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New software that runs on a smart phone can approximate in seconds computations that would take a supercomputer hours. The software works for problems whose form is know but whose particulars aren't; slider bars allow users to set the values for which they want the problems solved. Image courtesy of David Knezevic and Dinh Bao Phuong Huynh
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Many engineering disciplines rely on
supercomputers to simulate complicated physical phenomena. Now, researchers in
MIT’s Department of Mechanical Engineering have developed software that can
perform such simulations on an ordinary smart phone. Although the current
version of the software is for demonstration purposes, the work could lead to
applications that let engineers perform complicated calculations in the field
and to better control systems for vehicles or robotic systems.
The new software works in cases where
the general form of a problem is known in advance, but not the particulars. For
instance, says Phuong Huynh, a postdoc who worked on the project, a computer
simulation of fluid flow around an obstacle in a pipe could depend on a single
parameter: the radius of the obstacle. But for a given value of the parameter,
calculating the fluid flow could take an hour on a supercomputer with 500 processing
units. The researchers’ new software can provide a very good approximation of
the same calculation in a matter of seconds.
“This is a very relevant situation,”
says David Knezevic, another postdoc in the department who helped lead the
project. “Often in engineering contexts, you know a priori that your problem is
parameterized, but you don’t know until you get into the field what parameters
you’re interested in.”
Each new problem the researchers’
software is called upon to solve requires its own mathematical model. The
models, however, take up very little space in memory: A cell phone could hold
thousands of them. The software, which is available for download, comes preloaded with models for
nine problems, including heat propagation in objects of several different
shapes, fluid flow around a spherical obstacle, and the effects of forces
applied to a cracked pillar. As the researchers develop models for new classes
of problems, they post them on a server, from which they can be downloaded.
Advance work
But while the models are small, creating them is a complicated process that
does in fact require a supercomputer. “We’re not trying to replace a supercomputer,”
Knezevic says. “This is a model of computation that works in conjunction with
supercomputing. And the supercomputer is indispensable.”
Knezevic, his fellow postdoc Phuong
Huynh, and Ford Professor of Engineering Anthony T. Patera describe their
approach in a forthcoming issue of the journal Computers and Fluids. Once they have identified a
parameterized problem, they use a supercomputer to solve it for somewhere
between 10 and 50 different sets of values. Those values, however, are
carefully chosen to map out a large space of possible solutions to the problem.
The model downloaded to a smart phone finds an approximate solution for a new
set of parameters by reference to the precomputed solutions.
The key to the system, Knezevic says, is
the ability to quantify the degree of error in an approximation of a
supercomputing calculation, a subject that Patera has been researching for
almost a decade. As the researchers build a problem model, they select
parameters that will successively minimize error, according to analytic
techniques Patera helped developed. The calculation of error bounds is also a
feature of the phone application itself. For each approximate solution of a
parameterized problem, the app also displays the margin of error. The user can
opt to trade speed of computation for a higher margin of error, but the app can
generally get the error under 1% in less than a second.
Turning the tables
While the researchers’ software can calculate the behavior of a physical system
on the basis of its parameters, it could prove even more useful by doing the
opposite: calculating the parameters of a physical system on the basis of its
behavior. Instead of, say, calculating fluid flow around an obstacle based on
the obstacle’s size, the software could calculate the size of the obstacle
based on measurements of the fluid flow at the end of a pipe. Ordinarily, that
would require several different computations on a supercomputer, trying out
several different sets of parameters. But if testing, say, 30 options on a
supercomputer would take 30 hours; it might take 30 seconds on a phone. Indeed,
the researchers have already developed a second application that calculates
such “inverse problems.”
In the same way that a simulation of a
physical system describes its behavior on the basis of parametric measurements,
control systems, of the type that govern, say, automotive brake systems or
autonomous robots, determine devices’ behavior on the basis of sensor
measurements. Control-systems researchers spend a great deal of energy trying
to come up with practical approximations of complex physics in order to make
their systems responsive enough to work in real time. But Knezevic, Huynh and
Patera’s approach could make those approximations both more accurate and easier
to calculate.
Max Gunzberger, Frances Eppes Eminent
Professor of Scientific Computing at Florida
State University
says that the MIT researchers’ work has a “cuteness aspect” that has already
won it some attention. But “once you get over the cuteness factor,” he says,
“if you talk about serious science or serious engineering, there’s a potential
there,” Gunzberger points out that while the researchers’ demo concentrates on
fluid mechanics, “there’s lots of other problems that their approach can be applied
to. They built the structure that they themselves or others can start using to
solve problems in different application areas.”
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