Related papers: Identifying Drift, Diffusion, and Causal Structure…
A potent class of generative models known as Diffusion Probabilistic Models (DPMs) has become prominent. A forward diffusion process adds gradually noise to data, while a model learns to gradually denoise. Sampling from pre-trained DPMs is…
Multi-agent trajectory prediction is crucial for various practical applications, spurring the construction of many large-scale trajectory datasets, including vehicles and pedestrians. However, discrepancies exist among datasets due to…
Stochastic differential equation mixed-effects models (SDEMEMs) are flexible hierarchical models that are able to account for random variability inherent in the underlying time-dynamics, as well as the variability between experimental units…
It is shown how Adler's trace dynamics can be applied to stochastic mechanics and other complex classical dynamical systems. Emergent non-commutivity due to the fractal nature of sample trajectories is closely related to the fact that the…
We present a universal framework for simulating $N$-dimensional linear It\^o stochastic differential equations (SDEs) on quantum computers with additive or multiplicative noises. Building on a unitary dilation technique, we establish a…
This article develops a stochastic differential equation (SDE) for modeling the temporal evolution of queue length dynamics at signalized intersections. Inspired by the observed quasiperiodic and self-similar characteristics of the queue…
In this paper, we investigate the convergence rate of the averaging principle for stochastic differential equations (SDEs) with $\beta$-H\"older drift driven by $\alpha$-stable processes. More specifically, we first derive the Schauder…
Graph representations offer powerful and intuitive ways to describe data in a multitude of application domains. Here, we consider stochastic processes generating graphs and propose a methodology for detecting changes in stationarity of such…
The proposed BSDE-based diffusion model represents a novel approach to diffusion modeling, which extends the application of stochastic differential equations (SDEs) in machine learning. Unlike traditional SDE-based diffusion models, our…
Anomalous diffusion and L\'evy flights, which are characterized by the occurrence of random discrete jumps of all scales, have been observed in a plethora of natural and engineered systems, ranging from the motion of molecules to climate…
Recovering continuous-time dynamics from discrete observations is difficult because local supervision (e.g., pointwise regression targets, derivative approximations, or equation residuals) loses fidelity as the observation interval grows.…
We consider the question of estimating the drift and the invariant density for a large class of scalar ergodic diffusion processes, based on continuous observations, in $\sup$-norm loss. The unknown drift $b$ is supposed to belong to a…
Scene graphs (SGs) represent objects and their relationships as structured graphs, enabling applications in image generation, robotics, and 3D understanding. Recent work suggests that conditioning image generation on scene graphs improves…
Mathematically modelling diffusive and advective transport of particles in heterogeneous layered media is important to many applications in computational, biological and medical physics. While deterministic continuum models of such…
We propose a general framework for conditional sampling in PDE-based inverse problems, targeting the recovery of whole solutions from extremely sparse or noisy measurements. This is accomplished by a function-space diffusion model and…
We explore the derivation of distributed parameter system evolution laws (and in particular, partial differential operators and associated partial differential equations, PDEs) from spatiotemporal data. This is, of course, a classical…
We present EDDY (Exact-marginal Diversification via Divergence-free dYnamics), a guidance mechanism for diffusion and flow matching models that promotes diversity among samples generated while maintaining quality. EDDY exploits symmetries…
Diffusion models have become the de facto framework for generating new datasets. The core of these models lies in the ability to reverse a diffusion process in time. The goal of this manuscript is to explain, from a PDE perspective, how…
Forecasting over graph-structured sensor networks demands models that capture both deterministic spatial trends and stochastic variability, while remaining efficient enough for repeated inference as new observations arrive. We propose…
Identifying unknown differential equations from a given set of discrete time dependent data is a challenging problem. A small amount of noise can make the recovery unstable, and nonlinearity and differential equations with varying…