ICES Professor Tan Bui-Thanh uses TACC systems to test new mathematical and computational approaches to statistical inverse problems

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 deal 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 has value in many other important areas.

Tan Bui-Thanh — lead of the Probabilistic and High Order Inference, Computation, Estimation, and Simulation (Pho-Ices) Group in the Institute for Computational Engineering and Sciences (ICES) at The University of Texas at Austin, 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, known as the NSF CAREER award, which 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."

"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 sciences 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 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.

"I have been very fortunate to have direct and instant support from TACC, which has provided me with computing hours and timely software trouble-shootings. These have facilitated my group to produce various preliminary results published in many papers, which in turn have helped establish the credibility for the research proposed in my NSF CAREER award."

"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 from their work on TACC systems in *Inverse Problems*, the *Journal of Computational Physics*, *SIAM Journal on Scientific Computing*, and *Water Resources Research*. The papers applied new scalable methods to various inverse modeling problems to mitigate the curse of dimensionality.

Using the Stampede1 supercomputer at TACC, they effectively used up to 16,384 computing cores and solved large, complex problems in a close to linear, rather than exponential, timescale. Bui-Thanh will expand on this research, which will continue to take advantage of TACC's large computing resources.

"I have been very fortunate to have direct and instant support from TACC, which has provided me with computing hours and timely software trouble-shootings," said Bui-Thanh. "These have facilitated my group to produce various preliminary results published in many papers, which in turn have helped establish the credibility for the research proposed in my NSF CAREER award."

The CAREER award compliments four other grants that Bui-Thanh received in 2018 from NSF, King Abdullah University of Science and Technology, UT System and the UT Austin Portugal Program, which together total $1.2 million, as well as grants in 2017 from the Department of Energy Fusion Energy Sciences and Advanced Scientific Computing Research, the Defense Threat Reduction Agency, and ExxonMobil that apply his inverse modeling methods to a range of critical problems.

"Since my proposed mathematical algorithms are designed for current and future large-scale computing systems, TACC will play an important role in the success of my research work," Bui-Thanh said.