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Many areas of science and engineering try to predict how an object will respond to a stimulus — how earthquakes propagate through the Earth or how a tumor will respond to treatment. This is difficult even when you know exactly what the object is made of, but how about when the object’s structure is unknown?

The class of problems that deals with such cases is known as inverse modeling. Based on information often gleaned at the surface — for instance, from ultrasound devices or seismometers — inverse modeling tries to determine what lies below, whether it is the size of a tumor or a fault in the Earth.

But doing so is fraught with challenges, in part because both the models that define a process and the imaging devices used to probe the depths are imperfect. So, to truly understand and provide useful information about a subject, a further step is needed: uncertainty quantification, a way of assessing how sure one is of a solution. Uncertainty quantification, also known as UQ, has become common in weather prediction (think of the forecasters’ “30 percent chance of rain”), but have value in many other important areas.

Tan Bui-Thanh — leader of the ICES Probabilistic and High Order Inference, Computation, Estimation, and Simulation (Pho-Ices) Group, and an assistant professor in the Department of Aerospace Engineering and Engineering Mechanics— is an expert in solving such problems.

In January, Bui-Thanh was awarded a prestigious 2019 National Science Foundation (NSF) Faculty Early Career Development award, jointly funded by the NSF Office of Advanced Cyberinfrastructure and the NSF Division of Mathematical Sciences. Known as the NSF CAREER award, the grant is designed to support early-career faculty “who have the potential to serve as academic role models in research and education, and to lead advances in the mission of their department or organization.” Activities pursued by early-career faculty build a firm foundation for a lifetime of leadership in integrating education and research.

“I’m honored to receive this award from NSF, which will enable me and my team to break new ground in the mathematical and computational modeling of intractable engineering and science problems,” said Bui-Thanh.

Bui-Thanh will use the five-year, $525,000 grant to develop an integrated education and cross-disciplinary research program that tackles big data-driven, uncertainty quantification problems related to inverse modeling. His project, entitled "CAREER: Scalable Approaches for Large-Scale Data-driven Bayesian Inverse Problems in High Dimensional Parameter Spaces," will bring together advances from stochastic programming, probability theory, parallel computing, and computer vision to produce a rigorous data reduction method and justifiable efficient sampling approaches for large-scale Bayesian inverse problems.

Bui-Thanh will apply the methods he develops to seismic wave propagation, exploring how waves of energy travel through the Earth's layers as a result of earthquakes, volcanic eruptions, large landslides or large man-made explosions. Using synthetic data initially, and eventually historical data from earthquakes, as data sources, he hopes to better model the composition of the Earth to predict how earthquakes may impact locations and structures at the surface.

“Our long-term goal is to estimate the structure of the earth with UQ,” Bui-Thanh explained. “If you can image the Earth quite well and solve for how an earthquake propagates in real time, you can help decision-makers know where there will be potential earthquakes, and use that information to set building codes, determine where and when to evacuate, and save lives.”

The research also has important applications in energy discovery, potentially helping companies discover new oil resources and determine the amount of fossil fuels left from existing wells. The mathematical methods will be general enough that researchers will be able to use them for a host of other inverse problems, like medical imaging and weather forecasting.

**Overcoming the Curse of Dimensionality**

The problem at the heart of Bui-Thanh’s research is known as the ‘curse of dimensionality.’ This refers to the fact that when one tries to gain more resolution or clarity in solving inverse problems, the difficulty of the calculations increases exponentially, frequently pushing them into the realm of impossibility.

For instance, using the high-performance computers at the Texas Advanced Computing Center (TACC), among the fastest in the world, it can take minutes or hours to perform a single simulation, also known as a sample, to determine the makeup of the Earth.

“If a problem needs 1,000 samples, we don’t have the time,” Bui-Thanh said. “But it may not be a thousand samples we need. It can require a million samples to obtain reliable uncertainty quantification estimations.”

For that reason, even with supercomputers getting faster every year, traditional methods can only get researchers so far. Bui-Thanh will augment traditional inverse methods with machine learning to make problems more solvable. In the case of seismic wave propagation, he hopes to employ a multi-disciplinary approach, including machine learning, to do fast approximations for often-large areas of less importance and focus the high-resolution simulations on often-small parts of the problem that are deemed most critical.

“We will develop new mathematical algorithms and rigorously justify that they can be accurate and effective,” he said. “We’ll do this in the context of big data and will apply it to new problems.”

In 2017-2018, Bui-Thanh and colleagues at UT Austin and other universities published preliminary results in *Inverse Problems, The Journal of Computational Physics, SIAM Journal on Scientific Computing*, and *Water Resources Research* that applied these new scalable methods to various inverse modeling problems.

The team mitigated the curse of dimensionality to solve large, complex problems in a close-to linear, rather than exponential, timescale. Using the Stampede1 supercomputer at TACC, they effectively used up to 16,384 computing cores. The NSF funding will expand on this research, which will continue to take advantage of TACC’s large computing resources.

In addition to his research, Bui-Thanh is writing a book on mathematical interplays between machine learning methods to inverse modeling algorithms and has been teaching a class based on this book bi-annually at UT Austin to help expand the pipeline of trained professionals able to apply inverse modeling and machine learning methods to important problems.

The CAREER award compliments four other grants that Bui-Thanh received this year (from NSF, King Abdullah University of Science and Technology, UT System and the UT Austin Portugal Program), which together total $1.2 million. In 2017, Bui-Thanh received grants from the Department of Energy Fusion Energy Sciences and Advanced Scientific Computing Research, the Defense Threat Reduction Agency, and ExxonMobil, to apply his inverse modeling methods to a range of critical problems.

Bui-Thanh earned his Ph.D. from MIT and served as a postdoc at both MIT and ICES before joining the UT faculty in 2013.