Classification with Runge-Kutta networks and feature space augmentation
نویسندگان
چکیده
<p style='text-indent:20px;'>In this paper we combine an approach based on Runge-Kutta Nets considered in [<i>Benning et al., J. Comput. Dynamics, 9, 2019</i>] and a technique augmenting the input space [<i>Dupont NeurIPS</i>, 2019] to obtain network architectures which show better numerical performance for deep neural networks point image classification problems. The is illustrated with several examples implemented PyTorch.</p>
منابع مشابه
Nonstandard explicit third-order Runge-Kutta method with positivity property
When one solves differential equations, modeling physical phenomena, it is of great importance to take physical constraints into account. More precisely, numerical schemes have to be designed such that discrete solutions satisfy the same constraints as exact solutions. Based on general theory for positivity, with an explicit third-order Runge-Kutta method (we will refer to it as RK3 method) pos...
متن کاملConvolutional Neural Networks combined with Runge-Kutta Methods
A convolutional neural network for image classification can be constructed following some mathematical ways since it models the ventral stream in visual cortex which is regarded as a multi-period dynamical system. In this paper, a new point of view is proposed for constructing network models as well as providing a direction to get inspiration or explanation for neural network. If each period in...
متن کاملRunge - Kutta Methods page RK 1 Runge - Kutta Methods
Literature For a great deal of information on Runge-Kutta methods consult J.C. Butcher, Numerical Methods for Ordinary Differential Equations, second edition, Wiley and Sons, 2008, ISBN 9780470723357. That book also has a good introduction to linear multistep methods. In these notes we refer to this books simply as Butcher. The notes were written independently of the book which accounts for som...
متن کاملUniversity of Cambridge Numerical Analysis Reports Practical Symplectic Partitioned Runge{kutta and Runge{kutta{nystrr Om Methods Practical Symplectic Partitioned Runge{kutta and Runge{kutta{nystrr Om Methods
We present new symmetric fourth and sixth-order symplectic Partitioned Runge{ Kutta and Runge{Kutta{Nystrr om methods. We studied compositions using several extra stages, optimising the eeciency. An eeective error, E f , is deened and an extensive search is carried out using the extra parameters. The new methods have smaller values of E f than other methods found in the literature. When applied...
متن کاملAccelerated Runge-Kutta Methods
Standard Runge-Kutta methods are explicit, one-step, and generally constant step-size numerical integrators for the solution of initial value problems. Such integration schemes of orders 3, 4, and 5 require 3, 4, and 6 function evaluations per time step of integration, respectively. In this paper, we propose a set of simple, explicit, and constant step-size Accerelated-Runge-Kutta methods that ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of computational dynamics
سال: 2021
ISSN: ['2158-2491', '2158-2505']
DOI: https://doi.org/10.3934/jcd.2021018