106 citations · 677 across the 72 of their papers we have counts for
79 papers
Rough variational principles and applications to adjoint systems
Ruiao Hu, Melvin Leok
We consider a Type-II variational principle driven by geometric rough path with split boundary conditions naturally suited to adjoint systems. From this rough variational principle…
A Type II Hamiltonian Variational Principle and Adjoint Systems for Lie Groups
Brian K. Tran, Melvin Leok
We present a novel Type II variational principle on the cotangent bundle of a Lie group which enforces Type II boundary conditions, i.e., fixed initial position and final momentum.…
Simplifying Momentum-based Positive-definite Submanifold Optimization with Applications to Deep Learning
Wu Lin, Valentin Duruisseaux, Melvin Leok +3
Riemannian submanifold optimization with momentum is computationally challenging because, to ensure that the iterates remain on the submanifold, we often need to solve difficult di…
Lie Group Forced Variational Integrator Networks for Learning and Control of Robot Systems
Valentin Duruisseaux, Thai Duong, Melvin Leok +1
Incorporating prior knowledge of physics laws and structural properties of dynamical systems into the design of deep learning architectures has proven to be a powerful technique fo…
Practical Perspectives on Symplectic Accelerated Optimization
Valentin Duruisseaux, Melvin Leok
Geometric numerical integration has recently been exploited to design symplectic accelerated optimization algorithms by simulating the Lagrangian and Hamiltonian systems from the v…
Geometric Methods for Adjoint Systems
Brian Tran, Melvin Leok
Adjoint systems are widely used to inform control, optimization, and design in systems described by ordinary differential equations or differential-algebraic equations. In this pap…