Related papers: Reconstruction of dynamic systems using genetic al…
The reconstruction of phase spaces is an essential step to analyze time series according to Dynamical System concepts. A regression performed on such spaces unveils the relationships among system states from which we can derive their…
Dynamical weather and climate prediction models underpin many studies of the Earth system and hold the promise of being able to make robust projections of future climate change based on physical laws. However, simulations from these models…
We propose a simple method of constructing a system of differential equations of chaotic behavior based on the regression only from a scalar observable time-series data. The estimated system enables us to reconstruct invariant sets and…
The Dynamical Graph Grammar (DGG) formalism can describe complex system dynamics with graphs that are mapped into a master equation. An exact stochastic simulation algorithm may be used, but it is slow for large systems. To overcome this…
The purpose of this research was to compare the robustness and performance of a local and global optimization algorithm when given the task of fitting the parameters of a common non-linear dose-response model utilized in the field of…
We propose a new polynomial-time algorithm for linear programming. We further extend the ideas used in this new linear programming algorithm for nonlinear programming problems. The new algorithm is based on the idea of treating the…
The process of transforming observed data into predictive mathematical models of the physical world has always been paramount in science and engineering. Although data is currently being collected at an ever-increasing pace, devising…
Modeling real-world systems requires accounting for noise - whether it arises from unpredictable fluctuations in financial markets, irregular rhythms in biological systems, or environmental variability in ecosystems. While the behavior of…
Multivariate polynomial dynamical systems over finite fields have been studied in several contexts, including engineering and mathematical biology. An important problem is to construct models of such systems from a partial specification of…
In this work, we show how a genetic algorithm (GA) can be used to find step-by-step solutions to introductory physics problems. Our perspective is that the underlying task for this is one of finding a sequence of equations that will lead to…
A set of algorithms is presented for efficient numerical calculation of the time evolution of classical dynamical systems. Starting with a first approximation for solving the differential equations that has a "reversible" character, we show…
A problem related to the development of algorithms designed to find the structure of artificial neural network used for behavioural (black-box) modelling of selected dynamic processes has been addressed in this paper. The research has…
This paper explores learning emulators for parameter estimation with uncertainty estimation of high-dimensional dynamical systems. We assume access to a computationally complex simulator that inputs a candidate parameter and outputs a…
Critical points separate distinct dynamical regimes of complex systems, often delimiting functional or macroscopic phases in which the system operates. However, the long-term prediction of critical regimes and behaviors is challenging given…
We study the problem of identifying the dynamics of a linear system when one has access to samples generated by a similar (but not identical) system, in addition to data from the true system. We use a weighted least squares approach and…
We develop a numerical method to reconstruct systems of ordinary differential equations (ODEs) from time series data without {\it a priori} knowledge of the underlying ODEs using sparse basis learning and sparse function reconstruction. We…
Discovering the governing equations of dynamical systems is a central problem across many scientific disciplines. As experimental data become increasingly available, automated equation discovery methods offer a promising data-driven…
Linear dynamical systems are a fundamental and powerful parametric model class. However, identifying the parameters of a linear dynamical system is a venerable task, permitting provably efficient solutions only in special cases. This work…
We present that, instead of establishing the equations of motion, one can model-freely reveal the dynamical properties of a black-box system using a learning machine. Trained only by a segment of time series of a state variable recorded at…
Finding repeated patterns or motifs in a time series is an important unsupervised task that has still a number of open issues, starting by the definition of motif. In this paper, we revise the notion of motif support, characterizing it as…