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jdtoscano94/README.md

Hi, thanks for stopping by!

I am a PhD candidate in the Division of Applied Mathematics at Brown University, working with Prof. George Karniadakis in the Crunch Group since 2022. I earned my Bachelor's in Mechanical Engineering from the Universidad de las Fuerzas Armadas ESPE in Ecuador, and started in research as an undergraduate collaborating remotely with the University at Buffalo on machine learning models of physical systems.

My research has three threads:

  • Agentic AI for scientific discovery and numerical algorithms (ATHENA, GRAFT-ATHENA)
  • Physics-informed AI for physical and biological systems (AIV, AIVT, MR-AIV, brain-wide cerebrospinal fluid flow)
  • Architectures, optimization, and learning theory for scientific ML (RBA, vRBA, KKANs, PIKANs)

Papers, code, talks, and videos: jdtoscano94.github.io

Tutorials and reference implementations: NABLA-SciML · Lectures: YouTube

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  1. NABLA-SciML NABLA-SciML Public

    Physics Informed Machine Learning Tutorials (Pytorch and Jax)

    Jupyter Notebook 687 202

  2. Instant-AIVT Instant-AIVT Public

    Official Implementation of "AIVT: Inference of turbulent thermal convection from measured 3D velocity data by physics-informed Kolmogorov-Arnold Networks"

    Jupyter Notebook 16 4