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Numerical simulations are ubiquitous in science and engineering. Machine learning for science investigates how artificial neural architectures can learn from these simulations to speed up scientific discovery and engineering processes. Most…

Reservoir computing approximation and generalization bounds are proved for a new concept class of input/output systems that extends the so-called generalized Barron functionals to a dynamic context. This new class is characterized by the…

In networked systems, the interplay between the dynamics of individual subsystems and their network interactions has been found to generate multistability in various contexts. Despite its ubiquity, the specific mechanisms and ingredients…

Neural circuits in the brain perform a variety of essential functions, including input classification, pattern completion, and the generation of rhythms and oscillations that support processes such as breathing and locomotion. There is also…

Reservoir computing provides an alternative to recurrent neural networks by overcoming the common problems of backpropagation through time and by training only a simple readout layer. The emerging field of quantum computing offers a new…

Neural networks are increasingly used in complex (data-driven) simulations as surrogates or for accelerating the computation of classical surrogates. In many applications physical constraints, such as mass or energy conservation, must be…

The concurrent rise of artificial intelligence and quantum information poses opportunity for creating interdisciplinary technologies like quantum neural networks. Quantum reservoir processing, introduced here, is a platform for quantum…

Photonic reservoir computing has been successfully utilized in time-series prediction as the need for hardware implementations has increased. Prediction of chaotic time series remains a significant challenge, an area where the conventional…

Reservoir Computing Networks (RCNs) belong to a group of machine learning techniques that project the input space non-linearly into a high-dimensional feature space, where the underlying task can be solved linearly. Popular variants of RCNs…

We present a dynamical system that naturally exhibits two unstable attractors that are completely enclosed by each others basin volume. This counter-intuitive phenomenon occurs in networks of pulse-coupled oscillators with delayed…

With the rising number of interconnected devices and sensors, modeling distributed sensor networks is of increasing interest. Recurrent neural networks (RNN) are considered particularly well suited for modeling sensory and streaming data.…

We consider the behaviour of attractors near invariant subspaces on varying a parameter that does not preserve the dynamics in the invariant subspace but is otherwise generic, in a smooth dynamical system. We refer to such a parameter as…

Reservoir Computing is an Unconventional Computation model to perform computation on various different substrates, such as recurrent neural networks or physical materials. The method takes a 'black-box' approach, training only the outputs…

Reservoir computing (RC) systems can efficiently forecast chaotic time series using nonlinear dynamical properties of an artificial neural network of random connections. The versatility of RC systems has motivated further research on both…

Reservoir computers are a type of neuromorphic computer that may be built a an analog system, potentially creating powerful computers that are small, light and consume little power. Typically a reservoir computer is build by connecting…

We consider a system of two identical linearly coupled Lorenz oscillators, presenting synchro- nization of chaotic motion for a specified range of the coupling strength. We verify the existence of global synchronization and…

Retentive Network (RetNet) represents a significant advancement in neural network architecture, offering an efficient alternative to the Transformer. While Transformers rely on self-attention to model dependencies, they suffer from high…

We introduce a general and simple structural design called Multiplicative Integration (MI) to improve recurrent neural networks (RNNs). MI changes the way in which information from difference sources flows and is integrated in the…

Recurrent neural networks (RNNs) are particularly well-suited for modeling long-term dependencies in sequential data, but are notoriously hard to train because the error backpropagated in time either vanishes or explodes at an exponential…

Reservoir computing (RC) is a novel approach to time series prediction using recurrent neural networks. In RC, an input signal perturbs the intrinsic dynamics of a medium called a reservoir. A readout layer is then trained to reconstruct a…