Related papers: Predicting Chaotic System Behavior using Machine L…
Water supplies are crucial for the development of living beings. However, change in the hydrological process i.e. climate and land usage are the key issues. Sustaining water level and accurate estimating for dynamic conditions is a critical…
This paper extends the notion of information processing capacity for non-independent input signals in the context of reservoir computing (RC). The presence of input autocorrelation makes worthwhile the treatment of forecasting and filtering…
We propose a hybrid method combining the deep long short-term memory (LSTM) model with the inexact empirical model of dynamical systems to predict high-dimensional chaotic systems. The deep hierarchy is encoded into the LSTM by…
Natural spatiotemporal processes can be highly non-stationary in many ways, e.g. the low-level non-stationarity such as spatial correlations or temporal dependencies of local pixel values; and the high-level variations such as the…
In this paper a new concept, namely the critical predictable time $T_c$, is introduced to give a more precise description of computed chaotic solutions of nonlinear differential equations: it is suggested that computed chaotic solutions are…
Systems exhibiting nonlinear dynamics, including but not limited to chaos, are ubiquitous across Earth Sciences such as Meteorology, Hydrology, Climate and Ecology, as well as Biology such as neural and cardiac processes. However, System…
When people learn mathematical patterns or sequences, they are able to identify the concepts (or rules) underlying those patterns. Having learned the underlying concepts, humans are also able to generalize those concepts to other numbers,…
The increasing integration of renewable energy sources (RESs) into modern power systems presents significant opportunities but also notable challenges, primarily due to the inherent variability of RES generation. Accurate forecasting of RES…
Reservoir computing (RC), is a class of computational methods such as Echo State Networks (ESN) and Liquid State Machines (LSM) describe a generic method to perform pattern recognition and temporal analysis with any non-linear system. This…
Accurate electrical load forecasting is crucial for optimizing power system operations, planning, and management. As power systems become increasingly complex, traditional forecasting methods may fail to capture the intricate patterns and…
Recent research has demonstrated Reservoir Computing's capability to model various chaotic dynamical systems, yet its application to Hamiltonian systems remains relatively unexplored. This paper investigates the effectiveness of Reservoir…
The increasing focus on predicting renewable energy production aligns with advancements in deep learning (DL). The inherent variability of renewable sources and the complexity of prediction methods require robust approaches, such as DL…
Chaotic systems are notoriously challenging to predict because of their sensitivity to perturbations and errors due to time stepping. Despite this unpredictable behavior, for many dissipative systems the statistics of the long term…
Collecting time series data spatially distributed in many locations is often important for analyzing climate change and its impacts on ecosystems. However, comprehensive spatial data collection is not always feasible, requiring us to…
Reservoir computers (RC) are a form of recurrent neural network (RNN) used for forecasting timeseries data. As with all RNNs, selecting the hyperparameters presents a challenge when training onnew inputs. We present a method based on…
Forecasting chaotic time series requires models that can capture the intrinsic geometry of the underlying attractor while remaining computationally efficient. We introduce a novel reservoir computing (RC) framework that integrates…
We present results for long term and intermediate term prediction algorithms applied to a simple mechanical model of a fault. We use long term prediction methods based, for example, on the distribution of repeat times between large events…
Many state-of-the-art algorithms for solving hard combinatorial problems in artificial intelligence (AI) include elements of stochasticity that lead to high variations in runtime, even for a fixed problem instance. Knowledge about the…
There exist several data-driven approaches that enable us model time series data including traditional regression-based modeling approaches (i.e., ARIMA). Recently, deep learning techniques have been introduced and explored in the context…
Reservoir computing - information processing based on untrained recurrent neural networks with random connections - is expected to depend on the nonlinear properties of the neurons and the resulting oscillatory, chaotic, or fixpoint…