Related papers: Stochastic generative methods for stable and accur…
Differentiable physical simulators are proving to be valuable tools for developing data-driven models for computational fluid dynamics (CFD). In particular, these simulators enable end-to-end training of machine learning (ML) models…
Stable random variables are motivated by the central limit theorem for densities with (potentially) unbounded variance and can be thought of as natural generalizations of the Gaussian distribution to skewed and heavy-tailed phenomenon. In…
We study a multigrid method for solving large linear systems of equations with tensor product structure. Such systems are obtained from stochastic finite element discretization of stochastic partial differential equations such as the…
Score-based generative modeling (SBGM) has achieved state-of-the-art performance in image generation, with the quality of generated images being highly dependent on the design of the forward (diffusion) process. Among these, models based on…
Subgrid parameterizations of mesoscale eddies continue to be in demand for climate simulations. These subgrid parameterizations can be powerfully designed using physics and/or data-driven methods, with uncertainty quantification. For…
A general class of dynamical systems which can be trained to operate in classification and generation modes are introduced. A procedure is proposed to plant asymptotic stationary attractors of the deterministic model. Optimizing the…
We extend the data-assimilation approach of Ling and Lozano-Dur\'an (AIAA 2025-1280) to develop machine-learning-based subgrid-scale stress (SGS) models for large-eddy simulation (LES) that are consistent with the numerical scheme of the…
In this paper, we propose a class of stochastic exponential discrete gradient schemes for SDEs with linear and gradient components in the coefficients. The root mean-square errors of the schemes are analyzed, and the structure-preserving…
Understanding the behavior of stochastic gradient methods is a central problem in modern machine learning. Recent work has highlighted diagonal linear networks as a simplified yet expressive setting for analyzing the optimization and…
We present a theoretical analysis of some popular adaptive Stochastic Gradient Descent (SGD) methods in the small learning rate regime. Using the stochastic modified equations framework introduced by Li et al., we derive effective…
Diffusion-based generative models use stochastic differential equations (SDEs) and their equivalent ordinary differential equations (ODEs) to establish a smooth connection between a complex data distribution and a tractable prior…
We derive high-dimensional scaling limits and fluctuations for the online least-squares Stochastic Gradient Descent (SGD) algorithm by taking the properties of the data generating model explicitly into consideration. Our approach treats the…
In this work we demonstrate that SVD-based model reduction techniques known for ordinary differential equations, such as the proper orthogonal decomposition, can be extended to stochastic differential equations in order to reduce the…
Modeling stochastic differential equations (SDEs) is crucial for understanding complex dynamical systems in various scientific fields. Recent methods often employ neural network-based models, which typically represent SDEs through a…
Chaotic dynamical systems such as turbulent flows are characterized by an exponential divergence of infinitesimal perturbations to initial conditions. Therefore, conventional adjoint/tangent sensitivity analysis methods that are successful…
A challenge in multivariate problems with discrete structures is the inclusion of prior information that may differ in each separate structure. A particular example of this is seismic amplitude versus angle (AVA) inversion to elastic…
We propose a novel Skew Gradient Embedding (SGE) framework for systematically reformulating thermodynamically consistent partial differential equation (PDE) models-capturing both reversible and irreversible processes-as generalized gradient…
Stochastic discriminative EM (sdEM) is an online-EM-type algorithm for discriminative training of probabilistic generative models belonging to the exponential family. In this work, we introduce and justify this algorithm as a stochastic…
In this article we expand and develop the authors' recent proposed methodology for efficient stochastic superparameterization (SP) algorithms for geophysical turbulence. Geophysical turbulence is characterized by significant intermittent…
Neural networks offer highly expressive turbulence closures, yet their complexity obscures the physical mechanisms they aim to model, and their computational cost can limit their tractability. To address these limitations, we introduce a…