Reconstructing the states of a nonlinear dynamical system

Reconstructing the states of a nonlinear dynamical system

The nature of the stock market is not considered and is an example of a nonlinear dynamical system. In this study, researchers from TUS and Saitama University have developed a new way to predict how such a nonlinear system will change over time, providing important insight into the field of data science. Credit: Katrina.Tuliao

We often deal with nonlinear dynamical systems that work flawlessly, such as the Earth’s climate and the stock market. To analyze them, the measurements taken were used to reconstruct the condition of the system. However, this depends on the quality of the data. Now, researchers from Japan have offered a completely new way to determine the right parts to result in a reconstruction. Their new technology has great ideas for the field of data science.

There are many different types of world that are often seen. That is, their output does not change in any way similar to their input. These features have a degree of uncertainty, where it is not clear how the system will respond to changes in its implementation. This is especially important in the case of dynamical systems, where the output of the sample changes with time. For such systems, time series data, or measurements from the system should be reviewed to determine how the system changes over time.

Because of the nature of the problem, many decided to analyze the time series data to identify the system. One of the latest developments in the state of the art system is the rebuilding of the state steam system, which can be used to rebuild those states where the system is unstable. the time. Those states are called “pullers.” However, the accuracy of the reconstructed specimens depends on the pieces used for the reconstruction, and due to the limited nature of the data, it is difficult to determine those pieces. to result in no further action.

Now, a new study will be published on April 1, 2022, at Nonlinear logic and its applications, IEICE, Professor Tohru Ikeguchi from Tokyo University of Science, his Ph.D. student mr. Kazuya Sawada from Tokyo University of Science, and Prof. Yutaka Shimada from Saitama University, Japan, used the geometric style of the entertainer to select new pieces of work.

“In order to rebuild the state using time management systems, two parts, the size of the state and the time delay, need to be organized, which is an important issue to be studied hard. in this field. to properly organize these pieces by looking at the geometric shape of the sculptor as a way to solve this problem, “said Prof. Ikeguchi.

To obtain the best properties of the segments, the researchers used a five-dimensional nonlinear dynamical system and increased the similarity of the intermediate distance curves between the reconstructed interest and the original puller. As a result, the pieces have a way of creating an interesting re -constructed object that is geometrically very close to the original.

Although the technique was able to produce reconstruction pieces, the researchers did not apply the noise that is familiar to real -world data, which can have serious problems with reconstruction. “In mathematics, this kind of work has been shown to work well, but there are a lot of considerations that need to be done before using this kind of real -world data. The data that is seen is infinite,” he said. and Prof. Ikeguchi.

Despite this, the pathway raises some of the limitations associated with determining the status of nonlinear dynamical systems found in various fields of science, economics, and engineering. “This research has provided a critical approach to contemporary data science, and we believe it is important for serving different types of data in the real world,” said Prof. Ikeguchi.

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More information:
Kazuya Sawada et al, Similarities of distance distribution between details on basic interests and reconstructions. Nonlinear logic and its applications, IEICE (2022). DOI: 10.1587 / nolta.13.385

Presented by Tokyo University of Science

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