“As a structural engineer, I know I’m in my community.”
With this greeting, Reginald DesRoches, the William and Stephanie Sick Dean of the George R. Brown School of Engineering at Rice University, welcomed more than 90 scholars and students attending the Math + X Symposium on Data Science and Inverse Problems in Geophysics. Funded by the Simons Foundation, the symposium was held Jan. 24-26 at Rice.
The symposium focused on the cross-fertilization among the analysis of inverse problems, data science and machine-learning geophysics.
“Machine and deep learning are seeking a comprehensive mathematical understanding. It may be possible to unlock the analysis of inverse problems out of the rigid framework at the intersection of various fields in mathematics. Both are foundational components of, and meet within data science,” said the symposium’s organizer, Maarten V. de Hoop, the Simons Chair and Professor of Computational and Applied Mathematics and Earth Science at Rice.
Twenty-five speakers from six nations addressed the group, including Stéphane Mallat, an applied mathematician with the Collège de France. His talk, titled “Unsupervised learning of stochastic models with deep scattering networks,” developed his ongoing research into wavelet theory and its implications for signal processing.
Wavelets, Mallat has shown, can be useful in compressing high-definition images. In his Math + X talk, Mallat said: “Deep neural networks have obtained remarkable results in modeling such random processes as faces and geometrical shapes. We have shown that we can obtain similar results by transforming Gaussian white noise with a non-linear operator computed by inverting a multiscale scattering transform.”
Other speakers included Nathan Kutz of the University of Washington, Michel Campillo of the Université Grenoble Alpes, and Victor Pankratius of the MIT Haystack Observatory. In his talk, “Computer-Aided Discovery: Can a Machine Win a Nobel Prize?”, Pankratius discussed how deep neural networks enable him and fellow researchers to detect atmospheric turbulence using GPS and MODIS satellite data.
“We demonstrate a novel machine learning approach that uses two types of data. The turbulence we detect can pose a real danger to aviation,” Pankratius said.
Elizabeth Rampe is a planetary geologist in NASA Johnson Space Center’s Astromaterials Research and Exploration Science (ARES) division. She is deputy principal investigator and instrument operations lead for the Chemistry and Mineralogy (CheMin) instrument on Curiosity, the Martian rover that landed on the surface of Mars in 2012.
“Our job was to look for evidence of microbial-habitable environments in the rocks and sediments in Gale Crater,” Rampe said. Curiosity drilled into the surface and supplied CheMin with powdered samples, then used X-rays to reveal the crystalline structure in the grains. The data is then relayed to Earth.
“The challenge for our team is to integrate all the data we collected and use multiple datasets to interpret the ancient Martian environment,” Rampe said.
The research of the symposium’s organizer, de Hoop, focuses on inverse problems, a method that permits researchers to start with a set of observations and work backward to calculate the causes that produced them.
“The Earth,” de Hoop said, “is an important platform for accomplishing the goal of exploiting machine and deep learning while unlocking inverse problems from their rigid framework. We will explore the interior of the Earth and reveal the undiscovered processes shaping the evolution of planets, while furthering the causes of sustainability and energy. Mars is on the horizon.”
The entire program of the symposium can be found at: