Below is a list of latest publications and presentations. Additional information including PDFs, slides, and codes will gradually be added in the near future.

## 2021

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

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

2021

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.

Robust Reservoir Computing Approaches for Predicting Cardiac Wave Dynamics

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

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

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.

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 Presented in SIAM Conference on Applications of Dynamical Systems, 2021 (DS21)*
2021

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.

An Integrated Interval Neural Network for Uncertainty Modeling in Inhomogeneous Materials

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

*In *
2021

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.

## 2020

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

## 2015

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

## 2013

A Multiscale Finite Element Simulation of Human Aortic Heart Valve

*Shahi, Shahrokh*,
and Mohammadi, Soheil

*In Applied Mechanics and Materials*
2013

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