Related papers: Parameter estimation, nonlinearity and Occam's raz…
The identification of states and parameters from noisy measurements of a dynamical system is of great practical significance and has received a lot of attention. Classically, this problem is expressed as optimization over a class of models.…
Analyzing data from dynamical systems often begins with creating a reconstruction of the trajectory based on one or more variables, but not all variables are suitable for reconstructing the trajectory. The concept of nonlinear observability…
Causal inference from observational data following the restricted structural causal model (SCM) framework hinges largely on the asymmetry between cause and effect from the data generating mechanisms, such as non-Gaussianity or nonlinearity.…
Discovering the underlying dynamics of complex systems from data is an important practical topic. Constrained optimization algorithms are widely utilized and lead to many successes. Yet, such purely data-driven methods may bring about…
In this document, some general results in approximation theory and matrix analysis with applications to sparse identification of time series models and nonlinear discrete-time dynamical systems are presented. The aforementioned theoretical…
System identification aims to build models of dynamical systems from data. Traditionally, choosing the model requires the designer to balance between two goals of conflicting nature; the model must be rich enough to capture the system…
Changes in parameters of a physical device can eventually lead to catastrophic failure. This paper discusses a parameter estimation method based on synchronization between a model and time series data. In particular, we examine the…
We develop an interpolation-based framework for noisy linear systems with unknown system matrix with bounded norm (implying bounded growth or non-increasing energy), and bounded process noise energy. The proposed approach characterizes all…
We propose a novel method for fast and scalable evaluation of periodic solutions of systems of ordinary differential equations for a given set of parameter values and initial conditions. The equations governing the system dynamics are…
The statistical behavior of a nonlinear system described by a mapping with phase rotation is studied. We use the Kolmogorov-Chapman equations for the multi-time probability distribution functions for investigation of dynamics under the…
We extend observability metrics based on the empirical observability Gramian from deterministic nonlinear systems to nonlinear stochastic systems in order to capture the impact of process noise on observability. We demonstrate that the…
For a model nonlinear dynamical system, we show how one may obtain its bifurcation behavior by introducing noise into the dynamics and then studying the resulting Langevin dynamics in the weak-noise limit. A suitable quantity to capture the…
This work presents an algorithm for determining the parameters of a nonlinear dynamic model of the respiratory system in patients undergoing assisted ventilation. Using the pressure and flow signals measured at the mouth, the model's…
The creativity and emergence of biological and psychological behavior are nonlinear. However, that does not necessarily mean only that the measurements of the behaviors are curvilinear. Furthermore, the linear model might fail to reduce…
Improving the interpretability of deep neural networks has recently gained increased attention, especially when the power of deep learning is leveraged to solve problems in physics. Interpretability helps us understand a model's ability to…
We propose a simple method to estimate the parameters involved in discrete dynamical systems from time series. The method is based on the concept of controlling chaos by constant feedback. The major advantages of the method are that it…
Fluctuations in parameters that are typically treated as fixed play a crucial role in the behavior of complex systems. However, to date, we lack a general non-equilibrium thermodynamic treatment of such a complex system. In this Letter, to…
We propose a novel approach for change-point detection and parameter learning in multivariate non-stationary time series exhibiting oscillatory behaviour. We approximate the process through a piecewise function defined by a sum of…
Nonlinear time series analysis is an active field of research that studies the structure of complex signals in order to derive information of the process that generated those series, for understanding, modeling and forecasting purposes. In…
A new technique is introduced to reconstruct a nonlinear stochastic model of the cardiorespiratory interaction. Its inferential framework uses a set of polynomial basis functions representing the nonlinear force governing the system…