Related papers: Learning Hamiltonian dynamics by reservoir compute…
Quantum reservoir computing is a machine learning framework that offers ease of training compared to other quantum neural networks, as it does not rely on gradient-based optimization. Learning is performed in a single step on the output…
Reservoir computing has been shown to be a useful framework for predicting critical transitions of a dynamical system if the bifurcation parameter is also provided as an input. Its utility is significant because in real-world scenarios, the…
The rapid growth of research in exploiting machine learning to predict chaotic systems has revived a recent interest in Hamiltonian Neural Networks (HNNs) with physical constraints defined by the Hamilton's equations of motion, which…
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…
We introduce a novel data-driven symplectic induced-order modeling (ROM) framework for high-dimensional Hamiltonian systems that unifies latent-space discovery and dynamics learning within a single, end-to-end neural architecture. The…
We consider model order reduction of parameterized Hamiltonian systems describing nondissipative phenomena, like wave-type and transport dominated problems. The development of reduced basis methods for such models is challenged by two main…
Hamiltonian systems are differential equations which describe systems in classical mechanics, plasma physics, and sampling problems. They exhibit many structural properties, such as a lack of attractors and the presence of conservation…
Reservoir computing (RC), a particular form of recurrent neural network, is under explosive development due to its exceptional efficacy and high performance in reconstruction or/and prediction of complex physical systems. However, the…
We propose and demonstrate a nonlinear control method that can be applied to unknown, complex systems where the controller is based on a type of artificial neural network known as a reservoir computer. In contrast to many modern…
Reservoir computing (RC) can efficiently process time-series data by transferring the input signal to randomly connected recurrent neural networks (RNNs), which are referred to as a reservoir. The high-dimensional representation of…
Understanding how training shapes the geometry of recurrent network dynamics is a central problem in time-series modeling. We study the emergence of low-dimensional dominant manifolds in the training of Reservoir Computing (RC) networks for…
We study the problem of learning an unknown quantum many-body Hamiltonian $H$ from black-box queries to its time evolution $e^{-\mathrm{i} H t}$. Prior proposals for solving this task either impose some assumptions on $H$, such as its…
In recent works we have used quantum tools in the analysis of the time evolution of several macroscopic systems. The main ingredient in our approach is the self-adjoint Hamiltonian $H$ of the system $\Sc$. This Hamiltonian quite often, and…
We study how the degree of nonlinearity in the input data affects the optimal design of reservoir computers, focusing on how closely the model's nonlinearity should align with that of the data. By reducing minimal RCs to a single tunable…
We propose an efficient quantum algorithm for simulating the dynamics of general Hamiltonian systems. Our technique is based on a power series expansion of the time-evolution operator in its off-diagonal terms. The expansion decouples the…
This study evaluates data-driven models from a dynamical system perspective, such as unstable fixed points, periodic orbits, chaotic saddle, Lyapunov exponents, manifold structures, and statistical values. We find that these dynamical…
Reservoir computing is a machine learning paradigm that uses a structure called a reservoir, which has nonlinearities and short-term memory. In recent years, reservoir computing has expanded to new functions such as the autonomous…
Embedding non-restrictive prior knowledge, such as energy conservation laws, into learning methods is a key motive to construct physically consistent dynamics models from limited data, relevant for, e.g., model-based control. Recent work…
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…
With the fast development of quantum technology, the sizes of both digital and analog quantum systems increase drastically. In order to have better control and understanding of the quantum hardware, an important task is to characterize the…