Naresh Kumar

Sahar Al Ajmi, Khizar Hayat, Alaa M. Al Obaidi et al.

Audio is one of the most used ways of human communication, but at the same time it can be easily misused to trick people. With the revolution of AI, the related technologies are now accessible to almost everyone, thus making it simple for the criminals to commit crimes and forgeries. In this work, we introduce a neural network method to develop a classifier that will blindly classify an input audio as real or mimicked; the word 'blindly' refers to the ability to detect mimicked audio without references or real sources. We propose a deep neural network following a sequential model that comprises three hidden layers, with alternating dense and drop out layers. The proposed model was trained on a set of 26 important features extracted from a large dataset of audios to get a classifier that was tested on the same set of features from different audios. The data was extracted from two raw datasets, especially composed for this work; an all English dataset and a mixed dataset (Arabic plus English) (The dataset can be provided, in raw form, by writing an email to the first author). For the purpose of comparison, the audios were also classified through human inspection with the subjects being the native speakers. The ensued results were interesting and exhibited formidable accuracy, as we were able to get at least 94% correct classification of the test cases, as against the 85% accuracy in the case of human observers.

Arushi Arushi, Naresh Kumar

Particle breakage due to collisional interactions plays a vital role in the development of several phenomena in science and engineering. The nonlinear collisional breakage equations (NCBEs) are a significant set of equations in this context. Solving the NCBE is computationally challenging due to its nonlinearity, high dimensionality, and complex kernel interactions. Solving NCBE problems is more complex in two- and three-dimensional problems. In these problems, it is more challenging to evaluate multidimensional moments and integrals, maintain solution stability, and achieve computational efficiency. Despite the importance of the NCBE in science and engineering, the development of efficient numerical methods for solving it in two- and three-dimensional problems has not been adequately explored. In this work, we have introduced a new framework for solving the NCBE across multiple dimensions using the conformal finite element method (FEM). To the best of our knowledge, this is the first work to solve the NCBE using the conformal FEM. The new framework employs high-order Lagrange elements in conjunction with the BDF2 scheme for time discretization. The present method preserves the important physical quantities such as the total count and hypervolume of the population particles. Convergence results for error estimates have also been derived for both semidiscrete and fully discrete schemes. Numerical experiments have been carried out for one-, two-, and three-dimensional problems. The numerical experiments have shown that the proposed method achieved high accuracy, optimal convergence rates, and computational efficiency.

Naresh Kumar, Seba Susan

Epidemiological models are best suitable to model an epidemic if the spread pattern is stationary. To deal with non-stationary patterns and multiple waves of an epidemic, we develop a hybrid model encompassing epidemic modeling, particle swarm optimization, and deep learning. The model mainly caters to three objectives for better prediction: 1. Periodic estimation of the model parameters. 2. Incorporating impact of all the aspects using data fitting and parameter optimization 3. Deep learning based prediction of the model parameters. In our model, we use a system of ordinary differential equations (ODEs) for Susceptible-Infected-Recovered-Dead (SIRD) epidemic modeling, Particle Swarm Optimization (PSO) for model parameter optimization, and stacked-LSTM for forecasting the model parameters. Initial or one time estimation of model parameters is not able to model multiple waves of an epidemic. So, we estimate the model parameters periodically (weekly). We use PSO to identify the optimum values of the model parameters. We next train the stacked-LSTM on the optimized parameters, and perform forecasting of the model parameters for upcoming four weeks. Further, we fed the LSTM forecasted parameters into the SIRD model to forecast the number of COVID-19 cases. We evaluate the model for highly affected three countries namely; the USA, India, and the UK. The proposed hybrid model is able to deal with multiple waves, and has outperformed existing methods on all the three datasets.

Arushi, Naresh Kumar

In this work, we develop and analyze a higher-order finite element method for the multidimensional fragmentation equation. To the best of our knowledge, this is the first study to establish a rigorous, conforming finite element framework for high-order spatial approximation of multidimensional fragmentation models. The scheme is formulated in a variational setting, and its stability and convergence properties are derived through a detailed mathematical analysis. In particular, the $L^2$ projection operator is used to obtain optimal-order spatial error estimates under suitable regularity assumptions on the exact solution. For temporal discretization, a second-order backward differentiation formula (BDF2) is adopted, yielding a fully discrete scheme that achieves second-order convergence in time. The theoretical analysis establishes $ L^2$-optimal convergence rates of ${\cal O}(h^{r+1})$ in space, together with second-order accuracy in time. The theoretical findings are validated through a series of numerical experiments in two and three space dimensions. The computational results confirm the predicted error estimates and demonstrate the robustness of the proposed method for various choices of fragmentation kernels and selection functions.