Related papers: Diffusion bridge with misspecification: theory con…
Since diffusion processes arise in so many different fields, efficient tech-nics for the simulation of sample paths, like discretization schemes, represent crucial tools in applied probability. Such methods permit to obtain approximations…
Following some recent works, we investigate the problem of optimising the total population size for logistic diffusive models with respect to resources distributions. Using the spatially heterogeneous Fisher-KPP equation, we obtain a…
We study the asymptotic theory of misspecified models for diffusion processes with noisy nonsynchronous observations. Unlike with correctly specified models, the original maximum-likelihood-type estimator has an asymptotic bias under the…
Transition phenomena between metastable states play an important role in complex systems due to noisy fluctuations. In this paper, the physics informed neural networks (PINNs) are presented to compute the most probable transition pathway.…
The use of stochastic differential equations in multi-objective optimization has been limited, in practice, by two persistent gaps: incomplete stability analyses and the absence of accessible implementations. We revisit a drift--diffusion…
We study the limit behaviour of upper and lower bounds on expected time averages in imprecise Markov chains; a generalised type of Markov chain where the local dynamics, traditionally characterised by transition probabilities, are now…
Diffusion-based robot navigation policies trained on large-scale imitation learning datasets, can generate multi-modal trajectories directly from the robot's visual observations, bypassing the traditional localization-mapping-planning…
The buildings and construction sector is a significant source of greenhouse gas emissions, with cement production alone contributing 7~\% of global emissions and the industry as a whole accounting for approximately 37~\%. Reducing emissions…
A variety of researchers have successfully obtained the parameters of low dimensional diffusion models using the data that comes out of atomistic simulations. This naturally raises a variety of questions about efficient estimation,…
Climate change is intensifying rainfall extremes, making high-resolution precipitation projections crucial for society to better prepare for impacts such as flooding. However, current Global Climate Models (GCMs) operate at spatial…
We provide examples of initial data which saturate the enhanced diffusion rates proved for general shear flows which are H\"{o}lder regular or Lipschitz continuous with critical points, and for regular circular flows, establishing the…
In this work it is shown how the immersed boundary method of (Peskin2002) for modeling flexible structures immersed in a fluid can be extended to include thermal fluctuations. A stochastic numerical method is proposed which deals with…
We derive a new theoretical interpretation of the reweighted losses that are widely used for training diffusion models. Our method is based on constructing a cascade of time-dependent variational lower bounds on the data log-likelihood,…
We propose a unified diffusion model-based correction and super-resolution method to enhance the fidelity and resolution of diverse low-quality data through a two-step pipeline. First, the correction step employs a novel enhanced stochastic…
Adaptive dynamical systems arise in a multitude of contexts, e.g., optimization, control, communications, signal processing, and machine learning. A precise characterization of their fundamental limitations is therefore of paramount…
In this article we consider a family of real-valued diffusion processes on the time interval $[0,1]$ indexed by their prescribed initial value $x \in \mathbb{R}$ and another point in space, $y \in \mathbb{R}$. We first present an…
Flow matching (FM) learns vector fields by regressing stochastic velocity targets along intermediate distributions $p_t$. We identify a geometric optimization bottleneck in this regression problem: when the covariance $\Sigma_t$ of $p_t$ is…
Many core problems in robotics can be framed as constrained optimization problems. Often on these problems, the robotic system has uncertainty, or it would be advantageous to identify multiple high quality feasible solutions. To enable…
In this study, we develop a stochastic optimal control approach with reinforcement learning structure to learn the unknown parameters appeared in the drift and diffusion terms of the stochastic differential equation. By choosing an…
Diffusion models have achieved remarkable success in generative modeling. Despite more stable training, the loss of diffusion models is not indicative of absolute data-fitting quality, since its optimal value is typically not zero but…