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Computer models play a key role in many scientific and engineering problems. One major source of uncertainty in computer model experiment is input parameter uncertainty. Computer model calibration is a formal statistical procedure to infer…
Stochastic schemes, designed to represent unresolved sub-grid scale variability, are frequently used in short and medium-range weather forecasts, where they are found to improve several aspects of the model. In recent years, the impact of…
Existing variance reduction techniques used in stochastic simulations for rare event analysis still require a substantial number of model evaluations to estimate small failure probabilities. In the context of complex, nonlinear finite…
Data-driven forecasts of air quality have recently achieved more accurate short-term predictions. Despite their success, most of the current data-driven solutions lack proper quantifications of model uncertainty that communicate how much to…
Deep neural networks can be roughly divided into deterministic neural networks and stochastic neural networks.The former is usually trained to achieve a mapping from input space to output space via maximum likelihood estimation for the…
Hybrid methods have been shown to outperform pure statistical and pure deep learning methods at forecasting tasks and quantifying the associated uncertainty with those forecasts (prediction intervals). One example is Exponential Smoothing…
Stochastic simulation methods can be applied successfully to model exact spatio-temporally resolved reaction-diffusion systems. However, in many cases, these methods can quickly become extremely computationally intensive with increasing…
Magnetic particle imaging reconstructs tracer distributions using a system matrix obtained through time-consuming, noise-prone calibration measurements. Methods for addressing imperfections in measured system matrices increasingly rely on…
Spatial processes observed in various fields, such as climate and environmental science, often occur on a large scale and demonstrate spatial nonstationarity. Fitting a Gaussian process with a nonstationary Mat\'ern covariance is…
Modeling high-dimensional, nonlinear dynamic structural systems under natural hazards presents formidable computational challenges, especially when simultaneously accounting for uncertainties in external loads and structural parameters.…
Inference on unknown quantities in dynamical systems via observational data is essential for providing meaningful insight, furnishing accurate predictions, enabling robust control, and establishing appropriate designs for future…
We address the question of how to use a machine learned parameterization in a general circulation model, and assess its performance both computationally and physically. We take one particular machine learned parameterization…
Extreme environmental events frequently exhibit spatial and temporal dependence. These data are often modeled using max stable processes (MSPs). MSPs are computationally prohibitive to fit for as few as a dozen observations, with supposed…
Stochastic modeling has become a popular approach to quantify uncertainty in flows through heterogeneous porous media. The uncertainty in heterogeneous structure properties is often parameterized by a high-dimensional random variable. This…
Scientific modeling faces a tradeoff between the interpretability of mechanistic theory and the predictive power of machine learning. While existing hybrid approaches have made progress by incorporating domain knowledge into machine…
The accurate representation of precipitation in Earth system models (ESMs) is crucial for reliable projections of the ecological and socioeconomic impacts in response to anthropogenic global warming. The complex cross-scale interactions of…
Quantum mechanics/molecular mechanics (QM/MM) molecular dynamics (MD) simulations have been developed to simulate molecular systems, where an explicit description of changes in the electronic structure is necessary. However, QM/MM MD…
FourCastNet 3 advances global weather modeling by implementing a scalable, geometric machine learning (ML) approach to probabilistic ensemble forecasting. The approach is designed to respect spherical geometry and to accurately model the…
Accurately quantifying air-sea fluxes is important for understanding air-sea interactions and improving coupled weather and climate systems. This study introduces a probabilistic framework to represent the highly variable nature of air-sea…
The literature is rich with studies, analyses, and examples on parameter estimation for describing the evolution of chaotic dynamical systems based on measurements, even when only partial information is available through observations.…