141 research outputs found
Models for time series prediction based on neural networks. Case study : GLP sales prediction from ANCAP.
A time series is a sequence of real values that can be considered as observations of a certain
system. In this work, we are interested in time series coming from dynamical systems. Such
systems can be sometimes described by a set of equations that model the underlying mechanism
from where the samples come. However, in several real systems, those equations are
unknown, and the only information available is a set of temporal measures, that constitute
a time series. On the other hand, by practical reasons it is usually required to have a prediction,
v.g. to know the (approximated) value of the series in a future instant t. The goal of
this thesis is to solve one of such real-world prediction problem: given historical data related
with the lique ed bottled propane gas sales, predict the future gas sales, as accurately as
possible. This time series prediction problem is addressed by means of neural networks,
using both (dynamic) reconstruction and prediction. The problem of to dynamically reconstruct
the original system consists in building a model that captures certain characteristics
of it in order to have a correspondence between the long-term behavior of the model and of
the system.
The networks design process is basically guided by three ingredients. The dimensionality
of the problem is explored by our rst ingredient, the Takens-Mañé's theorem. By means
of this theorem, the optimal dimension of the (neural) network input can be investigated.
Our second ingredient is a strong theorem: neural networks with a single hidden layer are
universal approximators. As the third ingredient, we faced the search of the optimal size
of the hidden layer by means of genetic algorithms, used to suggest the number of hidden
neurons that maximizes a target tness function (related with prediction errors). These
algorithms are also used to nd the most in uential networks inputs in some cases. The
determination of the hidden layer size is a central (and hard) problem in the determination
of the network topology.
This thesis includes a state of the art of neural networks design for time series prediction, including
related topics such as dynamical systems, universal approximators, gradient-descent
searches and variations, as well as meta-heuristics. The survey of the related literature is
intended to be extensive, for both printed material and electronic format, in order to have a
landscape of the main aspects for the state of the art in time series prediction using neural
networks. The material found was sometimes extremely redundant (as in the case of the
back-propagation algorithm and its improvements) and scarce in others (memory structures
or estimation of the signal subspace dimension in the stochastic case). The surveyed literature
includes classical research works ([27], [50], [52]) as well as more recent ones ([79] , [16]
or [82]), which pretends to be another contribution of this thesis.
Special attention is given to the available software tools for neural networks design and time
series processing. After a review of the available software packages, the most promising
computational tools for both approaches are discussed. As a result, a whole framework
based on mature software tools was set and used. In order to work with such dynamical
systems, software intended speci cally for the analysis and processing of time series was
employed, and then chaotic series were part of our focus.
Since not all randomness is attributable to chaos, in order to characterize the dynamical
system generating the time series, an exploration of chaotic-stochastic systems is required,
as well as network models to predict a time series associated to one of them. Here we
pretend to show how the knowledge of the domain, something extensively treated in the
bibliography, can be someway sophisticated (such as the Lyapunov's spectrum for a series
or the embedding dimension). In order to model the dynamical system generated by the time series we used the state-space model, so the time series prediction was translated in the prediction of the next system
state. This state-space model, together with the delays method (delayed coordinates) have
practical importance for the development of this work, speci cally, the design of the input
layer in some networks (multi-layer perceptrons - MLPs) and other parameters (taps in the
TFLNs). Additionally, the rest of the network components where determined in many cases
through procedures traditionally used in neural networks : genetic algorithms.
The criteria of model (network) selection are discussed and a trade-o between performance
and network complexity is further explored, inspired in the Rissanen's minimum description
length and its estimation given by the chosen software. Regarding the employed network
models, the network topologies suggested from the literature as adequate for the prediction
are used (TLFNs and recurrent networks) together with MLPs (a classic of arti cial neural
networks) and networks committees. The e ectiveness of each method is con rmed for the
proposed prediction problem. Network committees, where the predictions are a naive convex
combination of predictions from individual networks, are also extensively used.
The need of criteria to compare the behaviors of the model and of the real system, in the long
run, for a dynamic stochastic systems, is presented and two alternatives are commented.
The obtained results proof the existence of a solution to the problem of learning of the
dependence Input ! Output . We also conjecture that the system is dynamic-stochastic
but not chaotic, because we only have a realization of the random process corresponding to
the sales. As a non-chaotic system, the mean of the predictions of the sales would improve
as the available data increase, although the probability of a prediction with a big error is
always non-null due to the randomness present. This solution is found in a constructive and
exhaustive way. The exhaustiveness can be deduced from the next ve statements:
the design of a neural network requires knowing the input and output dimension,the
number of the hidden layers and of the neurons in each of them.
the use of the Takens-Mañé's theorem allows to derive the dimension of the input data
by theorems such as the Kolmogorov's and Cybenko's ones the use of multi-layer
perceptrons with only one hidden layer is justi ed so several of such models were
tested
the number of neurons in the hidden layer is determined many times heuristically
using genetic algorithms
a neuron in the output gives the desired prediction
As we said, two tasks are carried out: the development of a time series prediction model
and the analysis of a feasible model for the dynamic reconstruction of the system. With
the best predictive model, obtained by an ensemble of two networks, an acceptable average
error was obtained when the week to be predicted is not adjacent to the training set (7.04%
for the week 46/2011). We believe that these results are acceptable provided the quantity
of information available, and represent an additional validation that neural networks are
useful for time series prediction coming from dynamical systems, no matter whether they
are stochastic or not.
Finally, the results con rmed several already known facts (such as that adding noise to the
inputs and outputs of the training values can improve the results; that recurrent networks
trained with the back-propagation algorithm don't have the problem of vanishing gradients
in short periods and that the use of committees - which can be seen as a very basic of
distributed arti cial intelligence - allows to improve signi cantly the predictions).Una serie temporal es una secuencia de valores reales que pueden ser considerados como observaciones
de un cierto sistema. En este trabajo, estamos interesados en series temporales
provenientes de sistemas dinámicos. Tales sistemas pueden ser algunas veces descriptos por
un conjunto de ecuaciones que modelan el mecanismo subyacente que genera las muestras.
sin embargo, en muchos sistemas reales, esas ecuaciones son desconocidas, y la única información disponible es un conjunto de medidas en el tiempo, que constituyen la serie temporal.
Por otra parte, por razones prácticas es generalmente requerida una predicción, es decir,
conocer el valor (aproximado) de la serie en un instante futuro t. La meta de esta tesis es
resolver un problema de predicción del mundo real: dados los datos históricos relacionados
con las ventas de gas propano licuado, predecir las ventas futuras, tan aproximadamente
como sea posible. Este problema de predicción de series temporales es abordado por medio
de redes neuronales, tanto para la reconstrucción como para la predicción. El problema de
reconstruir dinámicamente el sistema original consiste en construir un modelo que capture
ciertas caracterÃsticas de él de forma de tener una correspondencia entre el comportamiento
a largo plazo del modelo y del sistema.
El proceso de diseño de las redes es guiado básicamente por tres ingredientes. La dimensionalidad
del problema es explorada por nuestro primer ingrediente, el teorema de Takens-Mañé.
Por medio de este teorema, la dimensión óptima de la entrada de la red neuronal puede ser
investigada. Nuestro segundo ingrediente es un teorema muy fuerte: las redes neuronales
con una sola capa oculta son un aproximador universal. Como tercer ingrediente, encaramos
la búsqueda del tamaño oculta de la capa oculta por medio de algoritmos genéticos, usados
para sugerir el número de neuronas ocultas que maximizan una función objetivo (relacionada
con los errores de predicción). Estos algoritmos se usan además para encontrar las entradas
a la red que influyen más en la salida en algunos casos. La determinación del tamaño de la
capa oculta es un problema central (y duro) en la determinación de la topologÃa de la red.
Esta tesis incluye un estado del arte del diseño de redes neuronales para la predicción de series
temporales, incluyendo tópicos relacionados tales como sistemas dinámicos, aproximadores
universales, búsquedas basadas en el gradiente y sus variaciones, asà como meta-heurÃsticas.
El relevamiento de la literatura relacionada busca ser extenso, para tanto el material impreso
como para el que esta en formato electrónico, de forma de tener un panorama de los
principales aspectos del estado del arte en la predicción de series temporales usando redes
neuronales. El material hallado fue algunas veces extremadamente redundante (como en
el caso del algoritmo de retropropagación y sus mejoras) y escaso en otros (estructuras de
memoria o estimación de la dimensión del sub-espacio de señal en el caso estocástico). La
literatura consultada incluye trabajos de investigación clásicos ( ([27], [50], [52])' asà como
de los más reciente ([79] , [16] or [82]).
Se presta especial atención a las herramientas de software disponibles para el diseño de redes
neuronales y el procesamiento de series temporales. Luego de una revisión de los paquetes
de software disponibles, las herramientas más promisiorias para ambas tareas son discutidas.
Como resultado, un entorno de trabajo completo basado en herramientas de software maduras fue definido y usado. Para trabajar con los mencionados sistemas dinámicos, software
especializado en el análisis y proceso de las series temporales fue empleado, y entonces
las series caóticas fueron estudiadas.
Ya que no toda la aleatoriedad es atribuible al caos, para caracterizar al sistema dinámico
que genera la serie temporal se requiere una exploración de los sistemas caóticos-estocásticos,
asà como de los modelos de red para predecir una serie temporal asociada a uno de ellos.
Aquà se pretende mostrar cómo el conocimiento del dominio, algo extensamente tratado en
la literatura, puede ser de alguna manera sofisticado (tal como el espectro de Lyapunov de
la serie o la dimensión del sub-espacio de señal).
Para modelar el sistema dinámico generado por la serie temporal se usa el modelo de espacio
de estados, por lo que la predicción de la serie temporal es traducida en la predicción
del siguiente estado del sistema. Este modelo de espacio de estados, junto con el método
de los delays (coordenadas demoradas) tiene importancia práctica en el desarrollo de este
trabajo, especÃficamente, en el diseño de la capa de entrada en algunas redes (los perceptrones
multicapa) y otros parámetros (los taps de las redes TLFN). Adicionalmente, el resto
de los componentes de la red con determinados en varios casos a través de procedimientos
tradicionalmente usados en las redes neuronales: los algoritmos genéticos.
Los criterios para la selección de modelo (red) son discutidos y un balance entre performance
y complejidad de la red es explorado luego, inspirado en el minimum description length de
Rissanen y su estimación dada por el software elegido.
Con respecto a los modelos de red empleados, las topologóas de sugeridas en la literatura
como adecuadas para la predicción son usadas (TLFNs y redes recurrentes) junto con perceptrones
multicapa (un clásico de las redes neuronales) y comités de redes. La efectividad
de cada método es confirmada por el problema de predicción propuesto. Los comités de
redes, donde las predicciones son una combinación convexa de las predicciones dadas por
las redes individuales, son también usados extensamente.
La necesidad de criterios para comparar el comportamiento del modelo con el del sistema
real, a largo plazo, para un sistema dinámico estocástico, es presentada y dos alternativas
son comentadas.
Los resultados obtenidos prueban la existencia de una solución al problema del aprendizaje
de la dependencia Entrada - Salida . Conjeturamos además que el sistema generador de
serie de las ventas es dinámico-estocástico pero no caótico, ya que sólo tenemos una realización del proceso aleatorio correspondiente a las ventas. Al ser un sistema no caótico, la media de las predicciones de las ventas deberÃa mejorar a medida que los datos disponibles
aumentan, aunque la probabilidad de una predicción con un gran error es siempre no nula debido
a la aleatoriedad presente. Esta solución es encontrada en una forma constructiva
y exhaustiva. La exhaustividad puede deducirse de las siguiente cinco afirmaciones :
el diseño de una red neuronal requiere conocer la dimensión de la entrada y de la
salida, el número de capas ocultas y las neuronas en cada una de ellas
el uso del teorema de takens-Mañé permite derivar la dimensión de la entrada
por teoremas tales como los de Kolmogorov y Cybenko el uso de perceptrones con solo
una capa oculta es justificado, por lo que varios de tales modelos son probados
el número de neuronas en la capa oculta es determinada varias veces heurÃsticamente
a través de algoritmos genéticos
una sola neurona de salida da la predicción deseada. Como se dijo, dos tareas son llevadas a cabo: el desarrollo de un modelo para la predicción de la serie temporal y el análisis de un modelo factible para la reconstrucción dinámica del sistema. Con el mejor modelo predictivo, obtenido por el comité de dos redes se logró obtener un error aceptable en la predicción de una semana no contigua al conjunto de
entrenamiento (7.04% para la semana 46/2011). Creemos que este es un resultado aceptable
dada la cantidad de información disponible y representa una validación adicional de que las
redes neuronales son útiles para la predicción de series temporales provenientes de sistemas
dinámicos, sin importar si son estocásticos o no.
Finalmente, los resultados experimentales confirmaron algunos hechos ya conocidos (tales
como que agregar ruido a los datos de entrada y de salida de los valores de entrenamiento
puede mejorar los resultados: que las redes recurrentes entrenadas con el algoritmo de
retropropagación no presentan el problema del gradiente evanescente en periodos cortos y
que el uso de de comités - que puede ser visto como una forma muy básica de inteligencia
artificial distribuida - permite mejorar significativamente las predicciones)
Biologically inspired evolutionary temporal neural circuits
Biological neural networks have always motivated creation of new artificial neural networks, and in this case a new autonomous temporal neural network system. Among the more challenging problems of temporal neural networks are the design and incorporation of short and long-term memories as well as the choice of network topology and training mechanism. In general, delayed copies of network signals can form short-term memory (STM), providing a limited temporal history of events similar to FIR filters, whereas the synaptic connection strengths as well as delayed feedback loops (ER circuits) can constitute longer-term memories (LTM). This dissertation introduces a new general evolutionary temporal neural network framework (GETnet) through automatic design of arbitrary neural networks with STM and LTM. GETnet is a step towards realization of general intelligent systems that need minimum or no human intervention and can be applied to a broad range of problems. GETnet utilizes nonlinear moving average/autoregressive nodes and sub-circuits that are trained by enhanced gradient descent and evolutionary search in terms of architecture, synaptic delay, and synaptic weight spaces. The mixture of Lamarckian and Darwinian evolutionary mechanisms facilitates the Baldwin effect and speeds up the hybrid training. The ability to evolve arbitrary adaptive time-delay connections enables GETnet to find novel answers to many classification and system identification tasks expressed in the general form of desired multidimensional input and output signals. Simulations using Mackey-Glass chaotic time series and fingerprint perspiration-induced temporal variations are given to demonstrate the above stated capabilities of GETnet
Improving time efficiency of feedforward neural network learning
Feedforward neural networks have been widely studied and used in many applications in science and engineering. The training of this type of networks is mainly undertaken using the well-known backpropagation based learning algorithms. One major problem with this type of algorithms is the slow training convergence speed, which hinders their applications. In order to improve the training convergence speed of this type of algorithms, many researchers have developed different improvements and enhancements. However, the slow convergence problem has not been fully addressed. This thesis makes several contributions by proposing new backpropagation learning algorithms based on the terminal attractor concept to improve the existing backpropagation learning algorithms such as the gradient descent and Levenberg-Marquardt algorithms. These new algorithms enable fast convergence both at a distance from and in a close range of the ideal weights. In particular, a new fast convergence mechanism is proposed which is based on the fast terminal attractor concept. Comprehensive simulation studies are undertaken to demonstrate the effectiveness of the proposed backpropagataion algorithms with terminal attractors. Finally, three practical application cases of time series forecasting, character recognition and image interpolation are chosen to show the practicality and usefulness of the proposed learning algorithms with comprehensive comparative studies with existing algorithms
Empirical state space modelling with application in online diagnosis of multivariate non-linear dynamic systems
Dissertation (Ph.D)--University of Stellenbosch, 1999.ENGLISH ABSTRACT: System identification has been sufficiently formalized for linear systems, but not for empirical
identification of non-linear, multivariate dynamic systems. Therefore this dissertation
formalizes and extends non-linear empirical system identification for the broad class of nonlinear
multivariate systems that can be parameterized as state space systems. The established,
but rather ad hoc methods of time series embedding and nonlinear modeling, using multilayer
perceptron network and radial basis function network model structures, are interpreted
in context with the established linear system identification framework.
First, the methodological framework was formulated for the identification of non-linear state
space systems from one-dimensional time series using a surrogate data method. It was clearly
demonstrated on an autocatalytic process in a continuously stirred tank reactor, that validation
of dynamic models by one-step predictions is insufficient proof of model quality. In addition,
the classification of data as either dynamic or random was performed, using the same
surrogate data technique. The classification technique proved to be robust in the presence of
up to at least 10% measurement and dynamic noise.
Next, the formulation of a nearly real-time algorithm for detection and removal of radial
outliers in multidimensional data was pursued. A convex hull technique was proposed and
demonstrated on random data, as well as real test data recorded from an internal combustion
engine. The results showed the convex hull technique to be effective at a computational cost
two orders of magnitude lower than the more proficient Rocke and Woodruff technique, used
as a benchmark, and incurred low cost (0.9%) in terms of falsely identifying outliers.
Following the identification of systems from one-dimensional time series, the methodological
framework was expanded to accommodate the identification of nonlinear state space systems
from multivariate time series. System parameterization was accomplished by combining
individual embeddings of each variable in the multivariate time series, and then separating
this combined space into independent components, using independent component analysis.
This method of parameterization was successfully applied in the simulation of the abovementioned
autocatalytic process. In addition, the parameterization method was implemented
in the one-step prediction of atmospheric N02 concentrations, which could become part of an
environmental control system for Cape Town. Furthermore, the combination of the embedding strategy and separation by independent component analysis was able to isolate
some of the noise components from the embedded data.
Finally the foregoing system identification methodology was applied to the online diagnosis
of temporal trends in critical system states. The methodology was supplemented by the
formulation of a statistical likelihood criterion for simultaneous interpretation of multivariate
system states. This technology was successfully applied to the diagnosis of the temporal
deterioration of the piston rings in a compression ignition engine under test conditions. The
diagnostic results indicated the beginning of significant piston ring wear, which was
confirmed by physical inspection of the engine after conclusion of the test. The technology
will be further developed and commercialized.AFRIKAANSE OPSOMMING: Stelselidentifikasie is weI genoegsaam ten opsigte van lineere stelsels geformaliseer, maar nie
ten opsigte van die identifikasie van nie-lineere, multiveranderlike stelsels nie. In hierdie tesis
word nie-lineere, empiriese stelselidentifikasie gevolglik ten opsigte van die wye klas van nielineere,
multiveranderlike stelsels, wat geparameteriseer kan word as toestandveranderlike
stelsels, geformaliseer en uitgebrei. Die gevestigde, maar betreklik ad hoc metodes vir
tydreeksontvouing en nie-lineere modellering (met behulp van multilaag-perseptron- en
radiaalbasisfunksie-modelstrukture) word in konteks met die gevestigde line ere
stelselidentifikasieraamwerk vertolk.
Eerstens is die metodologiese raamwerk vir die identifikasie van nie-lineere,
toestandsveranderlike stelsels uit eendimensionele tydreekse met behulp van In surrogaatdatametode
geformuleer. Daar is duidelik by wyse van 'n outokatalitiese proses in 'n deurlopend
geroerde tenkreaktor getoon dat die bevestiging van dinamiese modelle deur middel van
enkelstapvoorspellings onvoldoende bewys van die kwaliteit van die modelle is. Bykomend is
die klassifikasie van tydreekse as 6f dinamies Of willekeurig, met behulp van dieselfde
surrogaattegniek gedoen. Die klassifikasietegniek het in die teenwoordigheid van tot minstens
10% meetgeraas en dinamiese geraas robuust vertoon. /
Vervolgens is die formulering van In bykans intydse algoritme vir die opspoor en verwydering
van radiale uitskieters in multiveranderlike data aangepak. 'n Konvekse hulstegniek is
V:oorgestel en op ewekansige data, sowel as op werklike toetsdata wat van 'n binnebrandenjin
opgeneem is, gedemonstreer. Volgens die resultate was die konvekse hulstegniek effektief
teen 'n rekenkoste twee grootte-ordes kleiner as die meer vermoende Rocke en Woodrufftegniek,
wat as meetstandaard beskou is. Die konvekse hulstegniek het ook 'n lae loopkoste
(0.9%) betreffende die valse identifisering van uitskieters behaal.
Na aanleiding van die identifisering van stelsels uit eendimensionele tydreekse, is die
metodologiese raamwerk uitgebiei om die identifikasie van nie-lineere, toestandsveranderlike
stelsels uit multiveranderlike data te omvat. Stelselparameterisering is bereik deur individuele
ontvouings van elke veranderlike in die multidimensionele tydreeks met die skeiding van die
gesamenlike ontvouingsruimte tot onafhanklike komponente saam te span. Sodanige skeiding
is deur middel van onafhanklike komponentanalise behaal. Hierdie metode van parameterisering is suksesvc1 op die simulering van bogenoemde outokatalitiese proses
toegepas. Die parameteriseringsmetode is bykomend in die enkelstapvoorspelling van
atmosferiese N02-konsentrasies ingespan en sal moontlik deel van 'n voorgestelde
omgewingsbestuurstelsel vir Kaapstad uitmaak. Die kombinasie van die ontvouingstrategie en
skeiding deur onafhanklike komponentanalise was verder ook in staat om van die
geraaskomponente in die data uit te lig.
Ten slotte is die voorafgaande tegnologie vir stelselidentifikasie op die lopende diagnose van
tydsgebonde neigings in kritiese stelseltoestande toegepas. Die metodologie is met die
formulering van 'n statistiese waarskynlikheidsmaatstaf vir die gelyktydige vertolking van
multiveranderlike stelseltoestande aangevul. Hierdie tegnologie is suksesvol op die diagnose
van die tydsgebonde verswakking van die suierringe in 'n kompressieontstekingenj in tydens
toetstoestande toegepas. Die diagnostiese resultate het die aanvang van beduidende slytasie in
die suierringe aangedui, wat later tydens fisiese inspeksie van die enjin met afloop van die
toets, bevestig is. Die tegnologie sal verder ontwikkel en markgereed gemaak word
Function approximation in high-dimensional spaces using lower-dimensional Gaussian RBF networks.
by Jones Chui.Thesis (M.Phil.)--Chinese University of Hong Kong, 1992.Includes bibliographical references (leaves 62-[66]).Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Fundamentals of Artificial Neural Networks --- p.2Chapter 1.1.1 --- Processing Unit --- p.2Chapter 1.1.2 --- Topology --- p.3Chapter 1.1.3 --- Learning Rules --- p.4Chapter 1.2 --- Overview of Various Neural Network Models --- p.6Chapter 1.3 --- Introduction to the Radial Basis Function Networks (RBFs) --- p.8Chapter 1.3.1 --- Historical Development --- p.9Chapter 1.3.2 --- Some Intrinsic Problems --- p.9Chapter 1.4 --- Objective of the Thesis --- p.10Chapter 2 --- Low-dimensional Gaussian RBF networks (LowD RBFs) --- p.13Chapter 2.1 --- Architecture of LowD RBF Networks --- p.13Chapter 2.1.1 --- Network Structure --- p.13Chapter 2.1.2 --- Learning Rules --- p.17Chapter 2.2 --- Construction of LowD RBF Networks --- p.19Chapter 2.2.1 --- Growing Heuristic --- p.19Chapter 2.2.2 --- Pruning Heuristic --- p.27Chapter 2.2.3 --- Summary --- p.31Chapter 3 --- Application examples --- p.34Chapter 3.1 --- Chaotic Time Series Prediction --- p.35Chapter 3.1.1 --- Performance Comparison --- p.39Chapter 3.1.2 --- Sensitivity Analysis of MSE THRESHOLDS --- p.41Chapter 3.1.3 --- Effects of Increased Embedding Dimension --- p.41Chapter 3.1.4 --- Comparison with Tree-Structured Network --- p.46Chapter 3.1.5 --- Overfitting Problem --- p.46Chapter 3.2 --- Nonlinear prediction of speech signal --- p.49Chapter 3.2.1 --- Comparison with Linear Predictive Coding (LPC) --- p.54Chapter 3.2.2 --- Performance Test in Noisy Conditions --- p.55Chapter 3.2.3 --- Iterated Prediction of Speech --- p.59Chapter 4 --- Conclusion --- p.60Chapter 4.1 --- Discussions --- p.60Chapter 4.2 --- Limitations and Suggestions for Further Research --- p.61Bibliography --- p.6
Physics-based Machine Learning Approaches to Complex Systems and Climate Analysis
Komplexe Systeme wie das Klima der Erde bestehen aus vielen Komponenten, die durch eine komplizierte Kopplungsstruktur miteinander verbunden sind. Für die Analyse solcher Systeme erscheint es daher naheliegend, Methoden aus der Netzwerktheorie, der Theorie dynamischer Systeme und dem maschinellen Lernen zusammenzubringen. Durch die Kombination verschiedener Konzepte aus diesen Bereichen werden in dieser Arbeit drei neuartige Ansätze zur Untersuchung komplexer Systeme betrachtet.
Im ersten Teil wird eine Methode zur Konstruktion komplexer Netzwerke vorgestellt, die in der Lage ist, Windpfade des südamerikanischen Monsunsystems zu identifizieren. Diese Analyse weist u.a. auf den Einfluss der Rossby-Wellenzüge auf das Monsunsystem hin. Dies wird weiter untersucht, indem gezeigt wird, dass der Niederschlag mit den Rossby-Wellen phasenkohärent ist. So zeigt der erste Teil dieser Arbeit, wie komplexe Netzwerke verwendet werden können, um räumlich-zeitliche Variabilitätsmuster zu identifizieren, die dann mit Methoden der nichtlinearen Dynamik weiter analysiert werden können.
Die meisten komplexen Systeme weisen eine große Anzahl von möglichen asymptotischen Zuständen auf. Um solche Zustände zu beschreiben, wird im zweiten Teil die Monte Carlo Basin Bifurcation Analyse (MCBB), eine neuartige numerische Methode, vorgestellt. Angesiedelt zwischen der klassischen Analyse mit Ordnungsparametern und einer gründlicheren, detaillierteren Bifurkationsanalyse, kombiniert MCBB Zufallsstichproben mit Clustering, um die verschiedenen Zustände und ihre Einzugsgebiete zu identifizieren.
Bei von Vorhersagen von komplexen Systemen ist es nicht immer einfach, wie Vorwissen in datengetriebenen Methoden integriert werden kann. Eine Möglichkeit hierzu ist die Verwendung von Neuronalen Partiellen Differentialgleichungen. Hier wird im letzten Teil der Arbeit gezeigt, wie hochdimensionale räumlich-zeitlich chaotische Systeme mit einem solchen Ansatz modelliert und vorhergesagt werden können.Complex systems such as the Earth's climate are comprised of many constituents that are interlinked through an intricate coupling structure. For the analysis of such systems it therefore seems natural to bring together methods from network theory, dynamical systems theory and machine learning. By combining different concepts from these fields three novel approaches for the study of complex systems are considered throughout this thesis.
In the first part, a novel complex network construction method is introduced that is able to identify the most important wind paths of the South American Monsoon system. Aside from the importance of cross-equatorial flows, this analysis points to the impact Rossby Wave trains have both on the precipitation and low-level circulation. This connection is then further explored by showing that the precipitation is phase coherent to the Rossby Wave. As such, the first part of this thesis demonstrates how complex networks can be used to identify spatiotemporal variability patterns within large amounts of data, that are then further analysed with methods from nonlinear dynamics.
Most complex systems exhibit a large number of possible asymptotic states. To investigate and track such states, Monte Carlo Basin Bifurcation analysis (MCBB), a novel numerical method is introduced in the second part. Situated between the classical analysis with macroscopic order parameters and a more thorough, detailed bifurcation analysis, MCBB combines random sampling with clustering methods to identify and characterise the different asymptotic states and their basins of attraction.
Forecasts of complex system are the next logical step. When doing so, it is not always straightforward how prior knowledge in data-driven methods. One possibility to do is by using Neural Partial Differential Equations. Here, it is demonstrated how high-dimensional spatiotemporally chaotic systems can be modelled and predicted with such an approach in the last part of the thesis
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