Hi! I'm Martín,

Dynamics • Randomness • Learning

I’m a PhD candidate at FAU Erlangen–Nürnberg, Germany, working at the intersection of control theory, partial differential equations, and deep learning. My research focuses on randomized algorithms for dynamic systems.

About Me

I'm Martín Hernández Salinas

I am a mathematician with a strong background in partial differential equations, numerical analysis, and control theory. My academic path began in Chile, where I earned both my engineering and master’s degrees in mathematics at USM under the supervision of Dr. Rodrigo Lecaros and Dr. Sebastián Zamorano. I am currently pursuing my PhD at FAU Erlangen–Nürnberg under the supervision of Dr. Enrique Zuazua. My research lies at the interface of continuous-time models and modern machine learning, with a particular emphasis on developing efficient randomized algorithms—such as random batch methods—for applications ranging from PDEs defined on graphs to optimal control and deep learning. I am also interested in bridging theoretical insights with practical implementations through numerical experiments. I am passionate about interdisciplinary problems and strive to connect rigorous mathematical analysis with emerging computational techniques.

Research

Publications

Hernández, M., Lecaros, R., Zamorano, S. (2023). Averaged turnpike property for differential equations with random constant coefficients. Mathematical Control and Related Fields. AIMS
Hernández, M., Zuazua, E. (2024). Uniform Turnpike Property and Singular Limits. Acta Applicandae Mathematicae. Springer
Hernández, M., Dominguez-Corella, A. (2025). Mini-batch descent in semiflows. ESAIM-COCV. COCV

Preprints

Hernández, M., Lazar, M., Zamorano, S. (2024). Averaged observations and turnpike phenomenon for parameter-dependent systems. Preprint. arXiv:2404.17455
Hernández, M., Zuazua, E. (2024). Constructive Universal Approximation and Finite Sample Memorization by Narrow Deep ReLU Networks. Preprint. arXiv:2409.06555v1
Hernández, M., Zuazua, E. (2025). Random Batch Methods for PDE control on graphs. Preprint. arXiv:2409.06555v1

In Preparation

Hernández, M. (2025). Random domain decomposition for parabolic PDEs. Preprint.
Hernández, M., Álvarez-López, A. (2024). A mathematical framework for dropout in neural ODEs via random batch methods. Preprint.

For a full list of publications, please visit my Google Scholar profile.