# Taking the guesswork out of highly complex designs

## Powerful mathematical tools take the guesswork out of highly complex designs

Super-cavitating hydrofoils are deployed during take off ensuring the development of a lift force balancing the vessel’s weight.

Researchers from Brown University, led by Professor George Karniadakis, have joined forces with other leading institutions to develop powerful mathematical tools which simplify and reduce the myriad of ambiguities and variables involved in the design of highly complex military vessels.

Optimal design of military vessels depends on the reduction and resolution of an overwhelming number of factors such as predictability, incomplete information, and missing data.  These robust and powerful mathematical tools seek to reduce their impact on the systems’ design and performance.  Understanding what can amount to thousands of variables is paramount when it comes to designing a vehicle of the highest magnitude while  safeguarding its cost.   DARPA’S program entitled, “Enabling Quantification of Uncertainty in Physical Systems (EQUiPS)” has made seminal advances addressing these problems inherit in the design process.

Problems such as ascertaining how accurate a prediction might be, requires computational models to take into account when important data is incomplete, or missing.  Reducing these uncertainties also makes it easier to predict how a particular system will perform.   This is precisely the genius behind the EQUiPS program.

Uncertainty Quantification or UQ focuses on the use of methods to estimate how accurate a prediction might be.  With the development of advanced UQ tools, designers can attempt to ascertain the risks involved in specific designs, and thereby reduce them.  These advanced computational tools, spurned from the mathematicians who have created them, help to improve the certainty of how, for example hypersonic airspeeds of sea vessels are able to slice through strong currents of sea water.

A team at Brown University assists the EQUiPS effort and has developed the theory underlying what is called Design Under Uncertainty (DUU).  When the number of parameters or features can be in the thousands, DUU models help to simplify the design process for unconventional defense systems.  One such accomplishment is the design of a hydrofoil surface sea vessel that is able to achieve a speed of 120 knots.  Since there are no historical data for such a watercraft, a model of performance was needed to account for an exceedingly great number of uncertainties. The DUU protocol was able to seek out the best design and outcomes.

Through the framework developed under the program, the team was able to look at the entire design process, utilize different models, and deliver not only the best design candidate, but also all other possible designs complete with predicted outcomes.

“We see the world in three dimensions, but imagine how complicated everything would appear if it were composed of 28 dimensions—and how much simpler life would be if we could get those 28 dimensions down to seven,” Fahroo said. “That’s what a huge difference EQUiPS approaches can make.” (Fariba Fahroo, Program Manager)

Other institutions such as MIT, Virginia Tech, UC at Santa Cruz and the Naval Postgraduate School work closely with Brown on this hydrofoil system.  (Read full story.)