Related papers: Oh SnapMMD! Forecasting Stochastic Dynamics Beyond…

Stochastic dynamical systems have emerged as fundamental models across numerous application domains, providing powerful mathematical representations for capturing uncertain system behavior. In this paper, we address the problem of runtime…

Modeling the evolution of system with time-series data is a challenging and critical task in a wide range of fields, especially when the time-series data is regularly sampled and partially observable. Some methods have been proposed to…

Score-based diffusion models are frequently employed as structural priors in inverse problems. However, their iterative denoising process, initiated from Gaussian noise, often results in slow inference speeds. The Image-to-Image…

Multi-step stock index forecasting is vital in finance for informed decision-making. Current forecasting methods on this task frequently produce unsatisfactory results due to the inherent data randomness and instability, thereby…

Scientific machine learning (SciML) increasingly requires models that capture multimodal conditional uncertainty arising from ill-posed inverse problems, multistability, and chaotic dynamics. While recent work has favored highly expressive…

Learning discrete neural samplers is challenging due to the lack of gradients and combinatorial complexity. While stochastic optimal control (SOC) and Schr\"odinger bridge (SB) provide principled solutions, efficient SOC solvers like…

This paper proposes a two-stage framework named ST-PAD for spatio-temporal fluid dynamics modeling in the field of earth sciences, aiming to achieve high-precision simulation and prediction of fluid dynamics through spatio-temporal physics…

The solution of the path structured multimarginal Schr\"{o}dinger bridge problem (MSBP) is the most-likely measure-valued trajectory consistent with a sequence of observed probability measures or distributional snapshots. We leverage recent…

Diffusion models (DMs) have become the dominant paradigm of generative modeling in a variety of domains by learning stochastic processes from noise to data. Recently, diffusion denoising bridge models (DDBMs), a new formulation of…

The ability to make sense of the massive amounts of high-dimensional data generated from molecular dynamics (MD) simulations is heavily dependent on the knowledge of a low dimensional manifold (parameterized by a reaction coordinate or RC)…

Modeling car-following behavior is fundamental to microscopic traffic simulation, yet traditional deterministic models often fail to capture the full extent of variability and unpredictability in human driving. While many modern approaches…

We develop an approach to learn an interpretable semi-parametric model of a latent continuous-time stochastic dynamical system, assuming noisy high-dimensional outputs sampled at uneven times. The dynamics are described by a nonlinear…

The advent of single-cell technology has significantly improved our understanding of cellular states and subpopulations in various tissues under normal and diseased conditions by employing data-driven approaches such as clustering and…

We propose a new financial model, the stochastic volatility model with sticky drawdown and drawup processes (SVSDU model), which enables us to capture the features of winning and losing streaks that are common across financial markets but…

Over the past few years, research on deep graph learning has shifted from static graphs to temporal graphs in response to real-world complex systems that exhibit dynamic behaviors. In practice, temporal graphs are formalized as an ordered…

Capsule network (CapsNet) acts as a promising alternative to the typical convolutional neural network, which is the dominant network to develop the remaining useful life (RUL) estimation models for mechanical equipment. Although CapsNet…

Traffic flow prediction, a critical aspect of intelligent transportation systems, has been increasingly popular in the field of artificial intelligence, driven by the availability of extensive traffic data. The current challenges of traffic…

Time series forecasting remains a central challenge problem in almost all scientific disciplines. We introduce a novel load forecasting method in which observed dynamics are modeled as a forced linear system using Dynamic Mode Decomposition…

Thermodynamics with internal variables is a common approach in continuum mechanics to model inelastic (i.e., non-equilibrium) material behavior. While this approach is computationally and theoretically attractive, it currently lacks a…

Learning network dynamics from the empirical structure and spatio-temporal observation data is crucial to revealing the interaction mechanisms of complex networks in a wide range of domains. However, most existing methods only aim at…