George A Kevrekidis

Research

I work at the intersection of differential geometry and machine learning, developing structure-preserving methods for computation with an eye toward applications in science and engineering. I am broadly interested in translating geometric structure into concrete computational tools, from geometric approaches to deep learning and the numerical integration of dynamical systems to the classification and equivalence of differential equations. One example is contact geometry, which offers a natural source of such structure.

• Contact Geometry Contact Hamiltonian methods for structure-preserving computation: geometric integrators, symmetry and equivalence of differential equations, and a coordinate-free account of dissipation, thermodynamics, and optimization.
• Deep Learning for PDEs Neural methods for partial differential equations that respect geometric and physical structure: architectures, learned integrators, and the classification and equivalence of PDE families.

Selected Papers

• Towards Coordinate- and Dimension-Agnostic Machine Learning for Partial Differential Equations preprint

  arXiv:2505.16549  ·  with T. V. Phan, S. Villar, Y. G. Kevrekidis, J. M. Bello-Rivas

  An exterior-calculus framework for learning PDE dynamics independently of coordinates and spatial dimension, so a model trained in one space transfers to others.

• Data-driven, ML-assisted approaches to problem well-posedness

  PNAS Nexus  ·  2026, vol. 5(6)

  Data-driven and machine-learning tests for whether a problem is well-posed, spanning forward and inverse settings.

• Local Universal Splitting Integrators for Contact Hamiltonian Systems preprint

  arXiv:2605.09103  ·  2026

  Structure-preserving splitting integrators for contact Hamiltonian systems, assembled from symplectic and ODE integrators via a Lie-algebra density result.

Full list on Google Scholar →

About