Related papers: Neural delay differential equations: learning non-…

Many physical systems are described by nonlinear differential equations that are too complicated to solve in full. A natural way to proceed is to divide the variables into those that are of direct interest and those that are not, formulate…

This work introduces a non-intrusive model reduction approach for learning reduced models from partially observed state trajectories of high-dimensional dynamical systems. The proposed approach compensates for the loss of information due to…

Latent neural stochastic differential equations (SDEs) have recently emerged as a promising approach for learning generative models from stochastic time series data. However, they systematically underestimate the noise level inherent in…

Stochastic differential equations (SDEs) are one of the most important representations of dynamical systems. They are notable for the ability to include a deterministic component of the system and a stochastic one to represent random…

We propose a method to reproduce dynamic appearance textures with space-stationary but time-varying visual statistics. While most previous work decomposes dynamic textures into static appearance and motion, we focus on dynamic appearance…

Neural networks inspired by differential equations have proliferated for the past several years. Neural ordinary differential equations (NODEs) and neural controlled differential equations (NCDEs) are two representative examples of them. In…

Unveiling the underlying governing equations of nonlinear dynamic systems remains a significant challenge. Insufficient prior knowledge hinders the determination of an accurate candidate library, while noisy observations lead to imprecise…

The complexity of real-world geophysical systems is often compounded by the fact that the observed measurements depend on hidden variables. These latent variables include unresolved small scales and/or rapidly evolving processes, partially…

Neural differential equations offer a powerful approach for learning dynamics from data. However, they do not impose known constraints that should be obeyed by the learned model. It is well-known that enforcing constraints in surrogate…

One important problem in constructing the reduced dynamics of molecular systems is the accurate modeling of the non-Markovian behavior arising from the dynamics of unresolved variables. The main complication emerges from the lack of scale…

We introduce Neural Dynamical Systems (NDS), a method of learning dynamical models in various gray-box settings which incorporates prior knowledge in the form of systems of ordinary differential equations. NDS uses neural networks to…

We extend the methodology in [Yang et al., 2023] to learn autonomous continuous-time dynamical systems from invariant measures. The highlight of our approach is to reformulate the inverse problem of learning ODEs or SDEs from data as a…

Time series modeling and analysis have become critical in various domains. Conventional methods such as RNNs and Transformers, while effective for discrete-time and regularly sampled data, face significant challenges in capturing the…

This study examines the challenges of modeling complex and noisy data related to socioeconomic factors over time, with a focus on data from various districts in Odisha, India. Traditional time-series models struggle to capture both trends…

Non-Markovianity may significantly speed up quantum dynamics when the system interacts strongly with an infinite large reservoir, of which the coupling spectrum should be fine-tuned. The potential benefits are evident in many dynamics…

A central challenge in data-driven model discovery is the presence of hidden, or latent, variables that are not directly measured but are dynamically important. Takens' theorem provides conditions for when it is possible to augment these…

This article proposes for stochastic partial differential equations (SPDEs) driven by additive noise, a novel approach for the approximate parameterizations of the ``small'' scales by the ``large'' ones, along with the derivaton of the…

This paper has two interrelated foci: (i) obtaining stable and efficient data-driven closure models by using a multivariate time series of partial observations from a large-dimensional system; and (ii) comparing these closure models with…

We describe a method to model nonlinear dynamical systems using periodic solutions of delay-differential equations. We show that any finite-time trajectory of a nonlinear dynamical system can be loaded approximately into the initial…

This work presents a hybrid modeling approach to data-driven learning and representation of unknown physical processes and closure parameterizations. These hybrid models are suitable for situations where the mechanistic description of…