Related papers: Learning Deep Hidden Nonlinear Dynamics from Aggre…

This paper addresses the problem of decentralized learning to achieve a high-performance global model by asking a group of clients to share local models pre-trained with their own data resources. We are particularly interested in a specific…

When the dynamical data of a system only convey dynamic information over a limited operating range, the identification of models with good performance over a wider operating range is very unlikely. Nevertheless, models with such…

We propose a methodology that combines generative latent diffusion models with physics-informed machine learning to generate solutions of parametric partial differential equations (PDEs) conditioned on partial observations, which includes,…

Efficiently and reliably estimating uncertainty is an important objective in deep learning. It is especially pertinent to autoregressive sequence tasks, where training and inference costs are typically very high. However, existing research…

This paper aims to conduct a comprehensive theoretical analysis of current diffusion models. We introduce a novel generative learning methodology utilizing the Schr{\"o}dinger bridge diffusion model in latent space as the framework for…

Model reduction of high-dimensional dynamical systems alleviates computational burdens faced in various tasks from design optimization to model predictive control. One popular model reduction approach is based on projecting the governing…

Diffusion models typically generate data through a fixed denoising trajectory that is shared across all samples. However, generation targets can differ in complexity, suggesting that a single pre-defined diffusion process may not be optimal…

Generating high-quality synthetic time series is a fundamental yet challenging task across domains such as forecasting and anomaly detection, where real data can be scarce, noisy, or costly to collect. Unlike static data generation,…

Deep latent variable models learn condensed representations of data that, hopefully, reflect the inner workings of the studied phenomena. Unfortunately, these latent representations are not statistically identifiable, meaning they cannot be…

Nonequilibrium statistical mechanics exhibit a variety of complex phenomena far from equilibrium. It inherits challenges of equilibrium, including accurately describing the joint distribution of a large number of configurations, and also…

We introduce DeepMoD, a Deep learning based Model Discovery algorithm. DeepMoD discovers the partial differential equation underlying a spatio-temporal data set using sparse regression on a library of possible functions and their…

Various Graph Neural Networks (GNNs) have been successful in analyzing data in non-Euclidean spaces, however, they have limitations such as oversmoothing, i.e., information becomes excessively averaged as the number of hidden layers…

We present a data-driven pipeline for model building that combines interpretable machine learning, hydrodynamic theories, and microscopic models. The goal is to uncover the underlying processes governing nonlinear dynamics experiments. We…

We investigate the emergence of non-linear diffusivity in kinetically constrained, one-dimensional symmetric exclusion processes satisfying the gradient condition. Recent developments introduced new gradient dynamics based on the Bernstein…

Understanding the dynamics of neural networks in different width regimes is crucial for improving their training and performance. We present an exact solution for the learning dynamics of a one-hidden-layer linear network, with…

This paper proposes a new theoretical lens to view Wasserstein generative adversarial networks (WGANs). To minimize the Wasserstein-1 distance between the true data distribution and our estimate of it, we derive a distribution-dependent…

We consider the problem of forecasting complex, nonlinear space-time processes when observations provide only partial information of on the system's state. We propose a natural data-driven framework, where the system's dynamics are modelled…

The commonly used latent space embedding techniques, such as Principal Component Analysis, Factor Analysis, and manifold learning techniques, are typically used for learning effective representations of homogeneous data. However, they do…

Access to complete data in large-scale networks is often infeasible. Therefore, the problem of missing data is a crucial and unavoidable issue in the analysis and modeling of real-world social networks. However, most of the research on…

Learning interpretable representations of neural dynamics at a population level is a crucial first step to understanding how observed neural activity relates to perception and behavior. Models of neural dynamics often focus on either…