MATH + X Symposium on Data Science and Inverse Problems in Geophysics

Harnessing enormous amounts of data collected by sensors of different types is at the cusp of revolutionizing the earth sciences. The 2018 symposium will focus on the cross fertilization between the analysis of inverse problems, data science and machine learning in geophysics. Learning approaches have revolutionized machine vision, speech recognition, and a host of other domains. However, the development of machine learning algorithms for geophysical problems remains under-explored. The classical way of analyzing sensor data relies directly on partial differential equations, dynamical systems, etc, that are derived from the physics of the sensing scenario, that is, via inverse problems. Over the past decade, however, new machine learning techniques for interrogating data have been proposed and developed that bypass physics and learn models directly from data. The symposium will seek synergies between these points of view.

Deep learning is emerging as an important approach to glean information about processes in Earth’s interior. The cross fertilization between the analysis of inverse problems and machine learning is essentially still wide open, and new models in machine learning put forward exciting opportunities. Beyond their ability to capture, for example, multi-scale geometric aspects of the data, it has been shown that architectures such as deep convolutional networks can approximate certain inverse mappings. Contextual LSTM models show promise in learning ambient noise recordings. Notions of Gaussianization and manifold learning appear regularly in the discussion, while an important role seems to be played by the invariance properties of these models as well as their (unprecedented) ability to encode scale interactions, and the metric. A significant contribution to the representational power of deep networks comes from nonlinearities which give rise to non-convex regularizers, calling in turn for new ideas in optimization. Moreover a tight connection between inverse problems and data analysis leads to strategies for adaptive acquisition based on learning.

This workshop will bring together geophysicists, mathematicians, computer scientists and statisticians to present the state-of-the-art on the one hand, and emerging cross-disciplinary directions of research on the other hand, while enabling new collaborations.