Related papers: Spectral Properties of Effective Dynamics from Con…

A broad class of systems, including ecological, epidemiological, and sociological ones, are characterized by populations of individuals assigned to specific categories, e.g., a chemical species, an opinion or an epidemic state, that are…

Diffusion models exhibit impressive generative capabilities but are significantly impacted by exposure bias. In this paper, we make a key observation: the energy of predicted noisy samples in the reverse process continuously declines…

An approach to the description of subdynamics inside non-relativistic quantum field theory is presented, in which the notions of relevant observable, time scale and complete positivity of the time evolution are stressed. A scattering theory…

In order to study the stochastic Markov processes conditioned on a specific value of a time-integrated observable, the concept of ensembles of trajectories has been recently used extensively. In this paper, we consider a generic…

This paper introduces a novel method for approximating the dynamics of a large autonomous system projected onto a fixed subspace. The core contribution is a novel recursive algorithm to construct an effective time-dependent generator that…

We investigate entropy production in the small-mass (or overdamped) limit of Langevin-Kramers dynamics. The results generalize previous works to provide a rigorous derivation that covers systems with magnetic field as well as anisotropic…

We analyze the time reversed dynamics of generative diffusion models. If the exact empirical score function is used in a regime of large dimension and exponentially large number of samples, these models are known to undergo transitions…

The effective classical/quantum dynamics of a particle constrained on a closed line embedded in a higher dimensional configuration space is analyzed. By considering explicit examples it is shown how different reduction mechanisms produce…

This note provides a simple derivation of the overdamped approximation for kinetic (or underdamped) equilibrium Langevin dynamics, in cases where certain coefficients depend on the position variable. The equivalent small-mass limit of these…

We point out that the quantum dynamical map of an open quantum system can be generated by an effective Liouville operator. The effective Liouville shows the dynamical breaking of time reversibility. This breaking of reversibility is…

It is well-known that the dynamical spectrum of an ergodic measure dynamical system is related to the diffraction measure of a typical element of the system. This situation includes ergodic subshifts from symbolic dynamics as well as…

Score-based generative modelling (SGM) has proven to be a very effective method for modelling densities on finite-dimensional spaces. In this work we propose to extend this methodology to learn generative models over functional spaces. To…

We consider finite-dimensional many-body quantum systems described by time-independent Hamiltonians and Markovian master equations, and present a systematic method for constructing smaller-dimensional, reduced models that exactly reproduce…

Data-driven models for nonlinear dynamical systems based on approximating the underlying Koopman operator or generator have proven to be successful tools for forecasting, feature learning, state estimation, and control. It has become well…

The internal dynamics of macro-molecular systems is characterized by widely separated time scales, ranging from fraction of ps to ns. In ordinary molecular dynamics simulations, the elementary time step dt used to integrate the equation of…

A reduced chemical scheme involving a small number of variables is often sufficient to account for the deterministic evolution of the concentrations of the main species contributing to a reaction. However its predictions are questionable in…

Leveraging an algebraic approach built on minimal realizations and conditional expectations in quantum probability, we propose a method to reduce the dimension of quantum filters in discrete-time, while maintaining the correct distributions…

We introduce a constructive framework to learn effective Langevin equations from stationary time series. Unlike conventional approaches that require iterative calibration to match target statistics, our construction guarantees the observed…

Complex eigenspectra of transfer and Koopman operators describe rotational motion in dynamical systems. A particularly relevant situation in applications is when the rotation speed depends on the state-space position of the dynamics. We…

Hidden variable graphical models can sometimes imply constraints on the observable distribution that are more complex than simple conditional independence relations. These observable constraints can falsify assumptions of the model that…