Related papers: Generative Learning for Slow Manifolds and Bifurca…

How do score-based generative models (SBMs) learn the data distribution supported on a low-dimensional manifold? We investigate the score model of a trained SBM through its linear approximations and subspaces spanned by local feature…

When analyzing parametric statistical models, a useful approach consists in modeling geometrically the parameter space. However, even for very simple and commonly used hierarchical models like statistical mixtures or stochastic deep neural…

Deep Generative Machine Learning Models (DGMs) have been growing in popularity across the design community thanks to their ability to learn and mimic complex data distributions. DGMs are conventionally trained to minimize statistical…

Continuum mechanics simulators, numerically solving one or more partial differential equations, are essential tools in many areas of science and engineering, but their performance often limits application in practice. Recent modern machine…

Dynamical systems are used to model a variety of phenomena in which the bifurcation structure is a fundamental characteristic. Here we propose a statistical machine-learning approach to derive lowdimensional models that automatically…

We propose a deep generative Markov State Model (DeepGenMSM) learning framework for inference of metastable dynamical systems and prediction of trajectories. After unsupervised training on time series data, the model contains (i) a…

We consider the problem of learning a conditional Gaussian graphical model in the presence of latent variables. Building on recent advances in this field, we suggest a method that decomposes the parameters of a conditional Markov random…

We propose a latent score-based generative AI framework for learning stochastic, non-local closure models and constitutive laws in nonlinear dynamical systems of computational mechanics. This work addresses a key challenge of modeling…

This paper introduces a new probabilistic framework for supervised learning in neural systems. It is designed to model complex, uncertain systems whose random outputs are strongly non-Gaussian given deterministic inputs. The architecture…

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…

The generation of discontinuous distributions is a difficult task for most known frameworks such as generative autoencoders and generative adversarial networks. Generative non-invertible models are unable to accurately generate such…

Developing suitable approximate models for analyzing and simulating complex nonlinear systems is practically important. This paper aims at exploring the skill of a rich class of nonlinear stochastic models, known as the conditional Gaussian…

The increasing availability and accessibility of numerous overhead images allows us to estimate and assess the spatial arrangement of groups of geospatial target objects, which can benefit many applications, such as traffic monitoring and…

Estimation of parameters in differential equation models can be achieved by applying learning algorithms to quantitative time-series data. However, sometimes it is only possible to measure qualitative changes of a system in response to a…

Training generative models that capture rich semantics of the data and interpreting the latent representations encoded by such models are very important problems in un-/self-supervised learning. In this work, we provide a simple algorithm…

Increasing effort is put into the development of methods for learning mechanistic models from data. This task entails not only the accurate estimation of parameters but also a suitable model structure. Recent work on the discovery of…

Generative models have recently emerged as powerful surrogates for physical systems, demonstrating increased accuracy, stability, and/or statistical fidelity. Most approaches rely on iteratively denoising a Gaussian, a choice that may not…

We explore a data-driven approach for learning to optimize neural networks. We construct a dataset of neural network checkpoints and train a generative model on the parameters. In particular, our model is a conditional diffusion transformer…

Due to a huge volume of information in many domains, the need for classification methods is imperious. In spite of many advances, most of the approaches require a large amount of labeled data, which is often not available, due to costs 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…