Related papers: Conditional path sampling of stochastic differenti…
A systematic Bayesian framework is developed for physics constrained parameter inference ofstochastic differential equations (SDE) from partial observations. The physical constraints arederived for stochastic climate models but are…
Stochastic sampling methods are arguably the most direct and least intrusive means of incorporating parametric uncertainty into numerical simulations of partial differential equations with random inputs. However, to achieve an overall error…
The reconstruction and inference of stochastic dynamical systems from data is a fundamental task in inverse problems and statistical learning. While surrogate modeling advances computational methods to approximate these dynamics, standard…
We introduce a path sampling method for obtaining statistical properties of an arbitrary stochastic dynamics. The method works by decomposing a trajectory in time, estimating the probability of satisfying a progress constraint, modifying…
We develop an approach to learn an interpretable semi-parametric model of a latent continuous-time stochastic dynamical system, assuming noisy high-dimensional outputs sampled at uneven times. The dynamics are described by a nonlinear…
This paper introduces a drift optimization model of stochastic optimization problems driven by regulated stochastic processes. A broad range of problems across operations research, machine learning, and statistics can be viewed as…
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…
In this article, we introduce a system of stochastic differential equations (SDEs) consisting of time-dependent covariates and consider both fixed and random effects set-ups. We also allow the functional part associated with the drift…
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)…
Timeseries generated from a dynamical source can often be modeled as sample paths of a stochastic differential equation (SDE). The timeseries thus reflects the motion of a particle which flows along the direction provided by a drift /…
Many random processes can be simulated as the output of a deterministic model accepting random inputs. Such a model usually describes a complex mathematical or physical stochastic system and the randomness is introduced in the input…
Dynamical system models with delayed dynamics and small noise arise in a variety of applications in science and engineering. In many applications, stable equilibrium or periodic behavior is critical to a well functioning system. Sufficient…
We introduce a guided stochastic sampling method that augments sampling from diffusion models with physics-based guidance derived from partial differential equation (PDE) residuals and observational constraints, ensuring generated samples…
Sampling from unnormalized multimodal distributions with limited density evaluations remains a fundamental challenge in machine learning and natural sciences. Successful approaches construct a bridge between a tractable reference and the…
In the analysis of stochastic dynamical systems described by stochastic differential equations (SDEs), it is often of interest to analyse the sensitivity of the expected value of a functional of the solution of the SDE with respect to…
This study introduces a training-free conditional diffusion model for learning unknown stochastic differential equations (SDEs) using data. The proposed approach addresses key challenges in computational efficiency and accuracy for modeling…
The problem of drift estimation for the solution $X$ of a stochastic differential equation with L\'evy-type jumps is considered under discrete high-frequency observations with a growing observation window. An efficient and asymptotically…
Neural Stochastic Differential Equations (NSDEs) model the drift and diffusion functions of a stochastic process as neural networks. While NSDEs are known to make accurate predictions, their uncertainty quantification properties have been…
Dynamical systems that are subject to continuous uncertain fluctuations can be modelled using Stochastic Differential Equations (SDEs). Controlling such system results in solving path constrained SDEs. Broadly, these problems fall under the…
Many systems in physics, engineering, and biology exhibit multiscale stochastic dynamics, where low-dimensional slow variables evolve under the influence of high-dimensional fast processes. In practice, observations are often limited to a…