Métodos estadísticos
Ramsay & Hooker (2017): Específico a ecuaciones diferenciales y sistemas dinámicos.
Hastie et al. (2009): Referencia bibliografica de preferencia para referencia (corta) a metodos de estadística y aprendizaje automático.
Murphy (2022): Referencia moderna con un monton de material. Bueno para referncia rápida.
Physics-informed machine learning
Generales: Karniadakis et al. (2021) Thuerey et al. (2021)
Neural ODEs: Chen et al. (2018)
Physics-Informed Neural Networs (PINNs): Raissi et al. (2019)
Universal Differential Equations (UDEs): Rackauckas et al. (2020)
Programación diferenciable
Blondel & Roulet (2024)
Aplicaciones en geofísica
Glaciología: Bolibar et al. (2023)
Paleomagnetismo y tecnónica de placas: Sapienza et al. (2025)
- Ramsay, J., & Hooker, G. (2017). Dynamic data analysis. Springer New York, New York, NY. Doi, 10, 978–1.
- Hastie, T., Tibshirani, R., Friedman, J., & others. (2009). The elements of statistical learning. Springer series in statistics New-York.
- Murphy, K. P. (2022). Probabilistic Machine Learning: An introduction. MIT Press. http://probml.github.io/book1
- Karniadakis, G. E., Kevrekidis, I. G., Lu, L., Perdikaris, P., Wang, S., & Yang, L. (2021). Physics-informed machine learning. Nature Reviews Physics, 3(6), 422–440. 10.1038/s42254-021-00314-5
- Thuerey, N., Holl, P., Mueller, M., Schnell, P., Trost, F., & Um, K. (2021). Physics-based deep learning. arXiv Preprint arXiv:2109.05237.
- Chen, R. T., Rubanova, Y., Bettencourt, J., & Duvenaud, D. K. (2018). Neural ordinary differential equations. Advances in Neural Information Processing Systems, 31.
- Raissi, M., Perdikaris, P., & Karniadakis, G. E. (2019). Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics, 378, 686–707. 10.1016/j.jcp.2018.10.045
- Rackauckas, C., Ma, Y., Martensen, J., Warner, C., Zubov, K., Supekar, R., Skinner, D., Ramadhan, A., & Edelman, A. (2020). Universal differential equations for scientific machine learning. arXiv Preprint arXiv:2001.04385.
- Sapienza, F., Bolibar, J., Schäfer, F., Groenke, B., Pal, A., Boussange, V., Heimbach, P., Hooker, G., Pérez, F., Persson, P.-O., & Rackauckas, C. (2024). Differentiable Programming for Differential Equations: A Review. arXiv. 10.48550/arxiv.2406.09699
- Blondel, M., & Roulet, V. (2024). The elements of differentiable programming. arXiv Preprint arXiv:2403.14606.
- Bolibar, J., Sapienza, F., Maussion, F., Lguensat, R., Wouters, B., & Pérez, F. (2023). Universal differential equations for glacier ice flow modelling. Geoscientific Model Development, 16(22), 6671–6687. 10.5194/gmd-16-6671-2023
- Sapienza, F., Gallo, L. C., Bolibar, J., Pérez, F., & Taylor, J. (2025). Spherical Path Regression Through Universal Differential Equations With Applications to Paleomagnetism. Journal of Geophysical Research: Machine Learning and Computation, 2(4). 10.1029/2025jh000626