Machine Intelligence Modeling for Dynamical Problems

Abstract

Artificial intelligence (AI) has been a subject of intense media hype in the 21st century. In the last decade, AI has taken the world by storm, showing its potential to revolutionize public services, industries, legal, finance, and defence sectors by surpassing human levels of accuracy for a variety of applications. Major companies and startups around the globe are developing intelligent products and services with the help of AI techniques. Applications of AI can be observed in Tesla, Apple’s Siri, Amazon’s Alexa, and the newly introduced ChatGPT and Google Gemini. Some of the AI techniques include Artificial Neural Networks (ANNs), Experts Systems, Robotics, Natural Language Processing, and Fuzzy logic have shown exponential growth. However, the most successful AI technique, which has been influencing science and technology over the decades is ANNs. Furthermore, ANN has increasingly been used in highly sensitive areas such as healthcare, weather forecasting, biomedical informatics and criminal justice for high-stakes prediction that have a significant impact on human lives. As regards, machine intelligence (MI) techniques for handling multimodal dynamic systems have achieved a flurry of research and experienced rapid evolution. In the real world scenario, the dynamical systems are governed by different types of differential, integral and algebraic equations. Various numerical techniques such as the Euler, Runge-Kutta, finite element, finite volume, homotopy perturbation, homotopy transformation, and Adomian decomposition methods have effectively been employed to obtain the solutions of these dynamical problems. Despite the well-documented success of these aforementioned traditional methods, it is still evident that they are insufficient for addressing a variety of real-world non-linear problems. Additionally, each of these traditional methods possesses its own intrinsic value, limitations and applicability. Furthermore, they are problem-specific, some of them are not mesh-free and require repetitions of simulations. In contrast, neural network based approaches provide alternative and mesh free solutions for differential equations. It often characterized as a black box and predicts closed form solution in the given domain. In view of the above, the primary objective of this investigation has been to propose computationally efficient unsupervised MI techniques, specifically ANN models, for solving challenging real world dynamical problems. As such, Scalable Symplectic Artificial Neural Networks and a nature inspired machine learning algorithm known as Curriculum Learning have been employed to solve various oscillator and astrophysical problems. In order to investigate time series problems, Wavelet Neural Networks with L-BFGS optimization algorithm have been utilized. Additionally, to capture the physics inherent in dynamical problems and corresponding synthetic/generated (if available) data, a SciML algorithm, viz. modified Physics-informed Neural Networks has been proposed Lastly, dynamical problems of fractional order are also addressed by proposing unsupervised deep neural network.