Related papers: A Mathematical Framework for Linear Response Theor…
The question of deriving general force/flux relationships that apply out of the linear response regime is a central topic of theories for nonequilibrium statistical mechanics. This work applies an information theory perspective to compute…
We consider a class of evolution equations describing population dynamics in the presence of a carrying capacity depending on the population with delay. In an earlier work, we presented an exhaustive classification of the logistic equation…
We continue our study of the linear response of a nonequilibrium system. This Part II concentrates on models of open and driven inertial dynamics but the structure and the interpretation of the result remain unchanged: the response can be…
The long-term average response of observables of chaotic systems to dynamical perturbations can often be predicted using linear response theory, but not all chaotic systems possess a linear response. Macroscopic observables of complex…
We study the problem of system identification for stochastic continuous-time dynamics, based on a single finite-length state trajectory. We present a method for estimating the possibly unstable open-loop matrix by employing properly…
We present a general setting in which the formula describing the linear response of the physical measure of a perturbed system can be obtained. In this general setting we obtain an algorithm to rigorously compute the linear response. We…
The use of linear response theory for forced dissipative stochastic dynamical systems through the fluctuation dissipation theorem is an attractive way to study climate change systematically among other applications. Here, a mathematically…
Linear regression on network-linked observations has been an essential tool in modeling the relationship between response and covariates with additional network structures. Previous methods either lack inference tools or rely on restrictive…
Response theory provides a pathway for understanding the sensitivity of a system and for predicting how its statistical properties change when a perturbation is applied. In the case of complex and multiscale systems, to achieve enhanced…
We provide a link between response theory, pullback measures, and optimal fingerprinting method that paves the way for a) predicting the impact of acting forcings on time-dependent systems and b) attributing observed anomalies to acting…
Linear response theory, the backbone of non-equilibrium statistical physics, has recently been extended to explain how and why non-ergodic renewal processes are insensitive to simple perturbations, such as in habituation. It was established…
A central challenge in climate science and applied mathematics is developing data-driven models of multiscale systems that capture both stationary statistics and responses to external perturbations. Current neural climate emulators aim to…
Dynamical systems are often subject to forcing or changes in their governing parameters and it is of interest to study how this affects their statistical properties. A prominent real-life example of this class of problems is the…
We study the impact of stochastic perturbations to deterministic dynamical systems using the formalism of the Ruelle response theory and explore how stochastic noise can be used to explore the properties of the underlying deterministic…
Learning-based control methods typically assume stationary system dynamics, an assumption often violated in real-world systems due to drift, wear, or changing operating conditions. We study reinforcement learning for control under…
Dynamical systems theory has long provided a foundation for understanding evolving phenomena across scientific domains. Yet, the application of this theory to complex real-world systems remains challenging due to issues in mathematical…
In this paper, we propose an adaptive event-triggered reinforcement learning control for continuous-time nonlinear systems, subject to bounded uncertainties, characterized by complex interactions. Specifically, the proposed method is…
The ability of a brain or a neural network to efficiently learn depends crucially on both the task structure and the learning rule. Previous works have analyzed the dynamical equations describing learning in the relatively simplified…
This paper studies satisfaction of temporal properties on unknown stochastic processes that have continuous state spaces. We show how reinforcement learning (RL) can be applied for computing policies that are finite-memory and deterministic…
The prescribed-time stabilization problem for a general class of nonlinear systems with unknown input gain and appended dynamics (with unmeasured state) is addressed. Unlike the asymptotic stabilization problem, the prescribed-time…