Earth System Science increasingly relies on computational methods to infer, predict, and understand complex natural processes from large but incomplete observations. This course introduces the unifying framework of inverse problems, statistical learning, and experimental design that underpins modern scientific discovery across geophysics, atmospheric science, climate science, geology, and environmental science. Topics include linear and probabilistic inverse problems, uncertainty quantification, optimization, Bayesian inference, machine learning, generative AI, and the design of observational systems. Throughout the course, students develop practical skills by solving real Earth science problems using modern computational tools. Upon completion, students will be able to formulate inverse and learning problems, assess uncertainty in scientific conclusions, select appropriate computational models, and design data acquisition strategies that maximize information while recognizing the limitations of real-world observations.
References
- Menke, William. Geophysical data analysis: Discrete inverse theory. Academic press, 2018.
- Tarantola, Albert. Inverse problem theory and methods for model parameter estimation. Society for industrial and applied mathematics, 2005.
- Robinson, Enders A., and Sven Treitel. Geophysical signal analysis. Society of Exploration Geophysicists, 2000
- A. Blum, J. Hopcroft, and R. Kannan (2020) Foundations of Data Sciences, Cambridge University Press
- James, G., Witten, D., Hastie, T., & Tibshirani, R. (2013). An introduction to statistical learning (Vol. 112, p. 18). New York: Springer.
- Boyd, Stephen, and Lieven Vandenberghe. Introduction to applied linear algebra: vectors, matrices, and least squares. Cambridge university press, 2018.
- Simon J. D. Prince (2023). Understanding Deep Learning. MIT Press.
- Bishop, C. M., & Bishop, H. (2024). Deep Learning: Foundations and Concepts. Springer.