19 citations · 41 across the 6 of their papers we have counts for
6 papers
Training Image Derivatives: Increased Accuracy and Universal Robustness
Vsevolod I. Avrutskiy
Derivative training is an established method that can significantly increase the accuracy of neural networks in certain low-dimensional tasks. In this paper, we extend this improve…
Rational solutions of (1+1)-dimensional Burgers equation and their asymptotic
V. I. Avrutskiy, V. P. Krainov
A special initial condition for (1+1)-dimensional Burgers equation is considered. It allows to obtain new analytical solutions for an arbitrary low viscosity as well as for the inv…
Avoiding overfitting of multilayer perceptrons by training derivatives
V. I. Avrutskiy
Resistance to overfitting is observed for neural networks trained with extended backpropagation algorithm. In addition to target values, its cost function uses derivatives of those…
Neural networks catching up with finite differences in solving partial differential equations in higher dimensions
V. I. Avrutskiy
Fully connected multilayer perceptrons are used for obtaining numerical solutions of partial differential equations in various dimensions. Independent variables are fed into the in…
Backpropagation generalized for output derivatives
V. I. Avrutskiy
Backpropagation algorithm is the cornerstone for neural network analysis. Paper extends it for training any derivatives of neural network's output with respect to its input. By the…
Enhancing approximation abilities of neural networks by training derivatives
V. I. Avrutskiy
A method to increase the precision of feedforward networks is proposed. It requires a prior knowledge of a target function derivatives of several orders and uses this information i…