A team of researchers has been awarded the Wilkinson Prize for developing software that makes light work of complex mathematical models.

Models are invaluable tools for scientists studying everything from future climate to the human body. A traditional forward model uses observations as a starting point to make predictions about what will happen in the future. A corresponding adjoint model allows researchers to run a forward model in reverse to investigate the factors which led to a given outcome.

Whilst adjoint models can deliver crucial insights across a range of scientific disciplines, developing them is notoriously tricky. The dolfin-adjoint software however automates the process, putting these powerful models into the hands of scientists to whom they were previously inaccessible.

“Dolfin-adjoint allows scientists to not just ask what happens, but what the causes are and what input variables are important,” explains Dr Ham, who developed the software during his time as a Grantham Institute Fellow, along with Grantham Institute PhD alumnus Dr Funke, Imperial PhD alumnus Dr Patrick Farrell (now of the University of Oxford), and Dr Marie Rognes of Norway’s Simula Research Laboratory.

This is the first time that UK researchers have won the Wilkinson Prize, which is awarded every four years by Argonne National Laboratory, the National Physical Laboratory and the Numerical Algorithms Group.

While adjoint models have existed for some time, conventional methods for developing them are both time-consuming and labour-intensive. Developing the adjoints of complex models has consumed many years of scientist time, something that most research teams simply cannot afford.

“Developing these models was fiendishly difficult,” says Dr Farrell. “But together we worked out that in many cases we could automate the process from start to finish.”

Coupled with simulation software, dolfin-adjoint makes building an adjoint model far easier, and sometimes vastly more efficient.

 “It’s a game changer,” says Dr Ham. “Having an adjoint model to your forward model used to be a major research project. Now you add a few lines to your code and the adjoint is derived automatically.”

Building better tidal farms

Dr Simon Funke was one of the first to exploit the software’s capabilities during his PhD, where he and Dr Farrell collaborated with tidal farm companies on their plans to deploy underwater tidal turbines in Scotland’s Pentland Firth by 2020. In order to harvest as much energy as possible from a tidal farm on this scale, optimising the arrangement of the turbines is key.

“With up to 400 turbines it becomes very challenging to identify the best turbine farm layout,” says Dr Funke. Using dolfin-adjoint, he was able to calculate the optimal number of turbines and the most efficient way of positioning them.

Now based at Simula Research Laboratory in Norway, Dr Funke still works with dolfin-adjoint, this time applying it to blood flow models which are used to improve clinical decisions. “Our software can be used for a wide range of mathematical problems,” he adds.

Following on from his work on dolfin-adjoint, Dr Farrell meanwhile was awarded an EPSRC Early Career Fellowship at the University of Oxford, and also holds a visiting position at Simula.

The team will receive the $3,000 prize at the International Congress on Industrial and Applied Mathematics in August 2015, following the official announcement of the winners last week.

“It was very unexpected,” says Dr Ham. “We thought we had no chance of winning!”

To extend the capabilities available to users, the team continuously improves the software, which is available to download freely from the dolfin-adjoint website.