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NeuralPDE: Modelling Dynamical Systems from Data
Deutsche Jahrestagung für Künstliche Intelligenz, 2021Many physical processes such as weather phenomena or fluid mechanics are governed by partial differential equations (PDEs). Modelling such dynamical systems using Neural Networks is an active research field.
Andrzej Dulny, A. Hotho, Anna Krause
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A review of linear response theory for general differentiable dynamical systems
, 2009The classical theory of linear response applies to statistical mechanics close to equilibrium. Away from equilibrium, one may describe the microscopic time evolution by a general differentiable dynamical system, identify nonequilibrium steady states ...
D. Ruelle
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Differential Equations and Dynamical Systems [PDF]
Total variations and semiconjugacy by J. F. Alves and J. Sousa Ramos Pattern formation from boundary reaction by J. M. Arrieta, N. Consul, and A. Rodriguez-Bernal Asymptotics of periodic travelling waves of an infinite beam on a nonlinear elastic support by B. S. Bardin and S. D. Furta Variational principles for hyperbolic flows by L.
C. Rocha, Jack K. Hale, A. Galves
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Marrying Causal Representation Learning with Dynamical Systems for Science
Neural Information Processing SystemsCausal representation learning promises to extend causal models to hidden causal variables from raw entangled measurements. However, most progress has focused on proving identifiability results in different settings, and we are not aware of any ...
Dingling Yao+2 more
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Constrained dynamics and exterior differential systems
Journal of Physics A: Mathematical and General, 1991The authors reformulate the Dirac theory of constraints in terms of exterior differential systems. They recall the Griffith's approach to the variational problems, Legendre transformations, the primary and secondary constraints, and the gauge symmetries for degenerate first order variational problems of one independent variable. Several simple examples
Hartley, D. H.+2 more
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Differential evolution for dynamic optimization of differential-algebraic systems
Proceedings of 1997 IEEE International Conference on Evolutionary Computation (ICEC '97), 2002An efficient method is introduced for solving optimal control and optimal parameter selection problems of nonlinear differential-algebraic systems involving general constraints. These infinite-dimensional problems are first converted into the uncaused optimal parameter selection problems.
Ji-Pyng Chiou, Feng-Sheng Wang
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Differentiation of the Limit Mapping in a Dynamical System
Journal of the London Mathematical Society, 1983On considere l'iteration d'une application f definie sur un sous-ensemble d'une variete lisse M quand l'ensemble des points fixes de f forme une sous-variete de ...
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