Research to Aid Scientific Discovery
Sheikh Saqlain ’23
Srinagar, Kashmir, India
What drew you to this field of study?
I’ve always had a natural affinity toward math, and took a lot of math classes in high school. I started at UMass as an economics major but transferred to mathematics to pursue my passion. My sophomore year, I took a course on partial differential equations and was fascinated by how applicable they are to understanding so many phenomena in the natural world, such as oceans and the atmosphere. Later, I began learning about using neural networks to solve partial differential equations. This is a really novel approach, and I wanted to tinker and see what I could do with it.
How do you conduct your research?
My junior year at UMass, I conducted an independent study on the effects of dragging various obstacles through so-called droplet Bose-Einstein condensates, an elusive state of matter that exists at extremely low temperatures. This can be thought of as moving a paddle through a body of water and observing its effects. Since it’s hard to create these forms of matter physically, we developed computational simulations to study the effects in question. This computational work helps to inform the work of physicists.
For my thesis research, I am studying the use of machine learning techniques for simulations of physical systems. We use neural networks (which is also what ChatGPT is built from!) to help us find the equations that govern dynamical systems on lattices (interconnected systems of discrete objects).
What do you see as the impact—or potential impact—of your work?
My thesis research is in a very novel field, using methods that show a lot of promise in aiding scientific discovery. Essentially, we’re investigating if machine learning models can be used to generate equations using data from real-world observations. For example, can a machine learning model infer from a video of an apple falling or a pendulum swinging the equation that governs these motions?
How does your faculty mentor support your research?
I work closely on my research with Professors Panos Kevrekidis and Wei Zhu in the UMass Amherst Department of Mathematics and Statistics. We meet weekly to discuss my research results and any challenges I’m facing, and they offer advice to help me solve problems. They’re very knowledgeable in their fields, and share resources to help me become better informed. They’re always very supportive, acknowledging my work and trusting my instincts. I really enjoy the challenge of research, as well as the fact that there are no pre-determined answers. You never know what to expect, and you can’t just Google the answer.
What do you find most exciting about conducting research?
I really enjoy the challenge of research, as well as the fact that there are no pre-determined answers. You never know what to expect, and you can’t just Google the answer. That’s very exciting, but can also be scary. You have to deal with a lot of failed attempts.
I also enjoy the collaborative aspect of research and learning from my mentors. This inspires me to continue pursuing research, meeting more people, and gaining new perspectives on the topics that interest me.
What are you most proud of?
I am very proud to be the first author on a paper about the Bose-Einstein condensate research, which was recently accepted for publication in the Physical Review A Journal, a top journal in the field. A lot of work went into this research, so it was nice to have this official acknowledgement. My mentors were very helpful in making this happen, as the road to publishing was wholly unfamiliar to me. I also collaborated on this paper with a former visiting professor at UMass, Mithun Thudiyangal, and with Ricardo Carretero at San Diego State University, whom one of my mentors introduced me to.
How has your research enhanced your overall educational experience at UMass?
The research I have conducted at UMass Amherst has certainly shaped the coursework I participated in by making me aware of the deficiencies in my knowledge as well as exposing me to potentially interesting fields of study that I wouldn't have found otherwise.
What are your plans for the future?
I was inspired by my experience at UMass to apply to graduate programs in Applied Mathematics in order to pursue research as a career. I believe the research I conducted while at UMass contributed immensely to my acceptance to the PhD program in Mathematics at the Courant Institute of Mathematical Sciences at New York University, which I’ll start next year.
Why would you recommend UMass to a friend?
The mathematics department has amazing faculty, who are always very supportive and encouraging of students. Everyone pushes you to do better, and there’s always an opportunity to grow. Every time I’ve brought an idea to my mentors, they’ve taken time to listen to me, and encourage or guide me. Before sophomore year, I didn't know much about research. It is thanks to my mentors that I've learned so much and am now pursuing research as a career.