Related papers: Accurate Modeling of Reduced-State Dynamics

We show that the correlation and entanglement dynamics of spin systems can be understood in terms of propagation of spin waves. This gives a simple, physical explanation of the behaviour seen in a number of recent works, in which a…

The study of stochastic systems has received considerable interest over the years. Their dynamics can describe many equilibrium and nonequilibrium fluctuating systems. At the same time, nonequilibrium constraints interact with the time…

The identification of a nonlinear dynamic model is an open topic in control theory, especially from sparse input-output measurements. A fundamental challenge of this problem is that very few to zero prior knowledge is available on both the…

Modelling is an essential procedure in analyzing and controlling a given logical dynamic system (LDS). It has been proved that deterministic LDS can be modeled as a linear-like system using algebraic state space representation. However, due…

A mechanism describing state reduction dynamics in relativistic quantum field theory is outlined. The mechanism involves nonlinear stochastic modifications to the standard description of unitary state evolution and the introduction of a…

We introduce a minimization formulation for the determination of a finite-dimensional, time-dependent, orthonormal basis that captures directions of the phase space associated with transient instabilities. While these instabilities have…

We consider the model reduction problem for linear time-invariant dynamical systems having nonzero (but otherwise indeterminate) initial conditions. Building upon the observation that the full system response is decomposable as a…

The quasi-steady-state approximation (or stochastic averaging principle) is a useful tool in the study of multiscale stochastic systems, giving a practical method by which to reduce the number of degrees of freedom in a model. The method is…

This paper investigates contraction properties of switched dynamical systems for the case that all modes are non-contracting, thereby extending existing results that require at least one mode to be contracting. Leveraging the property that…

The decoupling of spin and density dynamics is a remarkable feature of quantum one-dimensional many-body systems. In a few-body regime, however, little is known about this phenomenon. To address this problem, we study the time evolution of…

Biological evolution of a population is governed by the fitness landscape, which is a map from genotype to fitness. However, a fitness landscape depends on the organisms environment, and evolution in changing environments is still poorly…

The theory of slow manifolds is an important tool in the study of deterministic dynamical systems, giving a practical method by which to reduce the number of relevant degrees of freedom in a model, thereby often resulting in a considerable…

While fields like Artificial Life have made huge strides in quantifying the mechanisms that distinguish living systems from non-living ones, particular mechanisms remain difficult to reproduce in silico. Known as open-endedness, we've been…

Model order reduction in high-dimensional, nonlinear dynamical systems if often enabled through fast-slow timescale separation. One such approach involves identifying a low-dimensional slow manifold to which the state rapidly converges and…

This study investigates the dynamics of alternating minimization applied to a bilinear regression task with normally distributed covariates, under the asymptotic system size limit where the number of parameters and observations diverge at…

Symmetries of the initial state of a quantum system and the quantum channels, which simultaneously affect parts of the system, can significantly simplify the description of the entanglement evolution. Using concurrence as the entanglement…

Biologists and physicists have a rich tradition of modeling living systems with simple models composed of a few interacting components. Despite the remarkable success of this approach, it remains unclear how to use such finely tuned models…

We develop a rigorous theory of external influences on finite discrete dynamical systems, going beyond the perturbation paradigm, in that the external influence need not be a small contribution. Indeed, the covariance condition can be…

Biological systems are modular, and this modularity evolves over time and in different environments. A number of observations have been made of increased modularity in biological systems under increased environmental pressure. We here…

We propose HyperDynamics, a dynamics meta-learning framework that conditions on an agent's interactions with the environment and optionally its visual observations, and generates the parameters of neural dynamics models based on inferred…