Filtering by Subject: Non-linear Dynamics
Published: 2019-12-31
Subjects: Applied Mathematics, Computer Sciences, Engineering, Non-linear Dynamics, Numerical Analysis and Computation, Numerical Analysis and Scientific Computing, Partial Differential Equations, Physical Sciences and Mathematics
Numerical modelling frequently involves a diagnostic quantity of interest (QoI) - often of greater importance than the PDE solution - which we seek to accurately approximate. In the case of coastal ocean modelling the power output of a tidal turbine farm is one such example. Goal-oriented error estimation and mesh adaptation can be used to provide meshes which are well-suited to achieving this [...]
Published: 2019-06-20
Subjects: Applied Mathematics, Artificial Intelligence and Robotics, Atmospheric Sciences, Climate, Computer Sciences, Dynamic Systems, Earth Sciences, Fluid Dynamics, Non-linear Dynamics, Oceanography and Atmospheric Sciences and Meteorology, Physical Sciences and Mathematics, Physics
In this paper, the performance of three deep learning methods for predicting short-term evolution and for reproducing the long-term statistics of a multi-scale spatio-temporal Lorenz 96 system is examined. The methods are: echo state network (a type of reservoir computing, RC-ESN), deep feed-forward artificial neural network (ANN), and recurrent neural network with long short-term memory [...]
Published: 2018-04-13
Subjects: Applied Mathematics, Dynamic Systems, Earth Sciences, Environmental Sciences, Geomorphology, Hydrology, Mathematics, Non-linear Dynamics, Physical Sciences and Mathematics, Physics, Statistical, Nonlinear, and Soft Matter Physics
Transport of water, nutrients or energy fluxes in many natural or coupled human-natural systems occurs along different pathways that often have a wide range of transport timescales and might exchange fluxes with each other dynamically (e.g., surface-subsurface). Understanding this type of transport is key to predicting how landscapes will change under changing forcing. Here, we present a general [...]