Using machine learning to replicate chaotic attractors and calculate Lyapunov exponents from data

Chaos
Jaideep PathakEdward Ott

Abstract

We use recent advances in the machine learning area known as "reservoir computing" to formulate a method for model-free estimation from data of the Lyapunov exponents of a chaotic process. The technique uses a limited time series of measurements as input to a high-dimensional dynamical system called a "reservoir." After the reservoir's response to the data is recorded, linear regression is used to learn a large set of parameters, called the "output weights." The learned output weights are then used to form a modified autonomous reservoir designed to be capable of producing an arbitrarily long time series whose ergodic properties approximate those of the input signal. When successful, we say that the autonomous reservoir reproduces the attractor's "climate." Since the reservoir equations and output weights are known, we can compute the derivatives needed to determine the Lyapunov exponents of the autonomous reservoir, which we then use as estimates of the Lyapunov exponents for the original input generating system. We illustrate the effectiveness of our technique with two examples, the Lorenz system and the Kuramoto-Sivashinsky (KS) equation. In the case of the KS equation, we note that the high dimensional nature of the system ...Continue Reading

References

Dec 1, 1986·Physical Review A: General Physics·J EckmannS Ciliberto
Mar 1, 1987·Physical Review A: General Physics·A Brandstater, H L Swinney
Jan 29, 2016·Nature·David SilverDemis Hassabis

❮ Previous
Next ❯

Citations

Jan 19, 2019·Proceedings of the National Academy of Sciences of the United States of America·Antonio C CostaGreg J Stephens
Aug 23, 2019·PLoS Computational Biology·Georgia KoppeDaniel Durstewitz
Sep 27, 2019·Scientific Reports·Pietro VerzelliLorenzo Livi
Apr 2, 2018·Chaos·D Ibáñez-SoriaG Ruffini
Jul 2, 2018·Chaos·Zhixin LuEdward Ott
Jul 14, 2018·Nature Reviews. Neuroscience·Danielle S BassettJoshua I Gold
Oct 10, 2018·Proceedings of the National Academy of Sciences of the United States of America·Huanfei MaLuonan Chen
Feb 6, 2020·Chaos·Martin LellepBruno Eckhardt
May 20, 2020·Physical Review. E·Takumi TokamiHiroshi Gotoda
Jul 3, 2020·Chaos·M A GanaieSarika Jalan
Apr 1, 2018·Chaos·Roland S Zimmermann, Ulrich Parlitz
Mar 4, 2020·Scientific Reports·Maryam Masnadi-Shirazi, Shankar Subramaniam
Nov 30, 2019·Chaos·Antoine Blanchard, Themistoklis P Sapsis
Jul 3, 2020·Chaos·Yu HuangChristian L E Franzke
Jun 12, 2018·Proceedings. Mathematical, Physical, and Engineering Sciences·Pantelis R VlachasPetros Koumoutsakos
Mar 3, 2019·Chaos·Thomas LymburnThomas Jüngling
Nov 5, 2019·Chaos·Afroza ShirinFrancesco Sorrentino
Oct 3, 2019·Chaos·Thomas LymburnThomas Jüngling
Nov 30, 2019·Chaos·Rosangela Follmann, Epaminondas Rosa
Mar 3, 2020·Chaos·Guorui ShenYe Yuan
Apr 1, 2019·Chaos·Min ZhouSteven M Anlage
Jan 3, 2020·Chaos·Shannon D AlgarThomas Jüngling
Jul 3, 2020·Chaos·Alexander HaluszczynskiChristoph Räth
Sep 27, 2018·Physical Review. E·Kengo Nakai, Yoshitaka Saiki
May 22, 2019·Physical Review. E·Tongfeng WengMichael Small
Jan 3, 2019·Chaos·Daniel CanadayDaniel J Gauthier
Jan 3, 2020·Chaos·Aaron GriffithDaniel J Gauthier
Sep 18, 2020·Journal of Physics. Condensed Matter : an Institute of Physics Journal·Kevin M Loew, R M Bradley
Nov 4, 2020·Chaos·Christopher E GonzalezChristophe Letellier
Dec 18, 2020·Physical Review. E·Francesco BorraMassimo Cencini

❮ Previous
Next ❯

Related Concepts

Trending Feeds

COVID-19

Coronaviruses encompass a large family of viruses that cause the common cold as well as more serious diseases, such as the ongoing outbreak of coronavirus disease 2019 (COVID-19; formally known as 2019-nCoV). Coronaviruses can spread from animals to humans; symptoms include fever, cough, shortness of breath, and breathing difficulties; in more severe cases, infection can lead to death. This feed covers recent research on COVID-19.

Blastomycosis

Blastomycosis fungal infections spread through inhaling Blastomyces dermatitidis spores. Discover the latest research on blastomycosis fungal infections here.

Nuclear Pore Complex in ALS/FTD

Alterations in nucleocytoplasmic transport, controlled by the nuclear pore complex, may be involved in the pathomechanism underlying multiple neurodegenerative diseases including Amyotrophic Lateral Sclerosis and Frontotemporal Dementia. Here is the latest research on the nuclear pore complex in ALS and FTD.

Applications of Molecular Barcoding

The concept of molecular barcoding is that each original DNA or RNA molecule is attached to a unique sequence barcode. Sequence reads having different barcodes represent different original molecules, while sequence reads having the same barcode are results of PCR duplication from one original molecule. Discover the latest research on molecular barcoding here.

Chronic Fatigue Syndrome

Chronic fatigue syndrome is a disease characterized by unexplained disabling fatigue; the pathology of which is incompletely understood. Discover the latest research on chronic fatigue syndrome here.

Evolution of Pluripotency

Pluripotency refers to the ability of a cell to develop into three primary germ cell layers of the embryo. This feed focuses on the mechanisms that underlie the evolution of pluripotency. Here is the latest research.

Position Effect Variegation

Position Effect Variagation occurs when a gene is inactivated due to its positioning near heterochromatic regions within a chromosome. Discover the latest research on Position Effect Variagation here.

STING Receptor Agonists

Stimulator of IFN genes (STING) are a group of transmembrane proteins that are involved in the induction of type I interferon that is important in the innate immune response. The stimulation of STING has been an active area of research in the treatment of cancer and infectious diseases. Here is the latest research on STING receptor agonists.

Microbicide

Microbicides are products that can be applied to vaginal or rectal mucosal surfaces with the goal of preventing, or at least significantly reducing, the transmission of sexually transmitted infections. Here is the latest research on microbicides.