The geometric structure of complex fluids. - François Gay-Balmaz; Tudor S. Ratiu (Adv. Appl. Math., 2009)

The Momentum Map Representation of Images. - Martins Bruveris; François Gay-Balmaz; Darryl D. Holm; Tudor S. Ratiu (J. Nonlinear Sci., 2011)

Exact geometric theory of dendronized polymer dynamics. - François Gay-Balmaz; Darryl D. Holm; Vakhtang Putkaradze; Tudor S. Ratiu (Adv. Appl. Math., 2012)

Invariant Higher-Order Variational Problems II. - François Gay-Balmaz; Darryl D. Holm; David M. Meier; Tudor S. Ratiu; François-Xavier Vialard (J. Nonlinear Sci., 2012)

Reduced Variational Formulations in Free Boundary Continuum Mechanics. - François Gay-Balmaz; Jerrold E. Marsden; Tudor S. Ratiu (J. Nonlinear Sci., 2012)

Double bracket flows, toda flows and rigid body toda. - Anthony M. Bloch; François Gay-Balmaz; Tudor S. Ratiu (Allerton, 2013)

Multisymplectic Lie group variational integrator for a geometrically exact beam in R3. - François Demoures; François Gay-Balmaz; Marin Kobilarov; Tudor S. Ratiu (Commun. Nonlinear Sci. Numer. Simul., 2014)

Dirac reduction for nonholonomic mechanical systems and semidirect products. - François Gay-Balmaz; Hiroaki Yoshimura (Adv. Appl. Math., 2015)

On Flexible Tubes Conveying Fluid: Geometric Nonlinear Theory, Stability and Dynamics. - François Gay-Balmaz; Vakhtang Putkaradze (J. Nonlinear Sci., 2015)

Discrete variational Lie group formulation of geometrically exact beam dynamics. - François Demoures; François Gay-Balmaz; Sigrid Leyendecker; Sina Ober-Blöbaum; Tudor S. Ratiu; Yves Weinand (Numerische Mathematik, 2015)

On Noisy Extensions of Nonholonomic Constraints. - François Gay-Balmaz; Vakhtang Putkaradze (J. Nonlinear Sci., 2016)

A Variational Formulation for Fluid Dynamics with Irreversible Processes. - François Gay-Balmaz; Hiroaki Yoshimura (GSI, 2017)

Dirac Structures in Nonequilbrium Thermodynamics. - Hiroaki Yoshimura; François Gay-Balmaz (GSI, 2017)

A Variational Formulation of Nonequilibrium Thermodynamics for Discrete Open Systems with Mass and Heat Transfer. - François Gay-Balmaz; Hiroaki Yoshimura (Entropy, 2018)

Stochastic Geometric Models with Non-stationary Spatial Correlations in Lagrangian Fluid Flows. - François Gay-Balmaz; Darryl D. Holm (J. Nonlinear Sci., 2018)

Variational Discretization Framework for Geophysical Flow Models. - Werner Bauer; François Gay-Balmaz (GSI, 2019)

From Variational to Bracket Formulations in Nonequilibrium Thermodynamics of Simple Systems. - François Gay-Balmaz; Hiroaki Yoshimura (GSI, 2019)

Dirac Structures in Open Thermodynamics. - Hiroaki Yoshimura; François Gay-Balmaz (GSI, 2019)

From Lagrangian Mechanics to Nonequilibrium Thermodynamics: A Variational Perspective. - François Gay-Balmaz; Hiroaki Yoshimura (Entropy, 2019)

Geometric Theory of Flexible and Expandable Tubes Conveying Fluid: Equations, Solutions and Shock Waves. - François Gay-Balmaz; Vakhtang Putkaradze (J. Nonlinear Sci., 2019)

Dirac Structures and Variational Formulation of Thermodynamics for Open Systems. - Hiroaki Yoshimura; François Gay-Balmaz (SPIGL, 2020)

A Finite Element Method for MHD that Preserves Energy, Cross-Helicity, Magnetic Helicity, Incompressibility, and div B = 0. - Evan S. Gawlik; François Gay-Balmaz (CoRR, 2020)

Lie Group Cohomology and (Multi)Symplectic Integrators: New Geometric Tools for Lie Group Machine Learning Based on Souriau Geometric Statistical Mechanics. - Frédéric Barbaresco; François Gay-Balmaz (Entropy, 2020)

Dirac structures and variational formulation of port-Dirac systems in nonequilibrium thermodynamics. - François Gay-Balmaz; Hiroaki Yoshimura (IMA J. Math. Control. Inf., 2020)

A conservative finite element method for the incompressible Euler equations with variable density. - Evan S. Gawlik; François Gay-Balmaz (J. Comput. Phys., 2020)

Infinite Dimensional Lagrange-Dirac Mechanics with Boundary Conditions. - Álvaro Rodríguez Abella; François Gay-Balmaz; Hiroaki Yoshimura (GSI (2), 2021)

Multisymplectic Variational Integrators for Fluid Models with Constraints. - François Demoures; François Gay-Balmaz (GSI, 2021)

From Quantum Hydrodynamics to Koopman Wavefunctions I. - François Gay-Balmaz; Cesare Tronci (GSI, 2021)

A Variational Perspective on the Thermodynamics of Non-isothermal Reacting Open Systems. - François Gay-Balmaz; Hiroaki Yoshimura (GSI, 2021)

Variational Geometric Description for Fluids with Permeable Boundaries. - François Gay-Balmaz; Meng Wu; Chris Eldred (GSI (2), 2021)

From Quantum Hydrodynamics to Koopman Wavefunctions II. - Cesare Tronci; François Gay-Balmaz (GSI, 2021)

Lagrangian Trajectories and Closure Models in Mixed Quantum-Classical Dynamics. - Cesare Tronci; François Gay-Balmaz (GSI (2), 2021)

Variational Integrators for Stochastic Hamiltonian Systems on Lie Groups. - Meng Wu; François Gay-Balmaz (GSI (2), 2021)

Dirac Structures in Thermodynamics of Non-simple Systems. - Hiroaki Yoshimura; François Gay-Balmaz (GSI, 2021)

Hamiltonian Variational Formulation for Non-simple Thermodynamic Systems. - Hiroaki Yoshimura; François Gay-Balmaz (GSI (2), 2021)

Multisymplectic variational integrators for barotropic and incompressible fluid models with constraints. - François Demoures; François Gay-Balmaz (CoRR, 2021)

A structure-preserving finite element method for compressible ideal and resistive MHD. - Evan S. Gawlik; François Gay-Balmaz (CoRR, 2021)

Selective decay for the rotating shallow-water equations with a structure-preserving discretization. - Rüdiger Brecht; Werner Bauer; Alexander Bihlo; François Gay-Balmaz; Scott P. MacLachlan (CoRR, 2021)

A Variational Finite Element Discretization of Compressible Flow. - Evan S. Gawlik; François Gay-Balmaz (Found. Comput. Math., 2021)

On computing the analytic-signal backbone of the unforced harmonic oscillator. - Joseph P. Wright; Peng F. Tang; Jin-Song Pei; François Gay-Balmaz; Joseph P. Havlicek (J. Comput. Appl. Math., 2021)

Variational discretization of the Navier-Stokes-Fourier system. - Benjamin Couéraud; François Gay-Balmaz (CoRR, 2022)

Variational and thermodynamically consistent finite element discretization for heat conducting viscous fluids. - Evan S. Gawlik; François Gay-Balmaz (CoRR, 2022)

A finite element method for MHD that preserves energy, cross-helicity, magnetic helicity, incompressibility, and div B = 0. - Evan S. Gawlik; François Gay-Balmaz (J. Comput. Phys., 2022)

Unified Discrete Multisymplectic Lagrangian Formulation for Hyperelastic Solids and Barotropic Fluids. - François Demoures; François Gay-Balmaz (J. Nonlinear Sci., 2022)

Koopmon trajectories in nonadiabatic quantum-classical dynamics. - Werner Bauer; Paul Bergold; François Gay-Balmaz; Cesare Tronci (CoRR, 2023)

A Discrete Exterior Calculus of Bundle-valued Forms. - Theo Braune; Yiying Tong; François Gay-Balmaz; Mathieu Desbrun (CoRR, 2024)

Variational integrators for stochastic Hamiltonian systems on Lie groups: properties and convergence. - François Gay-Balmaz; Meng Wu (CoRR, 2024)

( textit{KOOPMON} ) Trajectories in Nonadiabatic Quantum-Classical Dynamics. - Werner Bauer; Paul Bergold; François Gay-Balmaz; Cesare Tronci (Multiscale Model. Simul., 2024)

Lie-Poisson Neural Networks (LPNets): Data-based computing of Hamiltonian systems with symmetries. - Christopher Eldred; François Gay-Balmaz; Sofiia Huraka; Vakhtang Putkaradze (Neural Networks, 2024)

General Relativistic Lagrangian Continuum Theories Part I: Reduced Variational Principles and Junction Conditions for Hydrodynamics and Elasticity. - François Gay-Balmaz (J. Nonlinear Sci., 2024)

Complex Fluid Models of Mixed Quantum-Classical Dynamics. - François Gay-Balmaz; Cesare Tronci (J. Nonlinear Sci., 2024)

Structure-preserving and thermodynamically consistent finite element discretization for visco-resistive MHD with thermoelectric effect. - Evan S. Gawlik; François Gay-Balmaz; Bastien Manach-Pérennou (J. Comput. Phys., 2025)

CLPNets: Coupled Lie-Poisson neural networks for multi-part Hamiltonian systems with symmetries. - Christopher Eldred; François Gay-Balmaz; Vakhtang Putkaradze (Neural Networks, 2025)

Entropy functionals and equilibrium states in mixed quantum-classical dynamics. - Cesare Tronci; David Martínez-Crespo; François Gay-Balmaz (CoRR, 2025)

Variational Neural Networks for Observable Thermodynamics (V-NOTS). - Christopher Eldred; François Gay-Balmaz; Vakhtang Putkaradze (CoRR, 2025)