Mathematical Sciences for Artificial Intelligence

6 CFU; 48 hours of lecture ~12 weeks Overview: This course provides a foundation in earthquake physics and a summary of machine learning techniques used to predict geophysical characteristics of tectonic faulting. General objectives: Develop the theory of friction constitutive laws for tectonic faulting, earthquake nucleation and dynamic rupture propagation. Provide a foundational background in earthquake physics for understanding source parameters and scaling laws for earthquakes. Introduce concepts of fault weakening as related to the onset of elastodynamic rupture. Specific objectives: Provide a motivational summary of the rapidly expanding progress in the use of AI to predict earthquakes in the laboratory and how this knowledge is being used applied to tectonic faults. Discuss the physical mechanisms and AI methods for: 1) identifying clear and consistent precursors prior to lab earthquakes, 2) improving earthquake detection based on automated AI methods, 3) using a cascade of micro-failure events to foretell catastrophic failure with particular attention to laboratory earthquakes. Knowledge and understanding: Students will acquire knowledge about earthquake science, friction constitutive laws, and methods to forecast and predict seismicity. Application of knowledge and understanding: Students will gain knowledge of earthquakes, tectonic faults, and fault weakening mechanisms that lead to the transition from stable, aseismic slip to fully dynamic rupture. The location and timing of earthquakes will be placed in the context of the theory of plate tectonics and large scale deformation of Earth's surface. Autonomy of judgment: Students will gain facility with earthquake science, tectonic faulting and earthquake forecasting. Communication skills: Students will improve communication skills through classroom discussion and critical reading of the scientific literature. Detailed Summary: This course will provide a comprehensive summary of how machine learning (ML) is being used to predict frictional failure events, the lab equivalent of earthquakes, and improve our understanding of the physics of catastrophic earthquakes on tectonic faults. We will review the recent works, over the past few years, that solved a 50+ year old dilemma of how to predict the time to failure of lab earthquakes using laboratory seismic data. These works show: 1) that ML can predict the timing and magnitude of labquakes using acoustic emissions (AE) that originate in the lab fault zone, 2) that in addition to passive measurements of lab AE, active source measurements of changes in fault zone elastic properties during the lab seismic cycle can be used to predict lab earthquakes, and 3) that the lab-based work can be applied to tectonic faulting in at least special cases if not more generally. Recent work shows that labquakes are preceded by a cascade of AE events and systematic changes in elastic wave speed and transmitted amplitude that foretell catastrophic failure. As in all areas of AI, the methods being used for this problem evolve rapidly. We will discuss current techniques and traditional ML techniques based on regression. A primary goal of the course will be to provide the scientific background needed to understand tenets of earthquake physics while introducing students to ML/DL methods to predict failure time and magnitudes. We will also study DL-based methods to autoregressively forecast labquakes and fault zone shear stress. Students will learn how to use lab seismic data and also how to access earthquake data from regional networks in Italy and worldwide. Our studies of earthquake physics will include the evolution of frequency magnitude statistics during the lab seismic cycle, which provides an opportunity to use ML to interrogate the physics of impending failure. We will also see how precursors to lab earthquakes, that can be identified by AI, provide a sensible connection between the ML-based predictions, based on AE, and the physics of failure. In the lab, AE events represent a form of foreshock and, not surprisingly, the rate of foreshock activity correlates with fault slip rate and its acceleration toward failure. A central theme of the course will be to learn how lab earthquake prediction can improve forecasts of earthquake precursors and tectonic faulting.

Basic physics and math. Python coding. Ability to read English. Interest in improving your ability to code, write in English and to speak about earthquakes and ML in English

Articles from the literature such as: Lubbers, N., Barros, K.,Humphreys, C. J., & Johnson, P. A.(2017). Machine learningpredicts laboratory earth-quakes.Geophysical ResearchLetters,44, 9276–9282. https://doi.org/10.1002/2017GL074677 Borat, P. Rivière, J, Marone, C., Mali, A, Kifer, D. and P. Shokouhi, Using a physics-informed neural network and fault zone acoustic monitoring to predict lab earthquakes, Nat. Comm., 14:3693, doi.org/10.1038/s41467-023-39377-6, 2023 Laurenti, L., Tinti, E., Galasso, F., Franco, L., and C. Marone, Deep learning for laboratory earthquake prediction and autoregressive forecasting of fault zone stress, Earth and Plan. Sci. Lett., 598, 117825, doi.org/10.1016/j.epsl.2022.117825, 2022 Jaspereson, H., Bolton, D. C., Johnson, P. A., Guyer, R., Marone, C. and M. V. de Hoop, Attention network forecasts time-to-failure in laboratory shear experiments, J. Geophys. Res. Solid Earth, 126, 10.1029/2021JB022195, 2021. Johnson, P.A., Rouet-Leduc, B., Pyrak-Nolte, L.J., Beroza, G.C., Marone, C., Hulbert, C., Howard, A., Singer, P., Gordeev, D., Karaflos, D., Levinsong, C.J., Pfeiffer, P., Puk, K. M, and W. Reade, Laboratory earthquake forecasting: a machine learning competition, Proc. Natl. Acad. Sci., 118, 10.1073/pnas.2011362118, 2021. Shokouhi, P., Girkar, V., Rivière, J., Shreedharan, S., Marone, C., Giles, C. L., and D. Kifer, Deep learning can predict laboratory quakes from active source seismic data, Geophys. Res. Lett., 10.1029/2021GL093187, 2021.
 Shreedharan, S., Bolton, D. C., Rivière, J., and C. Marone, Competition between preslip and deviatoric stress modulates precursors for laboratory earthquakes, Earth and Plan. Sci. Lett., 553, 10.1016/j.epsl.2020.116623, 2021. Shreedharan, S., Bolton, D. C., Rivière, J., and C. Marone, Machine learning predicts the timing and shear stress evolution of lab earthquakes using active seismic monitoring of fault zone processes, J. Geophys. Res. Solid Earth, 126, 10.1029/2020JB021588, 2021. Bolton, D. C., Shokouhi, P., Rouet-Leduc, B., Hulbert, C., Rivière, J., Marone, C., and P. A. Johnson, Characterizing acoustic precursors to laboratory stick-slip failure events using unsupervised machine learning, Seis. Res. Letts., 10.1785/0220180367, 2019. Hulbert, C., Rouet-Leduc, B., Johnson, P. A., Ren, C. X., Rivière, J., Bolton, D. C., and C. Marone, Machine learning predictions illuminate similarity of fast and slow laboratory earthquakes, Nat. Geosc., 12, 69-74, 10.1038/s41561-018-0272-8, 2019. Lubbers, N., Bolton, D. C., Mohd-Yusof, J. Marone, C., Barros, K. and P. A. Johnson, Earthquake catalog-based machine learning identification of laboratory fault states and the effects of magnitude of completeness, Geophys. Res. Lett., 45, 13,269–13,276, 10.1029/2018GL079712, 2018. Marone, C., Training machines in Earthly ways, Nature Geosc., 11, 301-302, 2018. Rivière, J., Lv, Z., Johnson, P. A., and C. Marone, Evolution of b-value during the seismic cycle: Insights from laboratory experiments on simulated faults, Earth and Plan. Sci. Lett., 482, 407–413, 10.1016/j.epsl.2017.11.036, 2018. Rouet-Leduc, B., Hulbert, C., Bolton, D. C., Ren, C. X., Rivière, J., Marone C., Guyer, R. A., and P. A. Johnson, Estimating fault friction from seismic signals, Geophys. Res. Lett., 10.1002/2017GL076708, 2018.

The course is optional

Oral presentation of an article on application of machine learning to earthquake physics and written exam including solutions to problems and python coding.

Students will be expected to attend classroom meetings.