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Spotlight - Rajat Dwaraknath, PhD, Computational & Mathematical Engineering

Exhibit titled 'Conway's Trees of Life' at Stanford's Art of Science Exhibition 2024, which won the People's Choice Award. The tree-like sculptures are 3D renditions of the famous Conway's Game of Life, created by bringing its time evolution into the third spatial dimension. The models were designed using Python and the sculptures were 3D printed.

I was born and raised in Bangalore, India, and even as a kid in eighth grade I knew I loved math and physics. But sometimes, the things I really wanted to understand didn’t make sense to me immediately. At the time, my brother, who is eight years older than I am, was doing his undergraduate work in engineering physics, and he’d explain things to me in a way that I understood and found beautiful. He also began teaching me programming, which I loved, because in addition to learning something new, it made me feel like I had some control over the computer and could build things for myself.

During my undergraduate work in electrical engineering I had the opportunity to intern at Stanford’s Institute for Computational and Mathematical Engineering (ICME). It was pivotal for me, as I felt an exponential growth in my understanding. I realized that ICME - which focuses on understanding math, physics, and engineering concepts in the context of computers - was a perfect fit for me. Computers and technology are advancing rapidly and solving so many problems in the world; I wanted to use math and programming to be a part of that, and I knew that meant I needed to get a PhD and learn more.

I began my work at Stanford interested in whether it was possible to use mathematics to look at artificial intelligence systems and accurately determine whether the predictions they make will be correct. As of now, we can’t do that. It’s a difficult problem and a lot of people are working on it. But I came to realize that trying to provide guarantees on what the computer is doing means you need to make some assumptions and simplify things a lot to do the math. In the long run, it all became a little too abstract for me. I wanted a balance between working on math problems while also being able to implement them on modern hardware without losing touch with the real world. I decided to pivot.

Today my research strikes a balance between mathematics and engineering. I develop algorithms to tackle a wide range of problems in science, engineering and finance by integrating a mathematical framework called convex optimization with concepts from deep learning and reinforcement learning. In addition to the theoretical design of these algorithms, I also work to implement them efficiently on modern high-performance computing hardware. I love every aspect of this work, including the more applied focus it provides.

Something else very near to my heart is teaching. I’ve worked as a teaching assistant since my second year at Stanford, am currently a TA for a course in numerical linear algebra, and have won the ICME teaching assistant award twice. Learning new things has always brought me joy, and I want to share that feeling with others. I think that comes from how I didn’t always learn well in school, and how that changed when my brother found the right ways to help me understand. I now appreciate the value of good teaching, and that’s why I have a blog where I share visual explanations of hard math concepts to try and present them in a more understandable way.

I tell students they should never be quick to dismiss their potential to study engineering, even if they’re struggling to grasp certain concepts. People learn in different ways, and with time and the right exploration, you’ll likely find the explanations that make the information click for you. Engineering is a wide field with a breadth of problems that will resonate with you. Once things start clicking, if you feel the joy and passion for it, you can make it in this field.

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