Related papers: Rough flows
We investigate stochastic interpolation, a recently introduced framework for high dimensional sampling which bears many similarities to diffusion modeling. Stochastic interpolation generates a data sample by first randomly initializing a…
The Intelligent Driver Model (IDM), proposed in 2000, has become a foundational tool in traffic flow modeling, renowned for its simplicity, computational efficiency, and ability to capture diverse traffic dynamics. Over the past 25 years,…
We examine a Wong-Zakai type approximation of a family of stochastic differential equations driven by a general cadlag semimartingale. For such an approximation, compared with the pointwise convergence result by Kurtz, Pardoux and Protter…
In this paper we prove the strong averaging principle for a slow-fast system of rough differential equations. The slow and the fast component of the system are driven by a rather general random rough path and Brownian rough path,…
This paper aims to predict the traffic flow at one road segment based on nearby traffic volume and weather conditions. Our team also discover the impact of weather conditions and nearby traffic volume on the traffic flow at a target point.…
We introduce a family of stochastic models motivated by the study of nonequilibrium steady states of fluid equations. These models decompose the deterministic dynamics of interest into fundamental building blocks, i.e., minimal vector…
We investigate a family of approximate multi-step proximal point methods, framed as implicit linear discretizations of gradient flow. The resulting methods are multi-step proximal point methods, with similar computational cost in each…
We propose a quasi-Grassmannian gradient flow model for eigenvalue problems of linear operators, aiming to efficiently address many eigenpairs. Our model inherently ensures asymptotic orthogonality: without the need for initial…
Existence and uniqueness for rough flows, transport and continuity equations driven by general geometric rough paths are established.
"Consider the [turbidity] current as ... a river" R. A. Bagnold (1962); the foundation of contemporary deep marine sedimentology. Gravity currents, such as sediment-laden turbidity currents, are ubiquitous natural flows that are driven by a…
We introduce a differential structure for the space of weakly geometric p rough paths over a Banach space V for 2<p<3. We begin by considering a certain natural family of smooth rough paths and differentiating in the truncated tensor…
We propose a physics-constrained machine learning method-based on reservoir computing- to time-accurately predict extreme events and long-term velocity statistics in a model of turbulent shear flow. The method leverages the strengths of two…
Shallow flow or thin liquid film models are used for a wide range of physical and engineering problems. Shallow flow models allow capturing the free surface of the fluid with little effort and reducing the three-dimensional problem to a…
We consider again the fast-slow motions setups in the continuous time $\frac {dX_N(t)}{dt}=N^{1/2} \sig(X_N(t))(\xi(tN))+b(X_N(t)),\, t\in [0,T]$ and the discrete time $X_N((n+1)/N)=X_N(n/N)+N^{-1/2}\sig(X_N(n/N))\xi(n)+N^{-1}b(X_N(n/N)),\,…
We show how the theory of stochastic flows allows to recover in an elementary way a well known result of Warren on the sticky Brownian motion equation.
We use persistent homology to build a quantitative understanding of large complex systems that are driven far-from-equilibrium; in particular, we analyze image time series of flow field patterns from numerical simulations of two important…
Many problems in machine learning can be formulated as solving entropy-regularized optimal transport on the space of probability measures. The canonical approach involves the Sinkhorn iterates, renowned for their rich mathematical…
Spontaneous stochasticity is a modern paradigm for turbulent transport at infinite Reynolds numbers. It suggests that tracer particles advected by rough turbulent flows and subject to additional thermal noise, remain non-deterministic in…
A new paradigm recently emerged in financial modelling: rough (stochastic) volatility, first observed by Gatheral et al. in high-frequency data, subsequently derived within market microstructure models, also turned out to capture…
In this paper, we investigate reflected backward stochastic differential equations driven by rough paths (rough RBSDEs), which can be viewed as probabilistic representations of nonlinear rough partial differential equations (rough PDEs) or…