Javier Castro

Portrait of Javier Castro

Doctoral Researcher
TU Berlin

Research profile

Javier Castro works on scientific machine learning and numerical methods for partial differential equations. His research includes thermodynamically informed neural networks, weak-residual formulations, and curvature-aware optimization methods.

Research areas

Numerics · Machine Learning · Sampling

Five research keywords

scientific machine learning · partial differential equations · thermodynamically informed neural networks · weak-residual formulations · curvature-aware optimization

Contact and links

Public email

castro.medina@tu-berlin.de

Institution

TU Berlin

Academic links

Personal academic website

Curriculum vitae

DateAppointment / education
CurrentDoctoral researcher, Stochastic Analysis in the Sciences, Technische Universität Berlin; member of the FluCo team.
2022MSc in Applied Mathematics.
2021BSc in Engineering with a major in Mathematics.

Publications

This catalogue contains all publications by the member, including work from before joining SAiS. Journal versions and preprints are maintained as one record per scientific work.

  • THINNs: Thermodynamically Informed Neural Networks

    Physics-Informed Neural Networks (PINNs) are a class of deep learning models aiming to approximate solutions of PDEs by training neural networks to minimize the residual of the equation. Focusing on non-equilibrium fluctuating systems, we propose a physically informed choice of penalization that…

  • The Calderón’s problem via DeepONets

    Published · Vietnam Journal of Mathematics 52, 775–806 (2024). We consider the Dirichlet-to-Neumann operator and the direct and inverse Calderón’s mappings appearing in the Inverse Problem of recovering a smooth bounded and positive isotropic conductivity of a material filling a smooth…

  • The Kolmogorov Infinite Dimensional Equation in a Hilbert space Via Deep Learning Methods

    We consider the nonlinear Kolmogorov equation posed in a Hilbert space $H$, not necessarily of finite dimension. This model was recently studied by Cox et al. [24] in the framework of weak convergence rates of stochastic wave models. Here, we…

  • Deep Learning Schemes For Parabolic Nonlocal Integro-Differential Equations

    Published · Partial Differential Equations and Applications 3 (2022). In this paper we consider the numerical approximation of nonlocal integro differential parabolic equations via neural networks. These equations appear in many recent applications, including finance, biology and others, and have been…

Current SAiS projects

FluCo
Doctoral researcher in the ERC-funded team.

Talks and posters

Talks

DateTalk
2026THINNs: Thermodynamically Informed Neural Networks, SIAM Conference on Optimization, University of Edinburgh, UK.
2021Deep Learning Schemes for Parabolic Nonlocal Integro-Differential Equations, Jornadas Matemáticas de la Zona Sur, Universidad de La Frontera, Chile.

Posters

DatePoster
2026THINNs: Thermodynamically Informed Neural Networks, Conference on Mathematics of Machine Learning, TU Hamburg, Germany.
2026THINNs: Thermodynamically Informed Neural Networks, Foundations of Computational Mathematics (FoCM), Vienna, Austria.

Teaching

Selected teaching activities: information to be provided by the member.