Related papers: Forecast error growth: A dynamic-stochastic model

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…

Weather forecasting remains a crucial yet challenging domain, where recently developed models based on deep learning (DL) have approached the performance of traditional numerical weather prediction (NWP) models. However, these DL models,…

We consider statistics for stochastic evolution equations in Hilbert space with emphasis on stochastic partial differential equations (SPDEs). We observe a solution process under additional measurement errors and want to estimate a real or…

Multiscale stochastic dynamical systems have been widely adopted to a variety of scientific and engineering problems due to their capability of depicting complex phenomena in many real world applications. This work is devoted to…

It is critical yet challenging for deep learning models to properly characterize uncertainty that is pervasive in real-world environments. Although a lot of efforts have been made, such as heteroscedastic neural networks (HNNs), little work…

This study addresses the inverse problem of parameter estimation for Stochastic Differential Equations (SDEs) by minimizing a regularized discrepancy functional via Stochastic Gradient Descent (SGD). To achieve computational efficiency, we…

This paper provides a systematic method to build wind speed models based on stochastic differential equations (SDEs). The resulting models produce stochastic processes with a given probability distribution and exponential decaying…

Stochastic differential equations (SDEs) are increasingly used in longitudinal data analysis, compartmental models, growth modelling, and other applications in a number of disciplines. Parameter estimation, however, currently requires…

The Dynamic Nelson--Siegel (DNS) model is a widely used framework for term structure forecasting. We propose a novel extension that models DNS residuals as a Gaussian random field, capturing dependence across both time and maturity. The…

Wind power is playing an increasingly important role in electricity markets. However, it's inherent variability and uncertainty cause operational challenges and costs as more operating reserves are needed to maintain system reliability.…

Neural scaling laws, which in some domains can predict the performance of large neural networks as a function of model, data, and compute scale, are the cornerstone of building foundation models in Natural Language Processing and Computer…

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…

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 introduce a novel paradigm for learning non-parametric drift and diffusion functions for stochastic differential equation (SDE). The proposed model learns to simulate path distributions that match observations with non-uniform time…

The last decade has seen the success of stochastic parameterizations in short-term, medium-range and seasonal forecasts: operational weather centers now routinely use stochastic parameterization schemes to better represent model inadequacy…

This is a pedagogical review of the possible connection between the stochastic quantization in physics and the diffusion models in machine learning. For machine-learning applications, the denoising diffusion model has been established as a…

In this work, we extend the data-driven It\^{o} stochastic differential equation (SDE) framework for the pathwise assessment of short-term forecast errors to account for the time-dependent upper bound that naturally constrains the…

Due to the dynamics of underlying physics and external influences, the uncertainty of time series often varies over time. However, existing Denoising Diffusion Probabilistic Models (DDPMs) often fail to capture this non-stationary nature,…

The nested error regression model is a useful tool for analyzing clustered (grouped) data, and is especially used in small area estimation. The classical nested error regression model assumes normality of random effects and error terms, and…

In model-based reinforcement learning, most algorithms rely on simulating trajectories from one-step models of the dynamics learned on data. A critical challenge of this approach is the compounding of one-step prediction errors as the…