相关论文: Neural Lagrangian Schr\"odinger Bridge: Diffusion …
Population dynamics in fields such as molecular biology, epidemiology, and ecology exhibit highly stochastic and non-linear behaviour. In gene regulatory systems in particular, oscillations and multi-stability are especially common. Despite…
Solving statistical learning problems often involves nonconvex optimization. Despite the empirical success of nonconvex statistical optimization methods, their global dynamics, especially convergence to the desirable local minima, remain…
We study a semimartingale optimal transport problem interpolating between the Schr\"odinger bridge and the stretched Brownian motion associated with the Bass solution of the Skorokhod embedding problem. The cost combines an entropy term on…
The metapopulation framework is adopted in a wide array of disciplines to describe systems of well separated yet connected subpopulations. The subgroups or patches are often represented as nodes in a network whose links represent the…
We present a stochastic method for reconstructing missing spatial and velocity data along the trajectories of small objects passively advected by turbulent flows with a wide range of temporal or spatial scales, such as small balloons in the…
The Schr\"odinger bridge problem (SBP) aims at finding the measure $\hat{\mathbf{P}}$ on a certain path space which possesses the desired state-space distributions $\rho_0$ at time $0$ and $\rho_T$ at time $T$ while minimizing the KL…
Flow matching and diffusion bridge models have emerged as leading paradigms in generative speech enhancement, modeling stochastic processes between paired noisy and clean speech signals based on principles such as flow matching, score…
Diffusion models have risen to prominence in time series forecasting, showcasing their robust capability to model complex data distributions. However, their effectiveness in deterministic predictions is often constrained by instability…
The subject of this work has its roots in the so called Schroedginer Bridge Problem (SBP) which asks for the most likely distribution of Brownian particles in their passage between observed empirical marginal distributions at two distinct…
This paper presents a formulation of the reactive dynamic user equilibrium problem in continuum form using a network-level Macroscopic Fundamental Diagram (MFD). Compared to existing continuum models for cities -- all based in Hughes'…
Stochastic reduced-order models are widely used to represent the effective dynamics of complex systems, but estimating their drift and diffusion coefficients from data remains challenging. Standard approaches often rely on short-time…
Modeling how network-level traffic flow changes in the urban environment is useful for decision-making in transportation, public safety and urban planning. The traffic flow system can be viewed as a dynamic process that transits between…
We show that the minimum effort control of colloidal self-assembly can be naturally formulated in the order-parameter space as a generalized Schr\"{o}dinger bridge problem -- a class of fixed-horizon stochastic optimal control problems that…
Stochastically evolving geometric systems are studied in shape analysis and computational anatomy for modelling random evolutions of human organ shapes. The notion of geodesic paths between shapes is central to shape analysis and has a…
1. The utilisation distribution describes the relative probability of use of a spatial unit by an animal. It is natural to think of it as the long-term consequence of the animal's short-term movement decisions: it is the accumulation of…
Sampling from a distribution $p(x) \propto e^{-\mathcal{E}(x)}$ known up to a normalising constant is an important and challenging problem in statistics. Recent years have seen the rise of a new family of amortised sampling algorithms,…
Demographic (shot) noise in population dynamics scales with the square root of the population size. This process is very important, as it yields an absorbing state at zero field, but simulating it, especially on spatial domains, is a…
For a fixed flow-based generative model under a small inference budget, sample quality can depend strongly on where the sampler spends its few function evaluations. Flow matching and Schr\"odinger bridges define probability paths, yet their…
The Lambert problem originated in orbital mechanics. It concerns with determining the initial velocity for a boundary value problem involving the dynamical constraint due to gravitational potential with additional time horizon and endpoint…
Trajectory inference seeks to recover the temporal dynamics of a population from snapshots of its (uncoupled) temporal marginals, i.e. where observed particles are not tracked over time. Prior works addressed this challenging problem under…