相关论文: On large time behavior and selection principle for…

We consider a tight-binding Schroedinger equation with time dependent diagonal noise, given as a function of a Markov process. This model was considered previously by Kang and Schenker (J. Stat. Phys., 134(5-6):1005, arXiv:0808.2784), who…

We consider a two-dimensional Hamiltonian system perturbed by a small diffusion term, whose coefficient is state-dependent and non-degenerate. As a result, the process consists of the fast motion along the level curves and slow motion…

We present a new method for detecting superdiffusive behaviour and for determining rates of superdiffusion in time series data. Our method applies equally to stochastic and deterministic time series data (with no prior knowledge required of…

We develop a tensorial constitutive model for dense, shear-thickening particle suspensions subjected to time-dependent flow. Our model combines a recently proposed evolution equation for the suspension microstructure in rate-independent…

The remarkable performance of deep neural networks depends on the availability of massive labeled data. To alleviate the load of data annotation, active deep learning aims to select a minimal set of training points to be labelled which…

Diffusion models have recently shown significant potential in solving decision-making problems, particularly in generating behavior plans -- also known as diffusion planning. While numerous studies have demonstrated the impressive…

The Whittaker 2d growth model is a triangular continuous Markov diffusion process that appears in many scientific contexts. It has been theoretically intriguing to establish a large deviation principle for this 2d process with a scaling…

The drift diffusion model (DDM) is a model of sequential sampling with diffusion (Brownian) signals, where the decision maker accumulates evidence until the process hits a stopping boundary, and then stops and chooses the alternative that…

Large-scale empirical data, the sample size and the dimension are high, often exhibit various characteristics. For example, the noise term follows unknown distributions or the model is very sparse that the number of critical variables is…

In order to characterize the mechanisms governing the diffusion of particles in biological scenarios, it is essential to accurately determine their diffusive properties. To do so, we propose a machine learning method to characterize…

In this paper, a linear model of diffusion processes with unknown drift and diagonal diffusion matrices is discussed. We will consider the estimation problems for unknown parameters based on the discrete time observation in high-dimensional…

Diffusion models are a class of generative models that learn to synthesize samples by inverting a diffusion process that gradually maps data into noise. While these models have enjoyed great success recently, a full theoretical…

Here we study the long time behavior of an advection-diffusion equation with a general time varying (including random) shear flow imposing no-flux boundary conditions on channel walls. We derive the asymptotic approximation of the scalar…

We introduce a novel deep learning approach that harnesses the power of generative artificial intelligence to enhance the accuracy of contextual forecasting in sewerage systems. By developing a diffusion-based model that processes…

Recent progress in Quality Diversity Reinforcement Learning (QD-RL) has enabled learning a collection of behaviorally diverse, high performing policies. However, these methods typically involve storing thousands of policies, which results…

We propose a unifying theoretical framework for the analysis of first-passage time distributions in two important classes of stochastic processes in which the diffusivity of a particle evolves randomly in time. In the first class of…

We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…

Diffusion models have emerged as powerful generative frameworks by progressively adding noise to data through a forward process and then reversing this process to generate realistic samples. While these models have achieved strong…

Constrained policy search (CPS) is a fundamental problem in offline reinforcement learning, which is generally solved by advantage weighted regression (AWR). However, previous methods may still encounter out-of-distribution actions due to…

To make decisions organisms often accumulate information across multiple timescales. However, most experimental and modeling studies of decision-making focus on sequences of independent trials. On the other hand, natural environments are…