The field of surrogate modelling (which also goes by the name of digital twins sometimes) has seen a huge resurgence, especially with the boom in AI/ML, thanks to its largely mathematical origins.
Sridhar Chellappa, our next pathbreaker, Research Scientist at Bosch Research, leverages his background in Applied Mathematics and AI to solve engineering problems for diverse product categories within the automotive value chain.
Sridhar talks to Shyam Krishnamurthy from The Interview Portal about deciding to do a PhD in Applied Mathematics inspite of having a background in Electrical Engineering.
For students, applied mathematics is helping reinterpret engineering and scientific problems in concrete mathematical terms by mapping problems from diverse fields into a common mathematical framework.
Sridhar, what were your initial years like?
I was born in Chennai, but grew up across India since my father was employed at a bank and would get transferred once every three years. Thanks to that, my childhood and schooling were eventful as I could travel to different places and grew up getting exposed to different languages and cultures.
Early during school days, I developed the reading habit. I enjoyed reading a variety of books, both fiction and non-fiction. This gave me broad exposure to different topics. I was also quite active on the school cultural scene where I took part in quizzing, debates, dumb-charades, etc. At that point in life, academically, physics and astronomy were my main interests. I was not particularly interested either in engineering or mathematics, which eventually became my specializations.
What did you do for graduation/post graduation?
My undergraduation was at SASTRA University, Tamil Nadu where I studied electrical and electronics engineering.
For my masters, I went abroad to Europe with an Erasmus Mundus scholarship to pursue electrical engineering.
After my masters, I went on to do a PhD in Applied Mathematics. I also had a two-year postdoctoral stint.
What were some of the key influences that led you to such an offbeat, unconventional, and unique career in Corporate Research?
It is rather hard to say I “chose” this career. I was not all that clear about my area of interest during my school days. As I was into physics, I was keen on getting into the Chennai Mathematical Institute (CMI) for studying physics, but, unfortunately I could not qualify the entrance exam. While electrical engineering was not my first choice, I actually ended up enjoying the topics very much. It was thanks to that degree I also developed a keen interest in mathematical modeling and simulation.
I got the opportunity to do a summer fellowship at IIT-Kanpur during the third year of my undergraduate degree. It was one of the early events that shaped my career path.
Another key event was securing an internship at Alstom T&D India Ltd. for writing my undergraduate thesis. I received this opportunity, thanks to the then Associate Dean at SASTRA university. It served as a stepping stone to my Masters degree.
Receiving a fully-funded scholarship to pursue my masters was a significant turning point in my career. If not for the scholarship, I would not have gone abroad. The scholarship and the experiences during my masters, ultimately paved the way to my current position.
Another more dramatic turning point would be receiving an offer to pursue a PhD in applied mathematics at the Max Planck Institute, Magdeburg, Germany. By the end of my Masters, I was clear on pursuing a PhD in the topic of applied mathematics. However, I was turned down at several places I had applied to, as I did not have a sufficient background in mathematics curriculum. Therefore, I was very fortunate to receive the offer. If not, I would have ended up doing a PhD in electrical engineering instead. Although my path to my current career had its twists and turns, I am happy I ended up where I am.
Tell us about your career path
Honestly, looking back, I did not have a well-defined plan for my career. My interests evolved and I tried to actively seek avenues to expand my horizons.
In college, during my undergraduate days, thanks to subjects such as electric circuit theory and electromagnetics, I took a strong liking towards mathematical modeling. To gain knowledge beyond the immediate curriculum, I read a lot about different topics over the internet and also brushed up my fundamentals on those topics at the college library.
During the third year of undergraduate degree, I applied to and got selected for a summer research fellowship programme, sponsored by the Indian Academy of Sciences. I spent two months at IIT-Kanpur, under Prof. Mohan Kadalbajoo. The topic I explored was Numerical Methods for Electromagnetism. While the topic was to my liking, the weather in Kanpur was not. It was May/June, the peak of summer. It was a struggle just to be able to sit and concentrate. I would regularly head to the air-conditioned library, just to escape the heat. Despite that, the fellowship was instrumental in helping me identify my true interests in the topics of modeling and simulation.
My Bachelor’s thesis in industry was the next step. There, I developed a new modeling technique for a concrete use case and developed finite element simulations to validate it. I also was able to present my work at conferences.
My first exposure to industry was during the BTech thesis. Alstom (later taken over by GE Grid) had a research and development center in Chennai. I worked on modelling the electromagnetic losses in a product called gas-insulated substation (GIS). Modelling and validating the losses is critical as it directly affect the operating temperature, which is tightly regulated by standards.
The problem involved a good mix of mathematical modelling and simulation. I obtained a good degree of understanding in electromagnetism, finite-elment modelling. I was fortunate to have a great advisor at Alstom in Dr. Santhosh A. He encouraged me to get a deep understanding of the problem and take a systematic approach to solve it. My thesis enhanced the existing capabilities at the R&D center and I was also able to present the work at several conferences.
While my Masters degree says “Sustainable Transportation”, the Masters degree was mainly on electrical engineering. In 2014, EV was still a nascent topic, slowly gaining traction. The degree mainly focused on electrical engineering topics, which were particularly relevant to sustainable transportation (EV) technologies such as electrical drives, power electronics, grid power systems, etc.
The Masters programme was part of what is called the Erasmus Mundus Programme run by the European Union. There were several such masters courses under the Erasmus Mundus umbrella. Usually this masters programme was offered jointly by a consortium of universities based in Europe. The students were expected to spend one semester/one year in each of the universities. This not only offered them the chance to learn the topics at the best universities, but also have the opportunity to travel and experience different cultures. The track I chose, sustainable transportation, involved spending a semester each at three different universities.
I developed considerable knowledge on topics such as control systems, power electronics, electric drive systems, and signal processing. Even within these topics, I tried to maintain a strong emphasis on simulations.
I received a full scholarship to pursue this masters course. I got a tuition fee waiver and also a monthly subsistence allowance. Without this scholarship, it would have been financially very costly for me, and I doubt I would have pursued it.
Going forward, during my Masters abroad, I continued to focus on topics that involved developing a good mix of modeling/simulation and programming. NPTEL and MIT opencourseware videos on different topics really proved a goldmine for me. I then successfully secured a Master thesis internship at Bosch Corporate Research, Germany.
How did you end up with a PhD in Applied Mathematics?
I was in two-minds towards the 3rd semester of my Masters, whether to do an academic/university thesis or something at industry. To me, it was important that I do something with a stong focus on mathematical modelling and simulations. The opportunity I had at the University had a strong emphasis on electrical power systems/control systems. Therefore, I searched the internet for opportunities in the industry on the topics of modelling and simulation for electrical systems. I found the opportunity at Bosch through Google.
The topic was the mathematical modelling of high frequency losses in an electrical machine drive. The topic had a lot of continuity with my Bachelors thesis topic, but with a greater focus on finite element simulations. Working on actual industrial products was a fantastic experience.
The experience in Germany then led to finding a PhD position at the Max Planck Institute, Magdeburg. It was hard to convince the hiring committee of my interest in applied mathematics (while my entire academic background was in electrical engineering). Having done a rather mathematically focused Masters thesis at Bosch greatly helped convince the committee of my interest and ability. They certainly took a chance by selecting me for the position.
Getting the PhD position seemed the easy part when I was actually faced with the task of navigating the topic of my thesis viz., surrogate modeling. In simple terms, it is all about substituting a model of smaller complexity to mimic the functioning of a much larger and more complex model. However, it was anything but normal. It involved combining several advanced techniques in mathematics. The first year of PhD was extremely challenging. I would spend late hours into the night, reading books, papers, and understanding concepts that would be straightforward for someone with a proper mathematics background. Nevertheless, this trial by fire ensured that the remainder of my PhD was smooth sailing. It also gave me the confidence to face anything in life with a calm head.
The topic of surrogate modelling (which also goes by the name of digital twins sometimes) is kind of a hot topic now. Especially with the boom in AI/ML, this field has seen a huge resurgence from its largely mathematical origins. Topics such as physics-informed neural nets/operator networks, etc., all have their origins within surrogate modelling. It is already being applied in a big way across several industries. The goal is to learn about a system using limited data, and scale this learning to newer/unseen conditions or systems.
A great example is engineering design. Say I want to design my car’s geometry. Numerous parameters could influence the design, including data from my past designs. If I train a surrogate model on this data, for a few parameters/conditions (e.g., the material used, the angle of the windscreen, the thickness of the body, etc.), I can then use the trained model to anticipate the properties of the car for a new set of conditions. This capability, if realised, can offer immense speed-ups to the design workflow. Surrogate models are not restricted to one industry. Another example is its use in biomedical engineering. The ability to create a digital twin/model of the human heart using a few scans can potentially unlock a new era of advanced diagnostics. Many researchers, especially in Europe are actively working on this field.
I wouldn’t say there was a direct application of my EEE knowledge. But, some of the concepts I picked up, e.g., control systems, signal processing were immensely helpful, as they directly translate to my work during the PhD.
How did you get your first break?
My first break was publishing my first scientific paper in a journal. Till that time, I still lacked confidence as I was a recent transplant into the world of mathematics. Working towards the topic, I had several nice ideas. With great support from my supervisors, I was able to have the work published in a highly reputed journal in my field. That gave me immense confidence.
During Covid times, I volunteered to co-organise a reading group at my Institute, to keep all of us tuned to the scientific world even during the tough lockdown times. There I had the opportunity to listen to several great talks and discussions, particularly on the booming field of AI and ML. Until then, I had not really taken a big interest in the field, thinking it to be a passing fad. The reading group served as a big break by making me realise the significance of the topics and how closely related they are to applied mathematics. Post that, I devoted considerable time to better understand the field and ended up giving some talks myself.
I completed my PhD in 2022 and stayed on at the same institute for another two years as a Postdoc. It was largely a continuation of the topics I worked on during a PhD, but with the additional emphasis on AI/ML based methods. I also got to work on the topic of cardiac modelling during my Postdoc phase and also further applications of surrogate modelling to more relevant application areas.
The combination of traditional physics-based surrogate modelling and more recent AI/ML-based methods was exactly the profile that Bosch was looking for my current role. This role was for their R&D center in India, so I did not need a visa.
Having worked considerably on the method development side of surrogate modelling, I was keen to switch to roles that were application-oriented. I also had to move back to India for family reasons.
What were some of the challenges you faced? How did you address them?
As I mentioned previously, most of the challenges I faced were related to my ever-evolving interests. Once I got interested in a topic, I made sure to dedicate my full effort towards attaining it.
While applying for a PhD in Applied Mathematics, I was turned down at several places I had applied to, as I did not have a sufficient background in mathematics curriculum.
I was also not shy of asking for help. My friends and also seniors have helped me on several instances, whenever I got stuck or was unsure what to do.
Giving scientific talks is a part and parcel of PhD life. However, I always had stage fear and could not always speak fluently in front of an audience. To improve myself, I always used to get feedback from colleagues regarding any talk I gave – what was good, what aspects needed improvement, etc. I also took the effort to rehearse my talks by recording it and playing it back. Listening to my own talk several times, I was able to clearly identify the ups and downs of it. Slowly, I started to improve and now I can talk about my favorite topics with just a moment’s notice.
Where do you work now? What problems do you solve?
Currently, I am a research scientist at Bosch Research.
I leverage my background in applied mathematics and AI to solve engineering problems for diverse product categories within the automotive value chain. In addition to designing robust and safe systems for the market, there is always an emphasis on saving cost.
What skills are needed for your role? How did you acquire the skills?
Apart from the regular subject knowledge and programming skills, one needs to be persistent. Sometimes all a problem needs is more time attacking it. I learned to be persistent through my PhD life. Also, one must be ready to continuously learn and upskill to stay tuned with the rapid developments in the field.
What’s a typical day like?
A typical day involves meetings/discussions and things like code development (including lots of debugging). I also try to keep pace with the current research around the world and how it can be used to benefit my employer. Mentoring interns and students is also a crucial part of my day.
What is it you love about this job?
I love the structured freedom I have to explore topics (emphasis on structured). In pure research, one can get very deep in one topic. While that may be good, industry is all about return on investments. This means I always have my eyes on the big picture while also having the opportunity to test and try out lots of cool ideas.
How does your work benefit society?
In applied mathematics the approach is to reinterpret engineering and scientific problems in concrete mathematical terms. It is rather surprising how problems from diverse fields can be mapped to a common mathematical framework. Through mathematical modeling, we can make automotive systems more efficient and safe. Adding modeling and simulation as part of the product development cycle can also offer huge cost benefits. Mathematics can also uncover new value areas, e.g., using mathematics to design safe EV battery systems with sufficient range.
Tell us an example of a specific memorable work you did that is very close to you!
During my PhD, I got the opportunity to collaborate with colleagues at the university to apply the mathematical methods I had developed to model certain behavioural aspects of the human heart. That work is very close to me as I got to get into a rather unexpected application of my work. To see the throbbing heart on the computer screen and knowing that I made a small contribution towards it was a great thrill.
Your advice to students based on your experience?
Keep an open mind, learn from diverse sources. A career is not always a straight line, it can have its ups and downs. The important thing is to stay alert and always look out for new opportunities. Develop a good network of peers.
Future Plans?
The Indian automotive sector is quite strong and competitive. Homegrown product development and research in the fundamental sciences, particularly mathematics, is vital to maintain competitiveness and also to expand to greener markets. Being in corporate research, I hope to contribute towards this. I am also greatly excited by the possibilities that Generative AI has to offer. Autonomous driving is just the beginning.