Related papers: Data-Driven Dynamic Factor Modeling via Manifold L…

This paper introduces a novel nonparametric method for estimating high-dimensional dynamic covariance matrices with multiple conditioning covariates, leveraging random forests and supported by robust theoretical guarantees. Unlike…

Coherent X-ray scattering (CXS) techniques are capable of interrogating dynamics of nano- to mesoscale materials systems at time scales spanning several orders of magnitude. However, obtaining accurate theoretical descriptions of complex…

Implicit generative models have the capability to learn arbitrary complex data distributions. On the downside, training requires telling apart real data from artificially-generated ones using adversarial discriminators, leading to unstable…

Deep learning is widely applied in computer-aided pathological diagnosis, which alleviates the pathologist workload and provide timely clinical analysis. However, most models generally require large-scale annotated data for training, which…

We introduce an adjoint-based aerodynamic shape optimization framework that integrates a diffusion model trained on existing designs to learn a smooth manifold of aerodynamically viable shapes. This manifold is enforced as an equality…

Event-driven systems in fields such as neuroscience, social networks, and finance often exhibit dynamics influenced by continuously evolving external covariates. Motivated by these applications, we introduce a new class of multivariate…

Regression is an essential and fundamental methodology in statistical analysis. The majority of the literature focuses on linear and nonlinear regression in the context of the Euclidean space. However, regression models in non-Euclidean…

In this work, we develop a scalable approach for a flexible latent factor model for high-dimensional dynamical systems. Each latent factor process has its own correlation and variance parameters, and the orthogonal factor loading matrix can…

Real-world data generation often involves complex inter-dependencies among instances, violating the IID-data hypothesis of standard learning paradigms and posing a challenge for uncovering the geometric structures for learning desired…

Point cloud data are widely used in manufacturing applications for process inspection, modeling, monitoring and optimization. The state-of-art tensor regression techniques have effectively been used for analysis of structured point cloud…

Data augmentation is a key element in training high-dimensional models. In this approach, one synthesizes new observations by applying pre-specified transformations to the original training data; e.g.~new images are formed by rotating old…

We present Manifold Diffusion Fields (MDF), an approach that unlocks learning of diffusion models of data in general non-Euclidean geometries. Leveraging insights from spectral geometry analysis, we define an intrinsic coordinate system on…

Disentangled representation learning (DRL) aims to break down observed data into core intrinsic factors for a profound understanding of the data. In real-world scenarios, manually defining and labeling these factors are non-trivial, making…

Score-based methods, such as diffusion models and Bayesian inverse problems, are often interpreted as learning the data distribution in the low-noise limit ($\sigma \to 0$). In this work, we propose an alternative perspective: their success…

The fractional advection-dispersion equation (FADE) has attracted increased attention from researchers as it provides an accurate description for challenging phenomenas with long-range time memory and spatial interactions, such as the…

Practically, training diffusion models typically requires explicit time conditioning to guide the network through the denoising sampling process. Especially in deterministic methods like DDIM, the absence of time conditioning leads to…

Flow and diffusion models have demonstrated strong performance and training stability across various tasks but lack two critical properties of simulation-based methods: freedom of dimensionality and adaptability to different inference…

Sampling from learned high-dimensional distributions is a foundational computational problem. We introduce U-turn chains: Markov chains obtained by iterating short forward-backward steps of a diffusion model, in which each step proposes a…

In this work, we are interested in structure learning for a set of spatially distributed dynamical systems, where individual subsystems are coupled via latent variables and observed through a filter. We represent this model as a directed…

We present a new approach for constructing data-driven subgrid stress models for large eddy simulation of turbulent flows using anisotropic grids. The key to our approach is a Galilean, rotationally, reflectionally and unit invariant model…