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We propose a framework for probabilistic forecasting of dynamical systems based on generative modeling. Given observations of the system state over time, we formulate the forecasting problem as sampling from the conditional distribution of…
Normalizing flows have shown great success as general-purpose density estimators. However, many real world applications require the use of domain-specific knowledge, which normalizing flows cannot readily incorporate. We propose…
Diffusion reconstruction plays a critical role in various applications such as image editing, restoration, and style transfer. In theory, the reconstruction should be simple - it just inverts and regenerates images by numerically solving…
Flow matching (FM) constructs continuous-time ODE samplers by prescribing probability paths between a base distribution and a target distribution. In this note, we study FM through the lens of finite-sample plug-in estimation. In addition…
Diffusion models have recently attained significant interest within the community owing to their strong performance as generative models. Furthermore, its application to inverse problems have demonstrated state-of-the-art performance.…
Statistical Inference is the process of determining a probability distribution over the space of parameters of a model given a data set. As more data becomes available this probability distribution becomes updated via the application of…
We propose a new Neural Galerkin Normalizing Flow framework to approximate the transition probability density function of a diffusion process by solving the corresponding Fokker-Planck equation with an atomic initial distribution,…
Optofluidic force induction (OF2i) is an optical nanoparticle characterization scheme which achieves real-time optical counting with single-particle sensitivity and high throughput. In a recent paper [\v{S}imi\'c et al., Phys. Rev. Appl.…
Score-based diffusion models currently constitute the state of the art in continuous generative modeling. These methods are typically formulated via overdamped or underdamped Ornstein--Uhlenbeck-type stochastic differential equations, in…
Fluctuations and noise may alter the behavior of dynamical systems considerably. For example, oscillations may be sustained by demographic fluctuations in biological systems where a stable fixed point is found in the absence of noise. We…
Switching dynamical systems provide a powerful, interpretable modeling framework for inference in time-series data in, e.g., the natural sciences or engineering applications. Since many areas, such as biology or discrete-event systems, are…
We introduce DeepFHT, a survival-analysis framework that couples deep neural networks with first hitting time (FHT) distributions from stochastic process theory. Time to event is represented as the first passage of a latent diffusion…
Topology inference is a powerful tool to better understand the behaviours of network systems (NSs). Different from most of prior works, this paper is dedicated to inferring the directed topology of NSs from noisy observations, where the…
We introduce \textit{OneFlowSBI}, a unified framework for simulation-based inference that learns a single flow-matching generative model over the joint distribution of parameters and observations. Leveraging a query-aware masking…
We survey continuous-time generative modeling methods based on transporting a simple reference distribution to a data distribution via stochastic or deterministic dynamics. We present a unified framework in which diffusion models,…
The proliferation of computing devices has brought about an opportunity to deploy machine learning models on new problem domains using previously inaccessible data. Traditional algorithms for training such models often require data to be…
The Schr\"odinger bridge problem is concerned with finding a stochastic dynamical system bridging two marginal distributions that minimises a certain transportation cost. This problem, which represents a generalisation of optimal transport…
In this work, we study the class of stochastic process that generalizes the Ornstein-Uhlenbeck processes, hereafter called by \emph{Generalized Ornstein-Uhlenbeck Type Process} and denoted by GOU type process. We consider them driven by the…
Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction-diffusion processes are widely used to model such behaviour in disciplines ranging from biology to…
The statistical problem of parameter estimation in partially observed hypoelliptic diffusion processes is naturally occurring in many applications. However, due to the noise structure, where the noise components of the different coordinates…