Related papers: Model-free Forecasting of Rogue Waves using Reserv…
In the framework of physical reservoir computing (RC), machine learning algorithms designed for digital computers are executed using analog computer-like nonlinear physical systems that can provide energy-efficient computational power for…
Reservoir Computing (RC) refers to a Recurrent Neural Networks (RNNs) framework, frequently used for sequence learning and time series prediction. The RC system consists of a random fixed-weight RNN (the input-hidden reservoir layer) and a…
Reservoir computing is a computational framework suited for temporal/sequential data processing. It is derived from several recurrent neural network models, including echo state networks and liquid state machines. A reservoir computing…
We propose a learning-based robust predictive control algorithm that compensates for significant uncertainty in the dynamics for a class of discrete-time systems that are nominally linear with an additive nonlinear component. Such systems…
The real-time prediction of chaotic systems requires a nonlinear-reduced order model (ROM) to forecast the dynamics, and a stream of data from sensors to update the ROM. Data-driven ROMs are typically built with a two-step strategy: data…
A novel method for the numerical prediction of the slowly varying dynamics of nonlinear mechanical systems has been developed. The method is restricted to the regime of an isolated nonlinear mode and consists of a two-step procedure: In the…
Rogue waves are an intriguing nonlinear phenomenon arising across different scales, ranging from ocean waves through optics to Bose-Einstein condensates. We describe the emergence of rogue-like wave dynamics in a reaction-diffusion system…
Echo state networks are computationally lightweight reservoir models inspired by the random projections observed in cortical circuitry. As interest in reservoir computing has grown, networks have become deeper and more intricate. While…
A machine-learning approach called "reservoir computing" has been used successfully for short-term prediction and attractor reconstruction of chaotic dynamical systems from time series data. We present a theoretical framework that describes…
The Peregrine breather, today widely regarded as a prototype for spatio-temporally localized rogue waves on the ocean caused by nonlinear focusing, is analyzed by direct numerical simulations based on two-phase Navier-Stokes equations. A…
As the demand for more efficient and adaptive computing grows, nature-inspired architectures offer promising alternatives to conventional electronic designs. Microfluidic platforms, drawing on biological forms and fluid dynamics, present a…
Artificial Recurrent Neural Networks are a powerful information processing abstraction, and Reservoir Computing provides an efficient strategy to build robust implementations by projecting external inputs into high dimensional dynamical…
The Random Coupling Model (RCM) is a statistical approach for studying the scattering properties of linear wave chaotic systems in the semi-classical regime. Its success has been experimentally verified in various over-moded wave settings,…
In exploring the simulation of human rhythmic perception and synchronization capabilities, this study introduces a computational model inspired by the physical and biological processes underlying rhythm processing. Utilizing a reservoir…
We propose a learning-based robust predictive control algorithm that compensates for significant uncertainty in the dynamics for a class of discrete-time systems that are nominally linear with an additive nonlinear component. Such systems…
Next generation reservoir computing based on nonlinear vector autoregression (NVAR) is applied to emulate simple dynamical system models and compared to numerical integration schemes such as Euler and the $2^\text{nd}$ order Runge-Kutta. It…
A convolutional encoder-decoder-based transformer model is proposed for autoregressively training on spatio-temporal data of turbulent flows. The prediction of future fluid flow fields is based on the previously predicted fluid flow field…
Reservoir computing (RC) harnesses the intrinsic dynamics of a chaotic system, called the reservoir, to perform various time-varying functions. An important use-case of RC is the generation of target temporal sequences via a trainable…
Model predictive control (MPC) is an industry standard control technique that iteratively solves an open-loop optimization problem to guide a system towards a desired state or trajectory. Consequently, an accurate forward model of system…
We analyze the dynamics of modulation instability in optical fiber (or any other nonlinear Schr\"{o}dinger equation system) using the machine-learning technique of data-driven dominant balance. We aim to automate the identification of which…