  The thesis focuses on various techniques to find an alternate approximation
method that could be universally used for a wide range of CFD problems but with
low computational cost and low runtime. Various techniques have been explored
within the field of machine learning to gauge the utility in fulfilling the
core ambition. Steady advection diffusion problem has been used as the test
case to understand the level of complexity up to which a method can provide
solution. Ultimately, the focus stays over physics informed machine learning
techniques where solving differential equations is possible without any
training with computed data. The prevalent methods by I.E. Lagaris et.al. and
M. Raissi et.al are explored thoroughly. The prevalent methods cannot solve
advection dominant problems. A physics informed method, called as Distributed
Physics Informed Neural Network (DPINN), is proposed to solve advection
dominant problems. It increases the lexibility and capability of older methods
by splitting the domain and introducing other physics-based constraints as mean
squared loss terms. Various experiments are done to explore the end to end
possibilities with the method. Parametric study is also done to understand the
behavior of the method to different tunable parameters. The method is tested
over steady advection-diffusion problems and unsteady square pulse problems.
Very accurate results are recorded. Extreme learning machine (ELM) is a very
fast neural network algorithm at the cost of tunable parameters. The ELM based
variant of the proposed model is tested over the advection-diffusion problem.
ELM makes the complex optimization simpler and Since the method is
non-iterative, the solution is recorded in a single shot. The ELM based variant
seems to work better than the simple DPINN method. Simultaneously scope for
various development in future are hinted throughout the thesis.
