**Their goal is to deliver an open and flexible numerical simulation software for solutions to inverse problems**

**Their goal is to deliver an open and flexible numerical simulation software for solutions to inverse problems**

The subject of inverse problem solving is increasingly recurrent in academia. These are situations when scientists have measurements of something, but do not know exactly what it is, and they want to find out. For example: the size and geometric shape of an onshore or offshore petroleum or natural gas reservoir. Or the wind conditions at all points of a location where a wind farm is planned to be set up. Inverse problems require a different approach from that of direct problems: those in which scientists have access to the object being studied.

“A numerical model must be able to reproduce the behavior of its physical model. In a normal modeling problem, what usually happens is that you have access to the object, can test it in a laboratory, and can propose increasingly sophisticated equations that reproduce the behavior of that object. With an inverse problem, you have no access to the object, but you have ways of testing it: one can enter a black box that cannot be accessed, and measure an exit output. Based on this response, and on a bit of knowledge and assumptions that one has with regard to the object and the physical laws that govern it, it is possible to propose a model of the object,” explains Bruno Carmo, Overall Coordinator of the new project.

He lays out details of the interest in the subject BY the petroleum and natural gas industry. “Basically, it is important for optimizing the solution of seismic imaging issues, which are inverse problems: with regard to offshore, for example, there are the marine subsoil and the reservoirs with which we are not familiar. In order to know if there is oil or gas there, a boat equipped with an air gun shoot jets of air that generate sound waves. They reflect off the subsoil, a part of them is refracted, and those sound waves return to the surface and are captured by hydrophones. This is to find out what the subsoil is like. Then, software reads this information, based on the interpretation of the data, and gives us a ‘map’ of the prospected area.”

Of course, the industry already does this type of soil survey, but the “plus” of the RCGI project lies in the performance and flexibility of the software used to interpret the field information. “Performance is important, because the industry now does this at extremely high cost. But what is most important about our differential is its flexibility. Today, there are programs that handle these problems, but any alteration of the software is very complicated. Sometimes, it is not the geophysicist who makes the program, so the alterations can take weeks or even months – or, since it is commercial software, and there is not much flexibility, or since they are products that have been developed by the industry over a long period of time and have a highly expensive maintenance cost,” Carmo explains.

He and his team, consisting of more than 60 researchers, 12 of whom are foreigners (the biggest team put together for an RCGI project, to the present time), want to produce software in which the equations are written almost ‘symbolically’. “The software will automatically generate a code for solving the equations. That is, this job, which is usually done by the geophysicist or programmer – translating the equations into computational codes – would be performed entirely automatically. And we do not intend to merely optimize the generation of the numerical method for solving equations, but also the entire compilation and optimization phase for the computational architecture within the environment in which the program will be run.”

The project also has a group that will develop mesh generators. Carmo says that the world is somewhat lacking in open mesh generators with good performance and flexibility. “A mesh generator is software that, starting with a given geometry, divides it into smaller pieces to allow obtaining an approximate numerical solution of the equations that characterize it. In a numerical simulation, this is the most expensive part from the standpoint of man/hours.” According to him, the options that are available today still require much manual adjustment, so if the group is able to conceive of a mesh generator that is user-friendly and of a good quality, it could have a huge impact on the scientific community. “It must be something easy to use by those who are not well-versed in the computer sciences or in programming, but who have knowledge of physics and equations. The software language must be very similar to the language used by researchers,” he adds.

**Open source** – The project is set up for a duration of four years and the team will deliver open software that will serve to solve any inverse problem, in a variety of environments and knowledge areas. “We will study applications for different architectures, optimize and test for a variety of platforms: for the cloud, for clusters, for GPUs. We have to validate the tool for each one of them and it has to function on all of them,” Bruno states. He says the validation will be done with synthetic data, similar to the original.

The engineer explains that measurement of the software’s performance is found according to the computational time spent characterizing the object. “You cannot directly validate it, because in the case of a reservoir, for example, you will never know what is down below, but you can produce a model of the object, test it with an entrance, and see if the result is equal or similar to what you found in the field.” He says that the problem is considered solved when the difference between the exit output calculated by the software and the field measurement is small, within a given range of tolerance.

The new RCGI initiative consists of five working groups, each one having a Coordinator; numerical methods applied to finite differences (the responsibility of a team from USP’s Institute of Mathematics and Statistics – IME); sensitivity calculations (refers to the variation of the response of the object to each new input, or stimulus); high-order discontinuous methods; mesh generation and adaptation; and code generating and optimizing. “The Coordinators are myself and Professors Rafael Gioria, Emílio Silva, and Ernani Volpe, from Poli/USP; and Professor Saulo Barros, from IME,” Carmo added.

Within the RCGI, the new project ‘talks’ with several others, above all to the CO_{2} Abatement Program. For example, the software may be used to look for good places to dig a salt cavern, or to prospect for and fine nonconventional onshore natural gas reserves. “One important thing to note is that this is not a part of the CO_{2} Abatement Program, but has come at the behest of another Shell team, which deals with geophysics. It is an expansion for another, independent demand. We are entering another harvest, which is seismic.”

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