Related papers: Adapting reservoir computing to solve the Schr\"od…
In-materio computing exploits the intrinsic physical dynamics of materials to perform complex computations, enabling low-power, real-time data processing by embedding computation directly within physical layers. Here, we demonstrate a…
We tested the performance of reservoir computing (RC) in predicting the dynamics of a certain non-autonomous dynamical system. Specifically, we considered a van del Pol oscillator subjected to periodic external force with frequent phase…
Data assimilation addresses the general problem of how to combine model-based predictions with partial and noisy observations of the process in an optimal manner. This survey focuses on sequential data assimilation techniques using…
One of the most accurate methods for solving the time-dependent Schr\"{o}dinger equation uses a combination of the dynamic Fourier method with the split-operator algorithm on a tensor-product grid. To reduce the number of required grid…
Reservoir computing is a versatile paradigm in computational neuroscience and machine learning, that exploits the non-linear dynamics of a dynamical system - the reservoir - to efficiently process time-dependent information. Since its…
Mechanical systems exhibit complex dynamical behavior from harmonic oscillations to chaotic motion. The dynamics undergo qualitative changes due to changes to internal system parameters like stiffness and changes to external forcing.…
A reservoir computer is a complex nonlinear dynamical system that has been shown to be useful for solving certain problems, such as prediction of chaotic signals, speech recognition or control of robotic systems. Typically a reservoir…
Physical reservoir computing (PRC) is a promising brain-inspired computing architecture for overcoming the von Neumann bottleneck by utilizing the intrinsic dynamics of physical systems. However, a major obstacle to its real-world…
The authors have numerically studied how to enhance reservoir computing performance by thoroughly extracting their spin-wave device potential for higher-dimensional information generation. The reservoir device has a 1-input exciter and…
Model-free and data-driven prediction of tipping point transitions in nonlinear dynamical systems is a challenging and outstanding task in complex systems science. We propose a novel, fully data-driven machine learning algorithm based on…
Production forecasting is a key step to design the future development of a reservoir. A classical way to generate such forecasts consists in simulating future production for numerical models representative of the reservoir. However,…
Reservoir computing is a bio-inspired machine learning paradigm that exploits the intrinsic dynamics of nonlinear systems with fading memory for efficient temporal information processing. Microelectromechanical resonators offer a promising…
In the context of energy transition, industrial plants that heavily rely on electricity face more and more price volatility. To continue operating in these conditions, the directors become continually more willing to increase their…
In the quest for alternatives to traditional CMOS, it is being suggested that digital computing efficiency and power can be improved by matching the precision to the application. Many applications do not need the high precision that is…
A propagator for the one dimensional time-dependent Schr\"odinger equation with an asymmetric rectangular potential is obtained using the multiple-scattering theory approach. It allows for the consideration of the reflection and…
Several recent papers have shown that reservoir computers are useful for analyzing and predicting dynamical systems. Reservoir computers have also been shown to be useful for various classification problems. In this work, a reservoir…
Reservoir Computing is a novel computing paradigm which uses a nonlinear recurrent dynamical system to carry out information processing. Recent electronic and optoelectronic Reservoir Computers based on an architecture with a single…
We propose a novel dispersive regularization framework for the numerical simulation of the one-dimensional shallow water equations (SWE). The classical hyperbolic system is regularized by a third-order dispersive term in the momentum…
There is a wave of interest in using unsupervised neural networks for solving differential equations. The existing methods are based on feed-forward networks, {while} recurrent neural network differential equation solvers have not yet been…
We consider the cubic nonlinear Schr\"odinger equation posed on the spatial domain $\mathbb{R}\times \mathbb{T}^d$. We prove modified scattering and construct modified wave operators for small initial and final data respectively ($1\leq…