Advising

Graduate advising topics, prerequisites, and how to apply, with Prof. Adriano Côrtes at UFRJ.

I advise graduate students at PESC/COPPE and at the Department of Applied Mathematics (Mathematics Institute), and I supervise undergraduate research projects. The work sits at the boundary between Computational Science and Engineering and machine learning, so a project usually mixes numerical methods, physics, and modern neural network architectures.

Topics open for advising

Scientific Machine Learning

Surrogate models built on PINNs, neural operators (DeepONet, FNO) and graph neural networks. Hybrid formulations that carry conservation laws, symmetries, or the governing PDE into the architecture or the training loss.

Generative models for physical systems

Diffusion and flow-based models applied to porous media digital twins, oceanographic systems, and super-resolution of reduced-order model output.

High-Performance Computing

Scalable parallel solvers, isogeometric analysis, and large-scale simulation on GPU clusters. Projects here connect to PetIGA, PetIGA-MF, and EdgeCFD.

AI for biological data

Single-cell RNA sequencing applied to cancer research, epigenetic landscape dynamics, and retrieval-augmented language models for clinical guidelines.

What the work asks of you

A project in this group is computational from the first week. You do not need all of the following on day one, but you do need to be willing to build them:

  • Programming. Python is the working language. Julia, C, and C++ appear in the HPC projects.
  • Numerical methods. Finite elements, finite differences, or spectral methods, at the level of a first graduate course.
  • Machine learning. PyTorch, and the mathematics under it. A project that only calls a library rarely produces a thesis.
  • Linear algebra and PDEs. These are the load-bearing subjects. Weakness here shows up later as a blocked project.

Several projects run on GPU clusters, so experience with Linux, SLURM, and containers helps.

How to apply

Write to me — at adriano (arroba) im.ufrj.br for DMA/IM, or adricortes (arroba) cos.ufrj.br for PESC/COPPE — with the following, in one message:

  1. The topic above that interests you, and one paragraph on why.
  2. Your CV, or a link to your Lattes record.
  3. Your academic transcript.
  4. Whether you have, or plan to apply for, a scholarship.

Formal admission runs through the graduate programs, not through me. Check the calendar and the requirements at PESC/COPPE or at DMA/IM before you write.

Undergraduate students at UFRJ may also ask about iniciação científica projects, which follow the university calendar.