Related papers: Varying-coefficient stochastic differential equati…
Inspired by the ubiquitous use of differential equations to model continuous dynamics across diverse scientific and engineering domains, we propose a novel and intuitive approach to continuous sequence modeling. Our method interprets…
Stochastic partial differential equations (SPDEs) are the mathematical tool of choice for modelling spatiotemporal PDE-dynamics under the influence of randomness. Based on the notion of mild solution of an SPDE, we introduce a novel neural…
We present a method for learning latent stochastic differential equations (SDEs) from high-dimensional time series data. Given a high-dimensional time series generated from a lower dimensional latent unknown It\^o process, the proposed…
Differential equations (DEs) are commonly used to describe dynamic systems evolving in one (ordinary differential equations or ODEs) or in more than one dimensions (partial differential equations or PDEs). In real data applications the…
Increasingly larger data sets of processes in space and time ask for statistical models and methods that can cope with such data. We show that the solution of a stochastic advection-diffusion partial differential equation provides a…
Stochastic differential equations provide a rich class of flexible generative models, capable of describing a wide range of spatio-temporal processes. A host of recent work looks to learn data-representing SDEs, using neural networks and…
The Latent Stochastic Differential Equation (SDE) is a powerful tool for time series and sequence modeling. However, training Latent SDEs typically relies on adjoint sensitivity methods, which depend on simulation and backpropagation…
Non-uniform sampling arises when an experimenter does not have full control over the sampling characteristics of the process under investigation. Moreover, it is introduced intentionally in algorithms such as Bayesian optimization and…
Stochastic differential equations (SDEs) describe dynamical systems where deterministic flows, governed by a drift function, are superimposed with random fluctuations, dictated by a diffusion function. The accurate estimation (or discovery)…
The problem of model selection in the context of a system of stochastic differential equations (SDEs) has not been touched upon in the literature. Indeed, properties of Bayes factors have not been studied even in single SDE based model…
We present a Bayesian non-parametric way of inferring stochastic differential equations for both regression tasks and continuous-time dynamical modelling. The work has high emphasis on the stochastic part of the differential equation, also…
Discovering the underlying relationships among variables from temporal observations has been a longstanding challenge in numerous scientific disciplines, including biology, finance, and climate science. The dynamics of such systems are…
We present a novel deep learning method for estimating time-dependent parameters in Markov processes through discrete sampling. Departing from conventional machine learning, our approach reframes parameter approximation as an optimization…
We propose a novel framework for adaptively learning the time-evolving solutions of stochastic partial differential equations (SPDEs) using score-based diffusion models within a recursive Bayesian inference setting. SPDEs play a central…
We present an algorithm for the efficient sampling of conditional paths of stochastic differential equations (SDEs). While unconditional path sampling of SDEs is straightforward, albeit expensive for high dimensional systems of SDEs,…
Models defined by stochastic differential equations (SDEs) allow for the representation of random variability in dynamical systems. The relevance of this class of models is growing in many applied research areas and is already a standard…
Stochastic mathematical models are essential tools for understanding and predicting complex phenomena. The purpose of this work is to study the exit times of a stochastic dynamical system-specifically, the mean exit time and the…
Recent advances in stochastic differential equations (SDEs) have enabled robust modeling of real-world dynamical processes across diverse domains, such as finance, health, and systems biology. However, parameter estimation for SDEs…
Physical models with uncertain inputs are commonly represented as parametric partial differential equations (PDEs). That is, PDEs with inputs that are expressed as functions of parameters with an associated probability distribution.…
I propose a novel framework that integrates stochastic differential equations (SDEs) with deep generative models to improve uncertainty quantification in machine learning applications involving structured and temporal data. This approach,…