相关论文: STRODE: Stochastic Boundary Ordinary Differential …

Parameter estimation for ordinary differential equations (ODEs) plays a fundamental role in the analysis of dynamical systems. Generally lacking closed-form solutions, ODEs are traditionally approximated using deterministic solvers.…

Temporal difference (TD) learning is a foundational algorithm in reinforcement learning (RL). For nearly forty years, TD learning has served as a workhorse for applied RL as well as a building block for more complex and specialized…

We suggest a mechanism based on spike time dependent plasticity (STDP) of synapses to store, retrieve and predict temporal sequences. The mechanism is demonstrated in a model system of simplified integrate-and-fire type neurons densely…

We investigate stochastic averaging theory for locally Lipschitz discrete-time nonlinear systems with stochastic perturbation and its applications to convergence analysis of discrete-time stochastic extremum seeking algorithms. Firstly, by…

Multiscale stochastic dynamical systems have been widely adopted to a variety of scientific and engineering problems due to their capability of depicting complex phenomena in many real world applications. This work is devoted to…

Neural ordinary differential equations (Neural ODEs) is a class of machine learning models that approximate the time derivative of hidden states using a neural network. They are powerful tools for modeling continuous-time dynamical systems,…

We propose a new approach to learning the subgrid-scale model when simulating partial differential equations (PDEs) solved by the method of lines and their representation in chaotic ordinary differential equations, based on neural ordinary…

Most machine learning methods are used as a black box for modelling. We may try to extract some knowledge from physics-based training methods, such as neural ODE (ordinary differential equation). Neural ODE has advantages like a possibly…

Probabilistic ordinary differential equation (ODE) solvers have been introduced over the past decade as uncertainty-aware numerical integrators. They typically proceed by assuming a functional prior to the ODE solution, which is then…

Stochastic differential equations (SDEs) have been widely used to model real world random phenomena. Existing works mainly focus on the case where the time series is modeled by a single SDE, which might be restrictive for modeling time…

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…

A nonintrusive model order reduction method for bilinear stochastic differential equations with additive noise is proposed. A reduced order model (ROM) is designed in order to approximate the statistical properties of high-dimensional…

Clinical time series data from electronic health records and medical registries offer unprecedented opportunities to understand patient trajectories and inform medical decision-making. However, leveraging such data presents significant…

Slow concept drift is a ubiquitous, yet under-studied problem in practical machine learning systems. In such settings, although recent data is more indicative of future data, naively prioritizing recent instances runs the risk of losing…

We study the phenomenon of spatiotemporal stochastic resonance (STSR) in a chain of diffusively coupled bistable oscillators. In particular, we examine the situation in which the \textit{global} STSR response is controlled by a…

In this paper, we study the problem of how to optimally steer the state covariance of a general continuous-time linear stochastic system over a finite time interval subject to additive noise. Optimality here means reaching a target state…

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…

We consider binary infinite order stochastic chains perturbed by a random noise. This means that at each time step, the value assumed by the chain can be randomly and independently flipped with a small fixed probability. We show that the…

This paper proposes the use of spectral element methods \citep{canuto_spectral_1988} for fast and accurate training of Neural Ordinary Differential Equations (ODE-Nets; \citealp{Chen2018NeuralOD}) for system identification. This is achieved…

We consider the problem of continuous-time policy evaluation. This consists in learning through observations the value function associated with an uncontrolled continuous-time stochastic dynamic and a reward function. We propose two…