Francesco Brarda

Francesco Brarda

Bio

I'm a Ph.D. student in Computational Mathematics at Emory University advised by Yuanzhe Xi.

My research lies at the intersection of numerical methods and machine learning, with the goal of making solvers for partial differential equations faster and more efficient. I am particularly interested in scientific machine learning, numerical PDEs, numerical linear algebra, and anything that mixes math with real-world applications. During my Ph.D., I have spent multiple summers in the CASC Division at Lawrence Livermore National Laboratory, and before grad school, I worked in France and Spain on parallel computing and mesh adaptation.

Beyond research, I am equally passionate about education. At Emory, I have enjoyed teaching a variety of mathematics courses and labs and mentoring students through reading programs. Outside of math, I love baking and playing volleyball.

You can reach me at francesco.brarda@emory.edu

Education

Positions

Research

Publications

  1. Attentive Graph Neural Preconditioning Methods for SPD Matrices. F. Brarda, Z. Zhang, V. Kalantzis, R. Li, Y. Xi.In preparation.
  2. Factored Sparse Approximate Inverse Preconditioning via Spectral Optimization. F. Brarda, T. Xu, V. Kalantzis, R. Li, Y. Xi. arXiv preprintarXiv:2606.22742
  3. Spectral-Refiner: Fine-Tuning of Accurate Spatiotemporal Neural Operator for Turbulent Flows. S. Cao, F. Brarda, R. Li, Y. Xi. ICLR 2025arXiv:2405.17211

Invited Talks

  1. Efficient Hybrid Spatial-Temporal Operator Learning. SIAM Student Seminar, GATech, Atlanta, GA. March 29, 2024.
  2. Development of a Massively Parallel Remeshing Code for Exascale Geometries. MICROCARD Workshop, Bordeaux, France. July 6–7, 2022.

Contributed Talks

  1. Efficient Hybrid Spatial-Temporal Operator Learning. SIAM Conference on Mathematics for Data Science, Atlanta, GA. October 21-25, 2024.
  2. Efficient Hybrid Spatial-Temporal Operator Learning. International Conference on Preconditioning Techniques, Atlanta, GA. June 10-12, 2024.
  3. Efficient Hybrid Spatial-Temporal Operator Learning. 18th Copper Mountain Conference on Iterative Methods, Copper Mountain, CO. April 14-19, 2024.
  4. Numerical Simulation of Pesticide Spray Distribution by UAV for Precision Agriculture. COMSOL Conference 2020 Europe, Grenoble, France. October 14-15, 2020.

Teaching

I try to keep my classes as collaborative as possible, dividing time between individual problem-solving, small-group work, and open discussions. We learn best from each other and by making mistakes, and this is exactly the environment I encourage in my classes.
For some topics, being able to visualize things is incredibly important. I mostly use tools that are already available online, but sometimes I build my own when I need something specific. Here is a demo I put together about spherical coordinates.

Instructor · Emory University

Teaching Assistant · Emory University

Outreach