GRAFT-ATHENA: Self-Improving Agentic Teams for Autonomous Discovery and Evolutionary Numerical Algorithms
arXiv, 2026
Agent teams that rewrite their own workflow between generations, improving the algorithms they discover.
PaperCode coming soon
About
I am a PhD candidate in Applied Mathematics at Brown University, advised by Prof. George Em Karniadakis in the Crunch Group. I work on scientific machine learning: neural network architectures and optimization methods that are reliable enough to model physical and biological systems, and agentic AI systems that design and evolve numerical algorithms on their own.
Before Brown I studied Mechanical Engineering at Universidad de las Fuerzas Armadas-ESPE in Ecuador and worked with Prof. Hongyue Sun and Prof. Luis Segura at the University at Buffalo on machine learning for advanced manufacturing. I hold an Sc.M. in Mechanical Engineering and Applied Mechanics from Brown (2026).
Research
My research has three threads. Papers are listed under the thread they belong to.
1Agentic AI for scientific discovery and numerical algorithms
LLM-based agent teams that diagnose, design, and evolve numerical algorithms for scientific computing. The agents propose methods, run them, read the results, and improve on their own previous attempts, so that algorithm design becomes an autonomous, self-improving loop.
ATHENA: Agentic Team for Hierarchical Evolutionary Numerical Algorithms
arXiv, 2025
A hierarchical team of LLM agents that evolves numerical solvers under a fixed compute budget.
PaperCode coming soon
2Physics-informed AI for physical and biological systems
Physics-informed methods that turn sparse, noisy measurements (particle tracks, MRI, velocity data) into full three-dimensional fields of velocity, pressure, temperature, or permeability. The main application is brain-wide cerebrospinal and glymphatic fluid flow, where direct measurement is impossible and clearance failure is linked to neurodegenerative disease. The same tools apply to turbulence and chemical reactors.
Brain fluid dynamics
MR-AIV reveals in vivo brain-wide fluid flow with physics-informed AI
Science Advances, 2026
First brain-wide 3D maps of interstitial and perivascular flow, with permeability and pressure, from dynamic contrast-enhanced MRI.
Data-Efficient Neural Operators Enable Brain-Wide Glymphatic Velocity Field Estimation from DCE-MRI
TechRxiv, 2026
Neural operators trained on MR-AIV outputs that estimate velocity fields in seconds.
Robust MR-AIV: A Systematic Study of Robustness Improvement and Sensitivity Analysis of MR-AIV
bioRxiv, 2026
How MR-AIV responds to noise, resolution, and modeling choices.
Inferring in vivo murine cerebrospinal fluid flow using artificial intelligence velocimetry with moving boundaries and uncertainty quantification
Interface Focus, 2024
AIV extended to moving vessel walls with uncertainty estimates for in vivo mouse data.
Turbulence and engineering systems
AIVT: Inference of turbulent thermal convection from measured 3D velocity data by physics-informed Kolmogorov-Arnold networks
Science Advances, 2025
Full temperature and pressure fields of Rayleigh-Bénard convection recovered from velocity measurements alone.
FMEnets: Flow, Material, and Energy networks for non-ideal plug flow reactor design
Chemical Engineering Science, 2025
Physics-informed networks that couple flow, species, and energy balances for reactor design.
3Architectures, optimization, and learning theory for scientific ML
The foundations the other two threads rest on: how physics-informed models should be built, how they should be trained, and why they generalize. This covers residual-based attention and its variational form, Kolmogorov-Arnold representations, and the learning dynamics of physics-informed networks.
From PINNs to PIKANs: Recent advances in physics-informed machine learning
Machine Learning for Computational Science and Engineering, 2025
A review of architectures, training strategies, and theory for physics-informed learning, MLP and KAN alike.
A variational framework for residual-based adaptivity in neural PDE solvers and operator learning
npj Artificial Intelligence, 2026
Adaptive weighting derived from a variational principle rather than heuristics, for PINNs and operator networks.
KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics
Neural Networks, 2025
A two-block architecture from Kurkova's theorem, and a study of how such networks learn.
Learning in PINNs: Phase transition, diffusion equilibrium, and generalization
Neural Networks, 2025
Training of physics-informed networks passes through a phase transition that predicts generalization.
A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networks
Computer Methods in Applied Mechanics and Engineering, 2024
Systematic benchmark of MLP versus KAN for PDEs and operator learning, with open code and data.
Residual-based attention in physics-informed neural networks
Computer Methods in Applied Mechanics and Engineering, 2024
A cheap pointwise weighting that removes the need for hand-tuned loss balancing.
Residual-based attention and connection to information bottleneck theory in PINNs
arXiv, 2023
Links residual-based attention to information bottleneck training stages.
Explicit Construction of Approximate Kolmogorov-Arnold Superpositions with C2-Smoothness
arXiv, 2025
A constructive smooth version of the Kolmogorov-Arnold representation.
Earlier work: machine learning for advanced manufacturing
Teeth mold point cloud completion via data augmentation and hybrid RL-GAN
Journal of Computing and Information Science in Engineering, 2023
Software and outreach
- NABLA-SciML Physics-informed machine learning tutorials in PyTorch and JAX, plus reference code for RBA, cKANs, KKANs, and vRBA.
- Instant-AIVT Official implementation of AIVT.
- MR-AIV Code for brain-wide fluid flow reconstruction from DCE-MRI.
- KKANs Reference implementation of Kurkova-Kolmogorov-Arnold Networks.
- vRBA Variational residual-based attention for PINNs and operator networks.
- YouTube channel Lectures and tutorials on physics-informed machine learning.
I organize the weekly Crunch Seminar at Brown University.
Honors
- 2026TU Ilmenau Publication Award, Mathematics and Natural Sciences, for the AIVT paper
- 2022, 2023Brown Graduate School Doctoral Fellowship
- 2021Valedictorian, Department of Mechanical Sciences and Engineering, ESPE
Invited talks
- Nov 2026GRAFT-ATHENA (upcoming). Minisymposium on Agentic AI for Scientific Discovery and Computing, SIAM Conference on Mathematics of Data Science, Salt Lake City. Session
- Jun 2026GRAFT-ATHENA. USACM Student Chapter online seminar series. Announcement Video
- May 2026ATHENA. ICERM Hot Topics Workshop on Agentic Scientific Computing and Scientific Machine Learning, Brown University. Workshop
- Feb 2026ATHENA. Scientific AI Agents seminar, Department of Applied and Computational Mathematics and Statistics, University of Notre Dame. Event
- Feb 2025Physics-informed machine learning: introduction, extensions and practical applications. Center for Scientific Computing and Data Science Research, UMass Dartmouth. Seminar
- Jan 2025Inferring turbulent velocity and temperature fields and their statistics from Lagrangian velocity measurements using physics-informed Kolmogorov-Arnold networks (PIKANs). Computational Mathematics + X special seminar, Caltech. Event Video
- Fall 2024Inferring in vivo murine cerebrospinal fluid flow with artificial intelligence velocimetry. AI Medical Imaging seminar, UT Austin.