Janis AIAD

I am an incoming Ph.D. student in Applied and Computational Mathematics at Caltech, starting in Fall 2026.

Previously, I worked with the Haizhao Yang Group in the Department of Mathematics at the University of Maryland, and with the Bruno Loureiro Group in the Department of Mathematics and Computer Science at École Normale Supérieure, Paris (Rue d’Ulm).

I study neural network optimization, with a focus on how depth and width affect training for scientific machine learning and PDEs.

My research code and ongoing projects are available on GitHub.

news

Oct 31, 2025	I'm participating and staffing at the 2025 International Geometric Science of Information Conference !
May 02, 2024	I will present my research at the 2024 European Conference on Operational Research

latest posts

Sep 18, 2022	A simple proof of an ENS Ulm exercise using Liouville's theorem
Jun 18, 2022	A simplified proof of an integral identity using density arguments

preprints and publications

Acknowledgements

I am especially grateful to the following people for their guidance, collaboration, and encouragement.

Computational Mathematics and Physics

Haizhao Yang and Shijun Zhang for our work on neural tangent kernels and Sobolev training for PDEs and scientific machine learning. See DeNN-NTK and MMNN for related projects.
Davide Boschetto for our research with MBDA Systems on quantum computing for NP-complete problems, which led to an oral presentation at EURO 2024.

Statistics and Causality

Charles-Albert Lehalle for introducing me to market microstructure and heavy-tailed phenomena in complex systems, and for our research on one year of nanosecond-scale NASDAQ order-book data.
Marianne Clausel, David Cortés, and Emilie Devijver for our work on hierarchical causal models, currently being prepared for the Journal of the Royal Statistical Society: Series C (Applied Statistics).