- Lie Group Forced Variational Integrator Networks for Learning and Control of Robot Systems
2022/11/29 by Valentin Duruisseaux, Thai Duong, Duruisseaux, Valentin +5 · 3 citations
Computer Science · Mathematics · Physics and Astronomy · #37J11 #65P10 #68T07 #68T40 #70E60 #Artificial intelligence #Classical mechanics #Computational Physics and Python Applications #Computer science #Control (management) #Control theory (sociology) #Double integrator #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #Geometry #Hamiltonian (control theory) #Hamiltonian mechanics #Hamiltonian system #I.2.6 #I.2.9 #Integrator #Lie group #Machine Learning (cs.LG) #Mathematical analysis #Mathematical optimization #Mathematics #Model Reduction and Neural Networks #Modeling and Simulation Systems #Physics #Rigid body #Rigid body dynamics #Robotics (cs.RO) #Symplectic integrator #Variational integrator
- Structure-preserving model order reduction of Hamiltonian systems
2021/09/25 by J. S. Hesthaven, Jan S. Hesthaven, Cecilia Pagliantini +6 · 3 citations
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Applied mathematics #Computer science #Conservation law #FOS: Mathematics #Geometry #Hamiltonian (control theory) #Hamiltonian mechanics #Hamiltonian system #Mathematical analysis #Mathematical optimization #Mathematics #Model Reduction and Neural Networks #Model order reduction #Moment map #Numerical Analysis (math.NA) #Numerical methods for differential equations #Phase space #Physics #Projection (relational algebra) #Pure mathematics #Quantum mechanics #Reduction (mathematics) #Symplectic geometry #Symplectic integrator #cs.NA #math.NA
- Data-driven Prediction of General Hamiltonian Dynamics via Learning Exactly-Symplectic Maps
2021/03/09 by Renyi Chen, Chen, Renyi, Molei Tao +1 · 11 citations
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Applied mathematics #Artificial intelligence #Artificial neural network #Computational Physics (physics.comp-ph) #Computer science #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Field (mathematics) #Geometry #Hamiltonian (control theory) #Hamiltonian mechanics #Hamiltonian system #Machine Learning (cs.LG) #Mathematical analysis #Mathematical optimization #Mathematics #Model Reduction and Neural Networks #Moment map #Neural Networks and Reservoir Computing #Nonlinear system #Numerical Analysis (math.NA) #Ode #Phase space #Physics #Pure mathematics #Quantum many-body systems #Separable space #Symplectic geometry #Symplectic integrator #Vector field #cs.LG #cs.NA #math.DS #math.NA #physics.comp-ph
- Introduction to Symplectic Topology
2017/06/22 by Dusa McDuff, Dietmar Salamon · 1 citation
Mathematics · #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Homotopy and Cohomology in Algebraic Topology #Symplectic geometry #Symplectomorphism #Section (typography) #Geometry and topology #Topology (electrical circuits) #Mathematical proof #Symplectic integrator #Uniqueness #Mathematics #Morphism #General topology #Pure mathematics #Symplectic manifold #Algebra over a field #Computer science #Topological space #Geometry #Combinatorics #Mathematical analysis
- Numerical Methods for Stochastic Systems Preserving Symplectic Structure
2002/01/01 by Grigori N. Milstein, G. N. Milstein, Yu. M. Repin +1 · 19 citations
Mathematics · Physics and Astronomy · #Applied mathematics #Computer science #Differential Equations and Numerical Methods #Hamiltonian system #Integrator #Mathematical analysis #Mathematics #Multiplicative function #Numerical methods for differential equations #Phase space #Quantum chaos and dynamical systems #Separable space #Symplectic geometry #Symplectic integrator #Symplectic manifold
- Discrete mechanics and variational integrators
2001/05/01 by Jerrold E. Marsden, Matthew West · 32 citations
Engineering · Mathematics · Physics and Astronomy · #Advanced Numerical Methods in Computational Mathematics #Applied mathematics #Backward Euler method #Computer science #Discretization #Dissipation #Integrator #Mathematical analysis #Mathematics #Model Reduction and Neural Networks #Noether's theorem #Numerical methods for differential equations #Physics #Quantum mechanics #Semi-implicit Euler method #Symplectic geometry #Symplectic integrator #Symplectic manifold #Variational integrator #Verlet integration