Related papers: Data-driven Discovery of Invariant Measures

Data-driven methods for the identification of the governing equations of dynamical systems or the computation of reduced surrogate models play an increasingly important role in many application areas such as physics, chemistry, biology, and…

Modeling complex dynamical systems under varying conditions is computationally intensive, often rendering high-fidelity simulations intractable. Although reduced-order models (ROMs) offer a promising solution, current methods often struggle…

We consider a deterministic system with two conserved quantities and infinity many invariant measures. However the systems possess a unique invariant measure when enough stochastic forcing and balancing dissipation are added. We then show…

There is studied an invariant measure structure of a class of ergodicl discrete dynamical systems by means of the measure generating function method

This work proposes a Stochastic Variational Deep Kernel Learning method for the data-driven discovery of low-dimensional dynamical models from high-dimensional noisy data. The framework is composed of an encoder that compresses…

Efficiently estimating system dynamics from data is essential for minimizing data collection costs and improving model performance. This work addresses the challenge of designing future control inputs to maximize information gain, thereby…

The paper studies the problem of filtering a discrete-time linear system observed by a network of sensors. The sensors share a common communication medium to the estimator and transmission is bit and power budgeted. Under the assumption of…

A multi-physics formulation for Data Driven Prognosis (DDP) is developed. Unlike traditional predictive strategies that require controlled off-line measurements or training for determination of constitutive parameters to derive the…

This paper considers optimal control of dynamical systems which are represented by nonlinear stochastic differential equations. It is well-known that the optimal control policy for this problem can be obtained as a function of a value…

We propose a novel method applied to extrasolar planetary dynamics to describe the system stability. The observations in this field serve the measurements mainly of radial velocity, transit time, and/or celestial position. These scalar time…

Dynamic mode decomposition has emerged as a leading technique to identify spatiotemporal coherent structures from high-dimensional data, benefiting from a strong connection to nonlinear dynamical systems via the Koopman operator. In this…

Physics-informed neural networks have emerged as a powerful tool in the scientific machine learning community, with applications to both forward and inverse problems. While they have shown considerable empirical success, significant…

The paper algorithmizes the problem of regime change point identification for data measured in a system exhibiting impulsive behaviors. This is a fundamental challenge for annotation of measurement data relevant, e.g., for designing…

We bring a control perspective to the problem of identifying paths of measures for sampling via dynamic measure transport (DMT). We highlight the fact that commonly used paths may be poor choices for DMT and connect existing methods for…

We introduce an approach which allows detecting causal relationships between variables for which the time evolution is available. Causality is assessed by a variational scheme based on the Information Imbalance of distance ranks, a…

Discovering the governing equations of a physical system and designing an effective feedback controller remains one of the most challenging and intensive areas of ongoing research. This task demands a deep understanding of the system…

Experimentally observed networks of interacting dynamical systems are inferred from recorded multivariate time series by evaluating a statistical measure of dependence, usually the cross-correlation coefficient, or mutual information. These…

Pattern-forming systems can exhibit a diverse array of complex behaviors as external parameters are varied, enabling a variety of useful functions in biological and engineered systems. First-principles derivations of the underlying…

Generalized dimensions of multifractal measures are usually seen as static objects, related to the scaling properties of suitable partition functions, or moments of measures of cells. When these measures are invariant for the flow of a…

Dissipative partial differential equations that exhibit chaotic dynamics tend to evolve to attractors that exist on finite-dimensional manifolds. We present a data-driven reduced order modeling method that capitalizes on this fact by…