Related papers: Analytic reconstruction of some dynamical systems
This paper extends the subjects dicussed in the Data Analysis and Dynamical Systems courses by looking at the subject of modelling data. This task is nontrivial as the underlying process could be non-linear. In the paper some common…
In our previous paper [N. Tsutsumi, K. Nakai and Y. Saiki, Chaos 32, 091101 (2022)], we proposed a method for constructing a system of differential equations of chaotic behavior from only observable deterministic time series, which we call…
We consider the Lorenz equations, a system of three dimensional ordinary differential equations modeling atmospheric convection. These equations are chaotic and hard to study even numerically, and so a simpler "geometric model" has been…
Recovering continuous-time dynamics from discrete observations is difficult because local supervision (e.g., pointwise regression targets, derivative approximations, or equation residuals) loses fidelity as the observation interval grows.…
We propose a technique for reformulation of state and parameter estimation problems as that of matching explicitly computable definite integrals with known kernels to data. The technique applies for a class of systems of nonlinear ordinary…
A method for exploring unstable structures generated by nonlinear dynamical systems is introduced. It is based on the sampling of initial conditions and parameters by Replica Exchange Monte Carlo (REM), and efficient both for the search of…
Distinguishability and, by extension, observability are key properties of dynamical systems. Establishing these properties is challenging, especially when no analytical model is available and they are to be inferred directly from…
We present a direct approach to the construction of Lagrangians for a large class of one-dimensional dynamical systems with a simple dependence (monomial or polynomial) on the velocity. We rederive and generalize some recent results and…
We give an introduction into diffraction theory for aperiodic order. We focus on an approach via dynamical systems and the phenomenon of pure point diffraction. We review recent results and sketch proofs. We then present a new uniform…
Causal structure discovery from observational data is fundamental to the causal understanding of autonomous systems such as medical decision support systems, advertising campaigns and self-driving cars. This is essential to solve well-known…
Efficient structural reanalysis for high-rank modification plays an important role in engineering computations which require repeated evaluations of structural responses, such as structural optimization and probabilistic analysis. To…
Predicting the evolution of a large system of units using its structure of interaction is a fundamental problem in complex system theory. And so is the problem of reconstructing the structure of interaction from temporal observations. Here,…
In this work, we propose an observation system based on the available data which solution is one-be-one mapping to the forward problem(with the unknown initial function) solution. It implies their solutions share the same linear structure…
We establish a theory for multivariate extreme value analysis of dynamical systems. Namely, we provide conditions adapted to the dynamical setting which enable the study of dependence between extreme values of the components of…
We present a general framework for classifying partially observed dynamical systems based on the idea of learning in the model space. In contrast to the existing approaches using model point estimates to represent individual data items, we…
Systems of interacting species, such as biological environments or chemical reactions, are often described mathematically by sets of coupled ordinary differential equations. While a large number $\beta$ of species may be involved in the…
A method to synchronize two chaotic systems with anticipation or lag, coupled in the drive response mode, is proposed. The coupling involves variable delay with three time scales. The method has the advantage that synchronization is…
We introduce the problem of reconstructing a sequence of multidimensional real vectors where some of the data are missing. This problem contains regression and mapping inversion as particular cases where the pattern of missing data is…
The goal of data-driven learning of dynamical systems is to interpret time series as a continuous observation of an underlying dynamical system. This task is not well-posed for a variety of reasons - such as multiple co-existing…
We consider stochastic dynamical systems defined by differential equations with a uniform random time delay. The latter equations are shown to be equivalent to deterministic higher-order differential equations: for an $n$-th order equation…