Related papers: Response Theory via Generative Score Modeling
In this review, we scrutinize historical and modern results on the linear response of dynamical systems to external perturbations with a particular emphasis on the celebrated relationship between fluctuations and dissipation expressed by…
These lecture notes introduce the statistical analysis of continuous-time generative models built from Markov dynamics. We begin with the stochastic-calculus foundations of score-based diffusion models, including time reversal, score…
We consider the Fluctuation Dissipation Theorem (FDT) of statistical physics from a mathematical perspective. We formalize the concept of "linear response function" in the general framework of Markov processes. We show that for processes…
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…
Generative diffusion models synthesize new samples by reversing a diffusive process that converts a given data set to generic noise. This is accomplished by training a neural network to match the gradient of the log of the probability…
Using a sensitive statistical test we determine whether or not one can detect the breakdown of linear response given observations of deterministic dynamical systems. A goodness-of-fit statistics is developed for a linear statistical model…
For systems close to equilibrium, the relaxation properties of measurable physical quantities are described by the linear response theory and the fluctuation-dissipation theorem (FDT). Accordingly, the response or the generalized…
Local climate information is crucial for impact assessment and decision-making, yet coarse global climate simulations cannot capture small-scale phenomena. Current statistical downscaling methods infer these phenomena as temporally…
A Response Function Theory and Scattering Theory applicable to the study of physical properties of systems driven arbitrarily away from equilibrium, specialized for dealing with ultrafast processes and in conditions of space resolution…
Generating graph-structured data requires learning the underlying distribution of graphs. Yet, this is a challenging problem, and the previous graph generative methods either fail to capture the permutation-invariance property of graphs or…
We introduce a general formulation of the fluctuation-dissipation relations (FDR) holding also in far-from-equilibrium stochastic dynamics. A great advantage of this version of the FDR is that it does not require the explicit knowledge of…
The fluctuation-dissipation theorem is a cornerstone result in statistical mechanics that can be used to translate the statistics of the free natural variability of a system into information on its forced response to perturbations. By…
Systems that evolve towards a state from which they cannot depart are common in nature. But the fluctuation-dissipation theorem, a fundamental result in statistical mechanics, is mainly restricted to systems near-stationarity. In processes…
Score-based diffusion models are a class of generative models whose dynamics is described by stochastic differential equations that map noise into data. While recent works have started to lay down a theoretical foundation for these models,…
Diffusion models generate high-quality synthetic data. They operate by defining a continuous-time forward process which gradually adds Gaussian noise to data until fully corrupted. The corresponding reverse process progressively "denoises"…
This study investigates the dynamics of Score-based Generative Models (SGMs) by treating the score estimation error as a stochastic source driving the Fokker-Planck equation. Departing from particle-centric SDE analyses, we employ an SPDE…
We propose a probabilistic framework for developing computational models of biological neural systems. In this framework, physiological recordings are viewed as discrete-time partial observations of an underlying continuous-time stochastic…
Many data-driven decision problems are formulated using a nominal distribution estimated from historical data, while performance is ultimately determined by a deployment distribution that may be shifted, context-dependent, partially…
General aspects of the Fluctuation-Dissipation Relation (FDR), and Response Theory are considered. After analyzing the conceptual and historical relevance of fluctuations in statistical mechanics, we illustrate the relation between the…
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…