Finite Element Fictitious Domain Method for Elliptic PDEs Over Curved-Complex Domains Swapnil Kale, Debasish Pradhan Mathematical Methods in the Applied Sciences, 2025 This study uses a simple uniform Cartesian mesh and finite element method with a penalty approach to decipher elliptic PDEs defined over curved‐complex domains, irrespective of the boundary trajectory. The convergence of the solution of the penalized problem to the original solution is equipped with the discrete error estimates in the and norms in terms of the penalty parameter and mesh size . Numerical investigations performed on different types of domain confirm the applicability and efficiency of the proposed method and validate the theoretical results.
Forecasting of financial time series data possessing stable distributions by employing Stochastic Differential Equations: A review Pratibha Bhandari, Neelesh S Upadhye, Debasish Pradhan 2023 IEEE Pune Section International Conference Punecon 2023, 2023 The paper acknowledges the complex behaviour of time series data, renowned for its inherent chaotic nature and inclination towards sudden, significant high jumps. To address such intricate data, the incorporation of stochastic differential equations (SDEs) with noise can be done to accurately represent the data and its inherent traits. To better comprehend the distribution sustained by the data, the paper explores the realms of stable distribution, particularly relevant for data exhibiting heavier tails. Therefore, this review highlights the utility of modelling white noise within the frame work of a non-Gaussian distribution governed by Lévy motion. In this context, it proposes using alpha stable Lévy motion due to its remarkable ability to closely mirror the data's characteristics. Thus harmonizing the noise modelling process with the data's intricate dynamics. It aims at the techniques proposed in various research papers and discerning the most effective approach for analyzing financial time series data. Additionally, it also outlines the major improvements and future implementations in this domain.
Classification of Corona Virus Infected Chest X-ray using Deep Convolutional Neural Network Nitish Patel, Debasish Pradhan 2021 International Conference on Intelligent Technologies Conit 2021, 2021 The coronavirus 2019 is a worldwide pandemic declared by the world health organization (WHO). It starts in China, Wuhan in November 2019 and spread all over the world. As time passed, the detection and clinical treatment of COVID-19 is developed by the researchers. COVID-19 is detected using a reverse transcription-polymerase chain reaction (RT-PCR) test, which is precise but requires two days to complete. Hence, the researchers proposed many classification models, which are mainly based on artificial intelligence. Mainly these classification models are using chest X-ray images for the detection of COVID-19. In this paper, we proposed a deep convolutional neural network model architecture to classify chest X-ray images. We called this model the base model, which is the first train to classify normal and abnormal chest X-ray images. Using the transfer learning technique, we retrained this model for four-classes classification (i.e., Normal, COVID-19, Pneumonia, and Pneumothorax). We obtain 73.9% accuracy for the base model (i.e., binary classification) and 83.2% accuracy for fine-tuned model (i.e., four-classes classification).
Parametric profiling of water-jet projectiles for eod disruptor using high-speed imaging technique Proceedings 31st International Symposium on Ballistics Ballistics 2019, 2019
