Related papers: Quantifying Uncertainty with a Derivative Tracking…

We extend the methodology in [Yang et al., 2023] to learn autonomous continuous-time dynamical systems from invariant measures. The highlight of our approach is to reformulate the inverse problem of learning ODEs or SDEs from data as a…

The real-time fault monitoring and control of the Vacuum Assisted Resin Transfer Moulding (VARTM) production process requires a knowledge of the position of the epoxy flow-front inside the mould. Therefore, a fast and accurate flow-front…

We propose a framework employing stochastic differential equations to facilitate the long-term stability analysis of power grids with intermittent wind power generations. This framework takes into account the discrete dynamics which play a…

This study investigates the dynamics of Score-based Generative Models (SGMs) by treating the score estimation error as a stochastic source driving the Fokker-Planck equation. Departing from particle-centric SDE analyses, we employ an SPDE…

In this work, we explore modeling change points in time-series data using neural stochastic differential equations (neural SDEs). We propose a novel model formulation and training procedure based on the variational autoencoder (VAE)…

We propose a new numerical method for one dimensional stochastic differential equations (SDEs). The main idea of this method is based on a representation of a weak solution of a SDE with a time changed Brownian motion, dated back to Doeblin…

With more renewable energy sources (RES) integrated into the power system, the intermittency of RES places a heavy burden on the system. The uncertainty of RES is traditionally handled by controllable generators to balance the real time…

This work introduces a new method to efficiently solve optimization problems constrained by partial differential equations (PDEs) with uncertain coefficients. The method leverages two sources of inexactness that trade accuracy for speed:…

We develop a new continuous-time stochastic gradient descent method for optimizing over the stationary distribution of stochastic differential equation (SDE) models. The algorithm continuously updates the SDE model's parameters using an…

Ordinary and stochastic differential equations (ODEs and SDEs) are widely used to model continuous-time processes across various scientific fields. While ODEs offer interpretability and simplicity, SDEs incorporate randomness, providing…

Accurate prediction of electric load is crucial in power grid planning and management. In this paper, we solve the electric load forecasting problem under extreme events such as scorching heats. One challenge for accurate forecasting is the…

We present a method for providing statistical guarantees on runtime safety and goal reachability for integrated planning and control of a class of systems with unknown nonlinear stochastic underactuated dynamics. Specifically, given a…

Geostationary satellites collect high-resolution weather data comprising a series of images which can be used to estimate wind speed and direction at different altitudes. The Derived Motion Winds (DMW) Algorithm is commonly used to process…

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…

We propose DiffusionRollout, a novel selective rollout planning strategy for autoregressive diffusion models, aimed at mitigating error accumulation in long-horizon predictions of physical systems governed by partial differential equations…

Diffusion models have emerged as powerful generative tools with applications in computer vision and scientific machine learning (SciML), where they have been used to solve large-scale probabilistic inverse problems. Traditionally, these…

This paper introduces a probabilistic approach for tracking the dynamics of unweighted and directed graphs using state-space models (SSMs). Unlike conventional topology inference methods that assume static graphs and generate point-wise…

Low-fidelity wake models are used for wind farm design and control optimization. To generalize to a wind farm model, individually-modeled wakes are commonly superimposed using approximate superposition models. Wake models parameterize…

Generation and load balance is required in the economic scheduling of generating units in the smart grid. Variable energy generations, particularly from wind and solar energy resources, are witnessing a rapid boost, and, it is anticipated…

This paper develops a data-driven approach to accurately predict the restoration time of outages under different scales and factors. To achieve the goal, the proposed method consists of three stages. First, given the unprecedented amount of…