Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
134 tokens/sec
GPT-4o
9 tokens/sec
Gemini 2.5 Pro Pro
47 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Lie Transform--based Neural Networks for Dynamics Simulation and Learning (1802.01353v2)

Published 5 Feb 2018 in cs.NE, cs.NA, and math.DS

Abstract: In the article, we discuss the architecture of the polynomial neural network that corresponds to the matrix representation of Lie transform. The matrix form of Lie transform is an approximation of the general solution of the nonlinear system of ordinary differential equations. The proposed architecture can be trained with small data sets, extrapolate predictions outside the training data, and provide a possibility for interpretation. We provide a theoretical explanation of the proposed architecture, as well as demonstrate it in several applications. We present the results of modeling and identification for both simple and well-known dynamical systems, and more complicated examples from price dynamics, chemistry, and accelerator physics. From a practical point of view, we describe the training of a Lie transform--based neural network with a small data set containing only 10 data points. We also demonstrate an interpretation of the fitted neural network by converting it to a system of differential equations.

Summary

We haven't generated a summary for this paper yet.