Related papers: Identifying Stochastic Dynamics from Non-Sequentia…

We consider the problem of designing a data-driven nonlinear state estimation (DANSE) method that uses (noisy) nonlinear measurements of a process whose underlying state transition model (STM) is unknown. Such a process is referred to as a…

We study nonlinear regression of real valued data in an individual sequence manner, where we provide results that are guaranteed to hold without any statistical assumptions. We address the convergence and undertraining issues of…

In this paper, we propose Stoch-IDENT, a novel framework for identifying stochastic partial differential equations (SPDEs) from observational data. Our method can handle linear and nonlinear high-order SPDEs driven by time-dependent Wiener…

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…

A large variety of dynamical systems, such as chemical and biomolecular systems, can be seen as networks of nonlinear entities. Prediction, control, and identification of such nonlinear networks require knowledge of the state of the system.…

Physics-informed neural networks have emerged as a powerful tool in the scientific machine learning community, with applications to both forward and inverse problems. While they have shown considerable empirical success, significant…

In this study, we introduce a sensitivity analysis methodology for stochastic systems in chemistry, where dynamics are often governed by random processes. Our approach is based on gradient estimation via finite differences, averaging…

Unsteady fluid systems are nonlinear high-dimensional dynamical systems that may exhibit multiple complex phenomena both in time and space. Reduced Order Modeling (ROM) of fluid flows has been an active research topic in the recent decade…

Temporal variations in biological systems and more generally in natural sciences are typically modelled as a set of Ordinary, Partial, or Stochastic Differential or Difference Equations. Algorithms for learning the structure and the…

Modeling and identification of high-dimensional stochastic processes is ubiquitous in many fields. In particular, there is a growing interest in modeling stochastic processes with simple and interpretable structures. In many applications,…

We present a data-driven approach to characterizing nonidentifiability of a model's parameters and illustrate it through dynamic as well as steady kinetic models. By employing Diffusion Maps and their extensions, we discover the minimal…

Inspired by the modeling of grain growth in polycrystalline materials, we consider a nonlinear Fokker-Plank model, with inhomogeneous diffusion and with variable mobility parameters. We develop large time asymptotic analysis of such…

Continuous diffusion is a natural framework for non-autoregressive generation but has generally lagged behind masked discrete diffusion models (MDMs) on discrete sequence generation. We argue that the bottleneck is not continuity itself,…

Continuous diffusion is a natural framework for non-autoregressive generation but has generally lagged behind masked discrete diffusion models (MDMs) on discrete sequence generation. We argue that the bottleneck is not continuity itself,…

We study the identification and estimation of structural parameters in dynamic panel data logit models where decisions are forward-looking and the joint distribution of unobserved heterogeneity and observable state variables is…

Structural resonance involves the absorption of inertial loads by a tuned structural elasticity: a process playing a key role in a wide range of biological and technological systems, including many biological and bio-inspired locomotion…

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…

The existence and characterisation of noise-driven bifurcations from the spatially homogeneous stationary states of a nonlinear, non-local Fokker--Planck type partial differential equation describing stochastic neural fields is established.…

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…

Nonlinear dynamic models are widely used for characterizing functional forms of processes that govern complex biological pathway systems. Over the past decade, validation and further development of these models became possible due to data…