Some people pass the time with hobbies like crossword puzzles or Sudoku. When Chris Rackauckas has a spare moment, he often uses it to answer questions about numerical differential equations that people have posed online. Rackauckas — previously an MIT applied mathematics instructor, now an MIT Computer Science and Artificial Intelligence Laboratory (CSAIL) research affiliate and the co-principal investigator of the MIT Julia Lab — has already posted thousands of these answers, and if you have a question, the odds are that he has already addressed it. His research, unsurprisingly, revolves around differential equations and on computational methods — using AI and other techniques — to solve them quickly and efficiently.

During his graduate studies in mathematics at the University of California at Irvine, which earned him a PhD in 2018, Rackauckas focused on medical and pharmacological applications of his work. In fact, he developed the core software and techniques for Pumas-AI — a Baltimore-based firm that provides software for pharmaceutical modeling and simulation purposes — when he was still a graduate student. He now serves as the company’s director of scientific research.

Since coming to MIT in 2019, Rackauckas has found a much wider range of applications for his “accelerated” differential equation solvers, including global climate modeling and building heating, ventilation, and air conditioning (HVAC) systems. He took time from his efforts to find ever-more rapid ways of attacking differential equations to talk about this work, which has earned him numerous honors, including the 2020 United States Air Force Artificial Intelligence Accelerator Scientific Excellence Award.

Q: How did you get into what you’re doing today?

A: As an undergraduate math major at Oberlin College, I mostly focused on the “methods courses” in scientific domains — statistical methods in psychology, time series econometrics, computational modeling in physics, and so forth. I didn’t have a well-thought-out game plan. I just wanted to understand how science is really done and how we know when our scientific approaches are giving us a correct model of a given system. Fortuitously, that path turned out to be a good one for someone in my current line of work.

In graduate school, I went into biology — specifically combining differential equation solvers with systems biology. The goal there was to make predictive models of how the randomness of a chemical, and its concentration, changes in the body, although at the time I was working with zebra fish. It turns out that systems biology is very close to systems pharmacology. You basically replace fish with humans.

Q: Why are differential equations so important in the world around us?

A: The way I like to describe it is that all scientific experiments are measuring how something changes. How do I go from an understanding of how things change to a prediction of what will happen? That’s what the process of solving a differential equation is all about. Simulations, which are experiments that we carry out on computers, can involve solving thousands upon thousands of differential equations.

Such a simulation might tell you, for instance, not only how a drug concentration changes over time but also how the effects of the drug on the body changes. It’s not the same for every person, so you have to adapt the equations for individuals, depending on their age, weight, etc.

Q: Given your focus on “accelerated” equation solvers, where can you find the best opportunities for speeding things up?

A: The clinical trials for a new drug have a set period of time; you can’t just make the human element faster. But in the preclinical domain, there’s always a period of analysis. Developing a new drug could cost $10 billion, so before you start something like that, you want to know the probability that a drug will work on its target population, as well as the optimal dose for an individual. That’s the purpose of preclinical analysis and quantitative systems pharmacology. Suppose that you typically spend three months on analysis and six months on clinical trials. If you can shorten that analysis from three months to a day — roughly a 100-fold acceleration — you will have cut the time to release a drug by a third.

Then there’s clinical pharmacology, where if you can understand how to get the first dose correct you might be able to save time on repeating elements of the trials. It turns out that my Pumas colleagues and I have already achieved a 175-fold acceleration in preclinical analyses carried out for Pfizer. Moderna also publicly used Pumas and our clinical analysis methods in its clinical analysis of the Covid-19 vaccine and other drugs.

Here’s another opportunity for time and cost savings: Mitsubishi has a facility in Japan for testing HVAC systems. You have to build the entire system and then test it in a building. Each experiment can cost millions of dollars. We’re now working with them to test out, say, 10 different ideas on a computer in order to pick out the one out of those 10 options that they ought to select for a prototype and subsequent experiments.

Q: Can you discuss some other examples of how your work is used?

A: The SciML.ai website keeps a (woefully incomplete) showcase of the amazing ways people have used these methods. CliMA — an Earth system model developed by scientists at Caltech, MIT, and other institutions — relies on the differential equation solvers that I wrote. Recently I was at an applied math conference where a group, independent of me, reported that they had used my software tools to make NASA launch simulations run 15,000 times faster.

Q: What are your plans for the future?

A: There are a lot of things in the pipeline. One application I’ve just started to pursue is predicting the flow of wildfires; another is to predict transient cardiac events like heart attacks, strokes, and arrythmias. A third area I’m moving into is in the realm of neuropsychopharmacology — trying to predict things like the individualized biosignals in bipolar disorder, depression, and schizophrenia in order to design drugs that are better suited for treating these disorders. This is an area where there is a dire need that can lead to much more effective treatments.

In between these projects, I might take a moment to answer the odd question about differential equations. You’ve got to relax sometime.

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