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Numerical approximations of partial differential equations (PDEs) areroutinely employed to formulate the solution of physics, engineering andmathematical problems involving functions of several variables, such as thepropagation of heat or sound, fluid flow, elasticity, electrostatics,electrodynamics, and more. While this has led to solving many complexphenomena, there are some limitations. Conventional approaches such as FiniteElement Methods (FEMs) and Finite Differential Methods (FDMs) requireconsiderable time and are computationally expensive. In contrast, data drivenmachine learning-based methods such as neural networks provide a faster, fairlyaccurate alternative, and have certain advantages such as discretizationinvariance and resolution invariance. This article aims to provide acomprehensive insight into how data-driven approaches can complementconventional techniques to solve engineering and physics problems, while alsonoting some of the major pitfalls of machine learning-based approaches.Furthermore, we highlight, a novel and fast machine learning-based approach(~1000x) to learning the solution operator of a PDE operator learning. We willnote how these new computational approaches can bring immense advantages intackling many problems in fundamental and applied physics.

Neural Operator: Is data all you need to model the world? An insight into the impact of Physics Informed Machine Learning