Linda Petzold has been responsible for many millions of machine cycles in some of the world’s most powerful computers. Not directly, of course; as a mathematician her needs are usually modest. But her contribution to the creation of techniques for solving differential-algebraic equations has kept scientists and engineers from many fields, as well as their computers, busy for years.

As a professor from the University of California, Santa Barbara, she started working on problems in solar energy, but in recent years has found many interesting problems to solve in biology. After all, what happens in a cell is just a series of processes that need to be described and understood. Petzold is not happy just to be presented with a mathematical problem; she likes to dig down and really understand a problem until she owns that problem. Her novel solutions and her famous code DASSL have allowed colleagues who have gone on to use her software to model many systems and solve many real world problems. She was awarded the Dahlquist prize in 1999 and is a member of the US National Academy of Engineering. She has since developed her own programme in computational science and engineering at UCSB, where she holds a joint appointment in the Computer Science and the Mechanical Engineering Departments.

Her approach has always been instinctively interdisciplinary, because that is where the interesting problems tend to live. Nothing seemed more natural to her than to extend her research into systems biology, approaching it like any other kind of engineering. Her PhD adviser, Prof Bill Gear, Emeritus Professor of Computer Science at University of Illinois and former President of SIAM, says she was an exceptional student even when she joined his group at the tender age of 19. He says: ‘She was probably the best student I have ever had. I measure students by “amplification factor”. With some students you get back what you put in, but in her case you got much more back from her than you put in. She would come to me once a week or so and she had already sorted out what the problem was that she was stuck on. For many students you have to take an hour on the blackboard just to get them to explain the problem. She would be back the next week having solved the problem and present me with a new one.

‘She is best known for DASSL, which got a lot of people interested in differential-algebraic equations. It’s all very well having a theorem, but it is something else to actually publish some code that people could use. It came just at the right time when computers were becoming powerful enough to run simulations of large systems. She has helped a lot of people with their simulations that have yielded results in a lot of engineering fields.’ Professor Frank Doyle, a colleague of Petzold at UCSB in the Chemical Engineering department and holder of the Duncan and Suzanne Mellichamp Chair in Process Control, says:

‘Linda is a fabulous collaborator – I have worked with her for about five years now, since the time I first arrived to UCSB. She is tremendously inquisitive, and is never satisfied with just “the solution”. She wants to know “why?”, “does it make sense?”, and “what are the ramifications?” She has a voracious appetite for new problems, and this is exemplified by her investment of a huge amount of her time in the area of systems biology.

‘She brings an ideal perspective to this field: the rigour for numerical simulation, the keen insights for multiscale phenomena, and the inquisitive approach to new application areas. In the short time since she has been thinking about these problems, she has had a major impact in advanced methods for solving discrete stochastic simulation problems, with novel insights generated in such diverse applications as bacterial virulence control, circadian rhythms, and eco-systems. On top of her numerous academic accomplishments, she manages to devote a significant amount of time to service, in the form of leadership for her department, and a wide variety of service and educational initiatives and groups. ‘Above all, Linda has a delightful personality and a great sense of humour – I always look forward to our scientific discussions, because they will be both enjoyable and intellectually stimulating.’*Linda Petzold: 'I think it is a very exciting time for engineering, because people are becoming able to manipulate things at a molecular level.'*

Petzold was born in Chicago. Her father was a mechanical engineer and this had a big effect on his daughter in terms of the subjects she chose to study. ‘It always seemed like Dad was having fun, so I thought that maybe I would grow up to be an engineer,’ she says. She was a bookish student at school who hated sports and always got top marks, but she never really felt she fitted in with her colleagues. She did High School in three years, saying she was keen to get out of it and start her proper life. Everything changed when she went to an NSF-funded mathematics summer camp organised by the University of Illinois.

Petzold says: ‘It was a life-changing experience. I met some of the smartest people I have ever known. When you grow up in Chicago, which has a pragmatic kind of culture, it’s not so socially acceptable to be smart – particularly if you are a girl. I spent eight weeks there one summer and realised I was not such a weirdo; there were other people like me and it was OK. I got the idea that I could do science.’

She chose to study at the University of Illinois, initially choosing chemistry, but she took a course in computer programming and was enthralled so she changed her major to mathematics/computer science

After graduating with top marks at the tender age of 19, she decided to stay on at Illinois, largely because she didn’t realise that you were supposed to change colleges when you graduated. ‘I still think that’s a strange myth, particularly when you go to a big school like Illinois. Being a grad student at that place is very different from being an undergraduate. It never really occurred to me to go anywhere else.’ At the time she had no idea how research groups worked and chose to do computer science simply because it was more likely to get her a good job when she finally left. She ended up working in Prof Bill Gear’s group, because he told her she could do whatever she wanted. She thought this was a great plan.

She decided she wanted to do maths on a computer, so she started working in numerical analysis, inventing a few new techniques. She found research difficult at first, because everything was so open-ended, but got the hang of it quickly.

Her first job after grad school was at Sandia National Laboratories in Livermore California. She had applied to several universities with no result, but she drew some substantial interest from several national laboratories. She found that Sandia Livermore was the one that really made her feel wanted and the whole group pushed the boat out for her interview taking her to San Francisco, where they went to the symphony and had a meal in Chinatown. Sandia turned out to be a great place for her. She fitted in well with the applied maths group and found it had plenty of resources for things like travel to meetings, which are often a major issue for academic groups. She did a variety of jobs, but her main brief was to ‘make yourself useful’. She was working on some Department of Energy-funded research projects on combustion and solar energy, but after about six months there was a change of tenant at the White House and her project was cancelled. Other researchers told her not to worry about this and things had a habit of coming back. Sure enough a few months later, she resumed her work under a slightly different guise funded by the Department of Defense.

She says: ‘You find that there are not that many different maths problems in the world. The same infrastructure can solve problems from an amazing variety of disciplines. I really believe in the power of infrastructure.’

She was working on the simulation of fluid flow in a pipe flow system of a solar receiver power plant, and she noticed the problems could be cast as a differential-algebraic equation. She decided to make herself useful by writing some software to help solve these equations. People started to use it. A colleague came to her with a problem and she found the problem killed her code. After months searching for bugs she decided the problem was mathematical rather than in the software. She read a paper about differential-algebraic equation problems and got the idea that the numerical difficulties she was experiencing might be related to something called the index of the differential-algebraic system. She decided to concentrate her efforts on solving the problems that would arise in a real world scenario, rather than worrying about a perfect mathematical solution to any conceivable problem.

She says: ‘I decided to start looking at real problems to see if I could find some structure to it and I could. Once you see how it works you can come up with a way to solve it. I like to get to the bottom of things and know why. I dig until I really own the problem. This opened up a whole new world of differential-algebraic equations. I came up with some new code and it solved lots of problems at Sandia and they were happy.

‘I had made myself useful! It had bought me goodwill and allowed me a lot of latitude to do what I wanted.’

She published her findings and at first there was some resistance from colleagues who suggested she would be better off spending her time on something more mainstream. However, she persevered with this class of problems, because it was clear to her that there were important applications at Sandia.

In 1985 she moved from Sandia to Lawrence Livermore Laboratory as lead of the mathematics group and really enjoyed the opportunities with which she had been presented. She travelled and spoke and presented at a lot of events, which allowed her to build a reputation. She had always imagined that one day she would go back to academia and made sure she had a good body of published work to help her get the right job.

By 1991 she was ready to make the move and was offered a full professorship at the University of Minnesota. She was soon to regret this decision, finding the department very political at the time. But she carried on for six years, working to develop algorithms and software for solving differential-algebraic equations, with applications to vehicle simulation and to tissue engineering While she had fairly modest requirements for computer power her codes were being used by engineers and scientists on the supercomputers, on a wide variety of problems. Having established an academic reputation she started looking to move and one of the reasons for the length of her stay at Minnesota was the extremely long lead time for professorial appointments. In 1997 she moved to UC Santa Barbara.

She says: ‘Santa Barbara was looking for someone to start a graduate programme in computational science and engineering, which is something in which I was very interested. I came and found a large number of excellent researchers who were committed to that idea and were supportive. They were people I thought would be good to work with and we had a very supportive Dean, so it was perfect. The work that I do is very multi-disciplinary. In the past I have had job offers from maths departments. Right now I am in two departments: computer science and engineering. No department really houses what I do. At this stage in my career that is a good thing, because it gives me flexibility. Early on in your career it might not be a good thing; it may be easier to be in the mainstream of an established field because people are not saying “What is it exactly that you do?” There is still a lot of resistance; we are still swimming upstream, because the academic world has been structured in a disciplinary manner for many years.’

Abut six years ago Petzold discovered systems biology. She says: ‘It is a tremendously fruitful area of research. What attracted me to it is a wealth of mathematical and computational problems that have different features to what I have seen before. The experimental techniques in biology, particularly the high throughput techniques, are generating huge amounts of data. Right now I have a grant with Professor Frank Doyle to study circadian rhythms – jetlag – looking at the chemical mechanisms that make it happen and how all these brain cells synchronise.

‘What I like about the problems in systems biology generally is that they are really hard. Most of the problems I am working with are at the cell level. I am developing techniques for discrete stochastic simulation. Really I am going back to what I worked on at Sandia, looking at chemical reactions but there is a lot of non-linear behaviour. Some people simulate these types of systems with ordinary differential equations (ODE) models and you can do a good job with these on lots of systems. But sometimes these processes are shown to be stochastically driven, because they are initiated by chemical species that are present in extremely small quantities. If you wanted to be even more accurate you could use molecular dynamics, but that would take a very long time. You have to go to a coarser level of approximation, which is discrete stochastic, but you can derive the ODEs of chemical kinetics at the limit. ‘The species that are present in large quantities can be simulated by ODEs, but we are looking at the appropriate level of approximation for each part of the system and some parts need a Monte Carlo approach. I am trying to get the computer to make these decisions automatically.

‘What makes the mathematics interesting and challenging in biology is that so much is unknown. There are limits to the experiments you can do in vivo and you may not be able to capture some parameters and there are issues about to what extent you can draw conclusions.

‘I am more hooked on this class of problems than I have been for some time. I think it is a very exciting time for engineering, because people are becoming able to manipulate things at a molecular level.’

Petzold is extremely happy with her decision to move to Santa Barbara and has received strong support from the hierarchy for her interdisciplinary approach. She anticipates no shortage of new problems to dig into and really own. Many more millions of machine cycles are expected to be burned by the results of her work, but perhaps by biologists as well as engineers.

Her other professional priority has also been to encourage more women to get involved in maths and science and she is a regular speaker to groups at all levels. Her position as a role model to the next generation of women scientists was acknowledged by the award of the first Sonya Kovalevsky Prize in 2003 awarded by SIAM. She says little has changed since she started her career, but that is not going to stop her trying.*John Murphy*

### Education

1974 BS in Mathematics, University of Illinois, Urbana

1978 PhD in Computer Science, Mathematics minor, University of Illinois, Urbana

### Professional Career

**1978-1985** Member of Technical Staff, Applied Mathematics Division, Sandia National Laboratories, Livermore, California**1985-1991** Group Leader, Numerical Mathematics Group, Lawrence Livermore National Laboratory, Livermore, California**1986-1993** Adjunct Professor, Department of Computer Science, University of Illinois at Urbana-Champaign**1991-1997** Professor, Department of Computer Science, Fellow, Minnesota Supercomputer Institute, University of Minnesota**1997-present** Professor and Chair (2003-2007), Department of Computer Science, Professor, Department of Mechanical and Environmental Engineering, Director, Computational Science and Engineering Program, University of California, Santa Barbara