1,001 research outputs found
Data-Driven Forecasting of High-Dimensional Chaotic Systems with Long Short-Term Memory Networks
We introduce a data-driven forecasting method for high-dimensional chaotic
systems using long short-term memory (LSTM) recurrent neural networks. The
proposed LSTM neural networks perform inference of high-dimensional dynamical
systems in their reduced order space and are shown to be an effective set of
nonlinear approximators of their attractor. We demonstrate the forecasting
performance of the LSTM and compare it with Gaussian processes (GPs) in time
series obtained from the Lorenz 96 system, the Kuramoto-Sivashinsky equation
and a prototype climate model. The LSTM networks outperform the GPs in
short-term forecasting accuracy in all applications considered. A hybrid
architecture, extending the LSTM with a mean stochastic model (MSM-LSTM), is
proposed to ensure convergence to the invariant measure. This novel hybrid
method is fully data-driven and extends the forecasting capabilities of LSTM
networks.Comment: 31 page
Wind Power Forecasting Methods Based on Deep Learning: A Survey
Accurate wind power forecasting in wind farm can effectively reduce the enormous impact on grid operation safety when high permeability intermittent power supply is connected to the power grid. Aiming to provide reference strategies for relevant researchers as well as practical applications, this paper attempts to provide the literature investigation and methods analysis of deep learning, enforcement learning and transfer learning in wind speed and wind power forecasting modeling. Usually, wind speed and wind power forecasting around a wind farm requires the calculation of the next moment of the definite state, which is usually achieved based on the state of the atmosphere that encompasses nearby atmospheric pressure, temperature, roughness, and obstacles. As an effective method of high-dimensional feature extraction, deep neural network can theoretically deal with arbitrary nonlinear transformation through proper structural design, such as adding noise to outputs, evolutionary learning used to optimize hidden layer weights, optimize the objective function so as to save information that can improve the output accuracy while filter out the irrelevant or less affected information for forecasting. The establishment of high-precision wind speed and wind power forecasting models is always a challenge due to the randomness, instantaneity and seasonal characteristics
Data-assisted reduced-order modeling of extreme events in complex dynamical systems
Dynamical systems with high intrinsic dimensionality are often characterized
by extreme events having the form of rare transitions several standard
deviations away from the mean. For such systems, order-reduction methods
through projection of the governing equations have limited applicability due to
the large intrinsic dimensionality of the underlying attractor but also the
complexity of the transient events. An alternative approach is data-driven
techniques that aim to quantify the dynamics of specific modes utilizing
data-streams. Several of these approaches have improved performance by
expanding the state representation using delayed coordinates. However, such
strategies are limited in regions of the phase space where there is a small
amount of data available, as is the case for extreme events. In this work, we
develop a blended framework that integrates an imperfect model, obtained from
projecting equations into a subspace that still contains crucial dynamical
information, with data-streams through a recurrent neural network (RNN)
architecture. In particular, we employ the long-short-term memory (LSTM), to
model portions of the dynamics which cannot be accounted by the equations. The
RNN is trained by analyzing the mismatch between the imperfect model and the
data-streams, projected in the reduced-order space. In this way, the
data-driven model improves the imperfect model in regions where data is
available, while for locations where data is sparse the imperfect model still
provides a baseline for the prediction of the system dynamics. We assess the
developed framework on two challenging prototype systems exhibiting extreme
events and show that the blended approach has improved performance compared
with methods that use either data streams or the imperfect model alone. The
improvement is more significant in regions associated with extreme events,
where data is sparse.Comment: Submitted to PLOS ONE on March 8, 201
Investigating the Predictability of a Chaotic Time-Series Data using Reservoir Computing, Deep-Learning and Machine- Learning on the Short-, Medium- and Long-Term Pricing of Bitcoin and Ethereum.
This study will investigate the predictability of a Chaotic time-series data using Reservoir computing (Echo State Network), Deep-Learning(LSTM) and Machine- Learning(Linear, Bayesian, ElasticNetCV , Random Forest, XGBoost Regression and a machine learning Neural Network) on the short (1-day out prediction), medium (5-day out prediction) and long-term (30-day out prediction) pricing of Bitcoin and Ethereum Using a range of machine learning tools, to perform feature selection by permutation importance to select technical indicators on the individual cryptocurrencies, to ensure the datasets are the best for predictions per cryptocurrency while reducing noise within the models. The predictability of these two chaotic time-series is then compared to evaluate the models to find the best fit model. The models are fine-tuned, with hyperparameters, design of the network within the LSTM and the reservoir size within the Echo State Network being adjusted to improve accuracy and speed. This research highlights the effect of the trends within the cryptocurrency and its effect on predictive models, these models will then be optimized with hyperparameter tuning, and be evaluated to compare the models across the two currencies. It is found that the datasets for each cryptocurrency are different, due to the different permutation importance, which does not affect the overall predictability of the models with the short and medium-term predictions having the same models being the top performers. This research confirms that the chaotic data although can have positive results for shortand medium-term prediction, for long-term prediction, technical analysis basedprediction is not sufficient
Data-driven discovery of coordinates and governing equations
The discovery of governing equations from scientific data has the potential
to transform data-rich fields that lack well-characterized quantitative
descriptions. Advances in sparse regression are currently enabling the
tractable identification of both the structure and parameters of a nonlinear
dynamical system from data. The resulting models have the fewest terms
necessary to describe the dynamics, balancing model complexity with descriptive
ability, and thus promoting interpretability and generalizability. This
provides an algorithmic approach to Occam's razor for model discovery. However,
this approach fundamentally relies on an effective coordinate system in which
the dynamics have a simple representation. In this work, we design a custom
autoencoder to discover a coordinate transformation into a reduced space where
the dynamics may be sparsely represented. Thus, we simultaneously learn the
governing equations and the associated coordinate system. We demonstrate this
approach on several example high-dimensional dynamical systems with
low-dimensional behavior. The resulting modeling framework combines the
strengths of deep neural networks for flexible representation and sparse
identification of nonlinear dynamics (SINDy) for parsimonious models. It is the
first method of its kind to place the discovery of coordinates and models on an
equal footing.Comment: 25 pages, 6 figures; added acknowledgment
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