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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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Dynamics of Systems with Unilateral Differential Constraints
Doklady Mathematics, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Salnikova, T. V. +2 more
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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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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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Characterizations, Dynamical Systems and Gradient Methods for Strongly Quasiconvex Functions
Journal of Optimization Theory and ApplicationsWe study differentiable strongly quasiconvex functions for providing new properties for algorithmic and monotonicity purposes. Furthermore, we provide insights into the decreasing behaviour of strongly quasiconvex functions, applying this for ...
Felipe Lara +2 more
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Delay differential systems for tick population dynamics
Journal of Mathematical Biology, 2014Ticks play a critical role as vectors in the transmission and spread of Lyme disease, an emerging infectious disease which can cause severe illness in humans or animals. To understand the transmission dynamics of Lyme disease and other tick-borne diseases, it is necessary to investigate the population dynamics of ticks.
Fan, Guihong +2 more
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Ordinary Differential Equations: Dynamical Systems
2007Ordinary differential equations (ode) are differential equations for functions which depend on one independent variable only. These ‘odes’ are simpler than partial differential equations which contain more than one independent variable. In almost all models or simulations independent variables are either time and/or space.
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Differential Forms and Dynamical Systems
2007One of the modern geometric views of dynamical systems is as vector fields on a manifold, with or without boundary. The starting point of this paper is the observation that, since one-forms are the natural expression of linear functionals on the space of vector fields, the interaction between the two makes some aspects of the study of equilibria and ...
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