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About me
About me
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portfolio
DeepOperatorML
We propose that the use of operator learning schemes (DeepONet, FNO) can vastly improve the computational cost of solving boundary value problems on unbounded domains when compared to classical methods using numerical integration. One such example is Rayleigh wave propagation on unbounded media. The project’s original goal was to reduce the cost of the Boundary Element Method using Operator Learning, but I later extended it for solving any physical system governed by PDEs. Currently, the repository consists of a python library written during my Master’s thesis that proposes a framework for solving data-driven scientific machine learning problems using several implemented architectures (a wide variety of DeepONets and FNOs).
Learning Chaos with OT & OL
We combine Neural Operators (e.g. DeepONet or FNO) with an Optimal Transport-based loss in order to preserve Invariant Measures in chaotic systems like Lorentz 63. This follows up on a 2023 Neurips paper. 
publications
DeepONet Surrogate Modeling for Continuum Mechanics in Unbounded Domains: Bypassing BEM Scalability via Operator Learning
Published in XLVI Ibero-Latin American Congress on Computational Methods in Engineering, 2025
Leonardo Santiago, George Karniadakis, Josué Labaki\ [Code]