What if you could perform supercomputing calculations in real-time, on your smartphone, in any location? 

Researchers at the Massachusetts Institute of Technology (MIT), collaborating with staff at the Texas Advanced Computing Center (TACC), have created an application that does just that.

The team performed a series of expensive high-fidelity simulations on the Ranger supercomputer to generate a small “reduced model” which was transferred to a Google Android smart phone. They were then able to solve problems on the phone and visualize the results on the fly.

The project proved the potential for reduced order methods to perform real-time and reliable simulations for complicated problems on handheld devices.

“You don’t need to have a high-powered computer on hand,” said David Knezevic, a post-doctoral associate in mechanical engineering at MIT working in the lab of Prof. Anthony Patera. “Once you've created the reduced model, you can do all the computations on a phone.”

This is not the first time that model reduction algorithms have been used to ameliorate the complexities of large-scale physical simulations.  The advantage of the system designed by Knezevic and his colleagues is its rigorous error bounds, which tell a user the range of possible solutions, and provide a metric of whether an answer is accurate or not. The error bounds are based on mathematical theory developed in Prof. Patera's research group at MIT over a number of years.

“We have a bound on how much accuracy we’re losing with our reduced model, so we can say with rigor that we’re doing supercomputing on a phone,” Knezevic said.

The reduced model is constructed by focusing the supercomputer simulations on a range of parameters that are of interest to the user.  Once the construction is finished, the model can be used to perform simulations for new parameters, nearly instantaneously, for use in real-world applications.

“We’re interested in accurate, real-time computing, and the calculations on the phone take less than two seconds,” Knezevic said.

So far the team has developed a number of demonstration problems that run on the system, mainly fluid dynamics, acoustics and heat flow simulations. However, many different problems can be handled with this method.

In its smartphone form, the researchers imagine their method could be applied to “in the field” inverse problems like landmine detection, as well as to design problems like determining the optimal shape for structures.

TACC provided access to Ranger to compute the problems and TACC staff collaborated with Knezevic to debug and parallelize the code so it could scale efficiently to thousands of processors on the system.

“The payoff for model reduction is larger when you can go from an expensive supercomputer solution to a calculation that takes a couple of seconds on a smart phone,” Knezevic explained. “That’s a speed up of orders of magnitude.”

The improvements allowed the team to compute three-dimensional solutions, and to work with the complicated class of non-linear equations in which the researchers were interested.

"After collaborating on the code for several months, it was much more powerful, flexible and efficient," said John Peterson, a research associate in the high performance computing group at TACC and a collaborator on the project.

Using the smart phone application, researchers can change values, improve the error bounds by increasing the complexity of the local calculation, and even visualize the solution interactively in three dimensions.

“It’s demonstrating that with a small processor, you can still get a meaningful answer to a big problem,“ Peterson said.

The real impact of the system may come in the application of these methods to aircraft or automobiles, which use control systems to react to inputs from the environment in order to achieve optimal safety and performance. Examples include traction control in cars and stabilization systems in jet fighters.

“If you have sensors feeding in data to the reduced order model system, then it could solve the equation corresponding to the input data, and indicate the appropriate response in real-time based on the calculations you performed on a supercomputer,” Knezevic said.

“The control system needs a simplified model of the aircraft so that it can make split-second updates to the ailerons and flaps,” Peterson added. “That simplified model is the reduced basis model.”

Creating a lightweight instantiation of this technology in the form of a smart phone application signals many new possibilities for reduced order modeling in applied science and engineering.

Concluded Knezevic: “When you tell people you can solve a problem that would normally take two hours on Ranger in one second, with guaranteed error bounds, people instantly understand what model reduction is all about.”