Related papers: TensorFlow Chaotic Prediction and Blow Up
In this paper, the prediction capabilities of recurrent neural networks are assessed in the low-order model of near-wall turbulence by Moehlis {\it et al.} (New J. Phys. {\bf 6}, 56, 2004). Our results show that it is possible to obtain…
Predicting chaotic systems is crucial for understanding complex behaviors, yet challenging due to their sensitivity to initial conditions and inherent unpredictability. Probabilistic Reservoir Computing (RC) is well-suited for long-term…
The emergence of nontrivial collective behavior in networks of coupled chaotic maps is investigated by means of a nonlinear mutual prediction method. The resulting prediction error is used to measure the amount of information that a local…
The prediction of complex nonlinear dynamical systems with the help of machine learning techniques has become increasingly popular. In particular, reservoir computing turned out to be a very promising approach especially for the…
We train an artificial neural network which distinguishes chaotic and regular dynamics of the two-dimensional Chirikov standard map. We use finite length trajectories and compare the performance with traditional numerical methods which need…
Predicting extreme events in chaotic systems, characterized by rare but intensely fluctuating properties, is of great importance due to their impact on the performance and reliability of a wide range of systems. Some examples include…
Machine learning algorithms have opened a breach in the fortress of the prediction of high-dimensional chaotic systems. Their ability to find hidden correlations in data can be exploited to perform model-free forecasting of spatiotemporal…
Predicting future states or actions of a given system remains a fundamental, yet unsolved challenge of intelligence, especially in the scope of complex and non-deterministic scenarios, such as modeling behavior of humans. Existing…
In many real world chaotic systems, the interest is typically in determining when the system will behave in an extreme manner. Flooding and drought, extreme heatwaves, large earthquakes, and large drops in the stock market are examples of…
This study investigates how dynamical systems may be learned and modelled with a neuromorphic network which is itself a dynamical system. The neuromorphic network used in this study is based on a complex electrical circuit comprised of…
Chaos reveals a fundamental paradox in the scientific understanding of Complex Systems. Although chaotic models may be mathematically deterministic, they are practically non-determinable due to the finite precision, which is inherent in all…
We present an implementation of a probabilistic first-order logic called TensorLog, in which classes of logical queries are compiled into differentiable functions in a neural-network infrastructure such as Tensorflow or Theano. This leads…
Although it is now understood that chaos in complex classical systems is the foundation of thermodynamic behavior, the detailed relations between the microscopic properties of the chaotic dynamics and the macroscopic thermodynamic…
An experimental approach is taken to study the dynamics of the dripping water faucet, a simple deterministic system. The time interval between successive drops may be affected by the many drops preceding it. The time interval is predicted…
Learning dynamical systems from incomplete or noisy data is inherently ill-posed, as a single observation may correspond to multiple plausible futures. While physics-based ensemble forecasting relies on perturbing initial states to capture…
We show that a reservoir computer is an effective tool for model-free prediction of extreme events in deterministic chaotic systems. This prediction allows us to suppress unwanted extreme events, by applying weak control perturbations to…
We study the problem of predicting rare critical transition events for a class of slow-fast nonlinear dynamical systems. The state of the system of interest is described by a slow process, whereas a faster process drives its evolution and…
Deep learning is a branch of artificial intelligence employing deep neural network architectures that has significantly advanced the state-of-the-art in computer vision, speech recognition, natural language processing and other domains. In…
Forecasting the dynamics of large complex networks from previous time-series data is important in a wide range of contexts. Here we present a machine learning scheme for this task using a parallel architecture that mimics the topology of…
Linearly stable shear flows first transition to turbulence in the form of localised patches. At low Reynolds numbers, these turbulent patches tend to suddenly decay, following a memoryless process typical of rare events. How far in advance…