Related papers: Joint Parameter and Parameterization Inference wit…

We present a novel framework combining Deep Operator Networks (DeepONets) with Physics-Informed Neural Networks (PINNs) to solve partial differential equations (PDEs) and estimate their unknown parameters. By integrating data-driven…

Interpreting data with mathematical models is an important aspect of real-world industrial and applied mathematical modeling. Often we are interested to understand the extent to which a particular set of data informs and constrains model…

Uncertainty quantification has been a core of the statistical machine learning, but its computational bottleneck has been a serious challenge for both Bayesians and frequentists. We propose a model-based framework in quantifying…

Climate models play a critical role in understanding and projecting climate change. Due to their complexity, their horizontal resolution of about 40-100 km remains too coarse to resolve processes such as clouds and convection, which need to…

In the era of big data, machine learning (ML) has become a powerful tool in various fields, notably impacting structural dynamics. ML algorithms offer advantages by modeling physical phenomena based on data, even in the absence of…

Machine learning (ML) classification models are increasingly being used in a wide range of applications where it is important that predictions are accompanied by uncertainties, including in climate and earth observation, medical diagnosis…

Global climate models represent small-scale processes such as clouds and convection using quasi-empirical models known as parameterizations, and these parameterizations are a leading cause of uncertainty in climate projections. A promising…

Machine Learning (ML) has widely been used for modeling and predicting physical systems. These techniques offer high expressive power and good generalizability for interpolation within observed data sets. However, the disadvantage of…

Scientific Machine Learning is a new class of approaches that integrate physical knowledge and mechanistic models with data-driven techniques for uncovering governing equations of complex processes. Among the available approaches, Universal…

The modeling and uncertainty quantification of closed curves is an important problem in the field of shape analysis, and can have significant ramifications for subsequent statistical tasks. Many of these tasks involve collections of closed…

Uncertainty quantification in Artificial Intelligence (AI)-based predictions of material properties is of immense importance for the success and reliability of AI applications in material science. While confidence intervals are commonly…

Physics-informed machine learning (PIML) integrates partial differential equations (PDEs) into machine learning models to solve inverse problems, such as estimating coefficient functions (e.g., the Hamiltonian function) that characterize…

Atmospheric models used for weather and climate prediction are traditionally formulated in a deterministic manner. In other words, given a particular state of the resolved scale variables, the most likely forcing from the sub-grid scale…

We investigate a new structure for machine learning classifiers applied to problems in high-energy physics by expanding the inputs to include not only measured features but also physics parameters. The physics parameters represent a…

Quantifying uncertainties for machine learning (ML) models is a foundational challenge in modern data analysis. This challenge is compounded by at least two key aspects of the field: (a) inconsistent terminology surrounding uncertainty and…

Rigorous statistical methods, including parameter estimation with accompanying uncertainties, underpin the validity of scientific discovery, especially in the natural sciences. With increasingly complex data models such as deep learning…

Advances in architectural design, data availability, and compute have driven remarkable progress in semantic segmentation. Yet, these models often rely on relaxed Bayesian assumptions, omitting critical uncertainty information needed for…

Scientific machine learning increasingly uses spectral methods to understand physical systems. Current spectral learning approaches provide only point estimates without uncertainty quantification, limiting their use in safety-critical…

Physics parameterizations are often needed for numerical weather prediction (NWP) of precipitation forecast. This is mainly because the resolutions of most computational atmospheric models are not fine enough to explicitly resolve sub-grid…

Uncertainty quantification in automated image analysis is highly desired in many applications. Typically, machine learning models in classification or segmentation are only developed to provide binary answers; however, quantifying the…