmic task. In this research, a systematic study of the major techniques and discoveries in this area has been conducted with an emphasis on the methods based on the spectral graph theory. In the last years, spectral graph partitioning approaches have become very popular and there has been a growing interest in their applications, mainly on account of their efficiency and mathematical elegance. Therefore, the main concepts of the spectral partitioning algorithms are comprehensively discussed in this research and some novel applications of these methods have been concluded at the end.

2015

1. A Study on the Effect of Collagen Fiber Orientation on Mechanical Response of Soft Biological Tissues

   Fathi, Farshid, Shahi, Shahrokh, and Mohammadi, Soheil

   Jurnal Teknologi 2015

   HTML

2013

1. A Multiscale Finite Element Simulation of Human Aortic Heart Valve

   Shahi, Shahrokh, and Mohammadi, Soheil

   In Applied Mechanics and Materials 2013

   HTML Blog
2. A comparative study of transversely isotropic material models for prediction of mechanical behavior of the aortic valve leaflet

   Shahi, Shahrokh, and Mohammadi, Soheil

   International Journal of Research in engineering and Technology 2013

   HTML