Soham graduated from the Birla Institute of Technology and Science, Pilani in 2013 with majors in physics and electronics and communications engineering. After spending about a year in a relative academic wilderness, he joined Iowa State University in the fall of 2014 as a graduate student in the physics department. He is currently working on his PhD in theoretical nuclear physics. His area of interest is application of effective field theory to the study of nuclear structure.
Project: Function Approximation Using Neural Networks
Goal of the project:
To approximate mathematical functions using neural networks.
Summary of work:
We have tried different neural network architectures to approximate various mathematical functions. We used different metrics to determine the best architecture for a particular type of function.
Results and future work:
Some of the functions that we tried had oscillatory components—for example, the Bessel and Scorer functions. In our explorations, we found out that such functions are best approximated by neural networks with a sinusoidal activation function. On the other hand, rational polynomials are better approximated by neural networks with a soft exponential activation function.
All the functions that we approximated here were functions of single variables. An obvious extension of this work is to design neural networks to approximate functions of multiple variables.
More importantly, the yet-to-be-realized grander aim of this project is to solve differential equations. Future work will be geared toward achieving that aim.