Related papers: Stochastic generative methods for stable and accur…
Sampling the phase space of molecular systems -- and, more generally, of complex systems effectively modeled by stochastic differential equations -- is a crucial modeling step in many fields, from protein folding to materials discovery.…
We study classical stochastic systems with discrete states, coupled to switching external environments. For fast environmental processes we derive reduced dynamics for the system itself, focusing on corrections to the adiabatic limit of…
An important class of spatio-temporal models is constructed by leveraging the hierarchical structure of dynamical (or, state-space) models. This paper proposes a new statistical dynamical model for spatio-temporal processes motivated by…
In this article we discuss several aspects of the stochastic dynamics of spin models. The paper has two independent parts. Firstly, we explore a few properties of the multi-point correlations and responses of generic systems evolving in…
Data-driven reduced order modeling of chaotic dynamics can result in systems that either dissipate or diverge catastrophically. Leveraging non-linear dimensionality reduction of autoencoders and the freedom of non-linear operator inference…
Stochastic methods are a crucial area in contemporary climate research and are increasingly being used in comprehensive weather and climate prediction models as well as reduced order climate models. Stochastic methods are used as…
Multiscale dynamics are frequently present in real-world processes, such as the atmosphere-ocean and climate science. Because of time scale separation between a small set of slowly evolving variables and much larger set of rapidly changing…
Stochastic linear modelling proposed in Tissot, M\'emin & Cavalieri (J. Fluid Mech., vol. 912, 2021, A51) is based on classical conservation laws subject to a stochastic transport. Once linearised around the mean flow and expressed in the…
Complex chaotic dynamics, seen in natural and industrial systems like turbulent flows and weather patterns, often span vast spatial domains with interactions across scales. Accurately capturing these features requires a high-dimensional…
In this work, we establish a direct connection between generative diffusion models (DMs) and stochastic quantization (SQ). The DM is realized by approximating the reversal of a stochastic process dictated by the Langevin equation,…
Contemporary electricity distribution systems are being challenged by the variability of renewable energy sources. Slow response times and long energy management periods cannot efficiently integrate intermittent renewable generation and…
We propose a method for quantifying uncertainty in high-dimensional PDE systems with random parameters, where the number of solution evaluations is small. Parametric PDE solutions are often approximated using a spectral decomposition based…
A surrogate model that accurately predicts distribution system voltages is crucial for reliable smart grid planning and operation. This letter proposes a fixed-point data-driven surrogate modeling method that employs a limited dataset to…
We present a novel generative modeling method called diffusion normalizing flow based on stochastic differential equations (SDEs). The algorithm consists of two neural SDEs: a forward SDE that gradually adds noise to the data to transform…
Stochastic gradient descent (SGD) is a key ingredient in the training of deep neural networks and yet its geometrical significance appears elusive. We study a deterministic model in which the trajectories of our dynamical systems are…
Score-based modeling through stochastic differential equations (SDEs) has provided a new perspective on diffusion models, and demonstrated superior performance on continuous data. However, the gradient of the log-likelihood function, i.e.,…
Learning continuous-time stochastic dynamics is a fundamental and essential problem in modeling sporadic time series, whose observations are irregular and sparse in both time and dimension. For a given system whose latent states and…
Stochastic unit commitment models typically handle uncertainties in forecast demand by considering a finite number of realizations from a stochastic process model for loads. Accurate evaluations of expectations or higher moments for the…
Stochastic differential equations (SDEs) and stochastic partial differential equations (SPDEs) are fundamental for modeling stochastic dynamics across the natural sciences and modern machine learning. Learning their solution operators with…
Stochastic convex optimization algorithms are the most popular way to train machine learning models on large-scale data. Scaling up the training process of these models is crucial, but the most popular algorithm, Stochastic Gradient Descent…