Hi! I'm Martín,

Dynamics • Randomness • Learning

I am a postdoctoral researcher at the University of California, Los Angeles (UCLA), in Prof. Yuhua Zhu’s group. My current work centers on continuous-time reinforcement learning at the interface of mean-field control and partial differential equations. I completed my Ph.D. at Friedrich-Alexander-Universität Erlangen–Nürnberg (FAU), Germany, under Prof. Enrique Zuazua; my previous work covers long-time behavior in optimal control, randomized numerical methods for dynamical systems and PDEs, and the expressivity of deep learning models.

Martin_Oberwolfach

About Me

I'm Martín Hernández Salinas

A brief overview of my academic background, current position, and research interests.

Who am I?

I am a mathematician working at the intersection of partial differential equations, numerical analysis, control theory, deep learning, and reinforcement learning.

What is my current position?

I am currently a postdoctoral researcher at the University of California, Los Angeles (UCLA), in Prof. Yuhua Zhu’s group, where I work on continuous-time reinforcement learning, particularly in multi-agent systems and mean-field control.

Where did I study?

My academic path began in Chile, where I earned both my engineering and master’s degrees in mathematics at Universidad Técnica Federico Santa María (USM), under the supervision of Prof. Rodrigo Lecaros and Prof. Sebastián Zamorano.

What did I do during my Ph.D.?

I earned my Ph.D. (Dr. rer. nat.) at Friedrich-Alexander-Universität Erlangen–Nürnberg (FAU), Germany, under the supervision of Prof. Enrique Zuazua. During this period, I focused on continuous-time models and on efficient randomized algorithms, such as random-batch methods, for PDEs, optimal control, and deep learning.

What are my research interests?

My current interests include continuous-time reinforcement learning, multi-agent systems, mean-field control theory, partial differential equations, and randomized methods for dynamical systems. More recently, part of my attention has also turned to understanding supervised learning models from a mathematical viewpoint.

What motivates my work?

I am naturally driven by curiosity. Despite my strong mathematical training, I remain an engineer at heart, interested not only in rigorous analysis but also in building, testing, and understanding how ideas work in practice. More than anything, I am motivated by science, discovery, and the bridge between theory and reality.

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

Hernández, M., Lazar, M., Zamorano, S. (2026)

Turnpike phenomenon for averaged optimal control

Optimization

Optimization

Preprints

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:2506.11809

Hernández, M. (2025)

Random domain decomposition for parabolic PDEs

Preprint

arXiv:2508.21557

Hernández, M., Álvarez-López, A. (2025)

Convergence, design and training of continuous-time dropout as a random batch method

Preprint

arXiv:2510.13134

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

Implementations

Tutorials

PINNs heat GIF

PINNs introductory code for the heat equation (PyTorch implementation).

PyTorch tutorial simulation

Hands-on PyTorch tutorial: build and train your first neural network.

Parabolic PDE on graphs

Library to solve Parabolic PDE on graphs.

Paper Codes

Multiclass UAT GIF

Universal binary classification via deep nets—without optimization.

Turnpike property plot

Turnpike property: finite-dimensional cases with uncertainty (GEKKO implementation)

Obstacle problem comparison

Random minimizing-movement for the obstacle problem (FEniCS implementation).

Find more implementations on my GitHub.

Contact Me

Please feel free to reach out regarding research, collaborations, or academic discussions.

Contact Information

Email UCLA: martinh[at]g.ucla.edu

Email FAU: martin.hernandez[at]fau.de

Office: Boelter Hall, Room 9413, UCLA

External Links