Related papers: Uncertainty Quantification for Forward and Inverse…
Learning operators from data is central to scientific machine learning. While DeepONets are widely used for their ability to handle complex domains, they require fixed sensor numbers and locations, lack mechanisms for uncertainty…
Systems governed by partial differential equations (PDEs) require computationally intensive numerical solvers to predict spatiotemporal field evolution. While machine learning (ML) surrogates offer faster solutions, autoregressive inference…
The spatiotemporal resolution of Partial Differential Equations (PDEs) plays important roles in the mathematical description of the world's physical phenomena. In general, scientists and engineers solve PDEs numerically by the use of…
Due to the importance of uncertainty quantification (UQ), Bayesian approach to inverse problems has recently gained popularity in applied mathematics, physics, and engineering. However, traditional Bayesian inference methods based on Markov…
We present a critical survey on the consistency of uncertainty quantification used in deep learning and highlight partial uncertainty coverage and many inconsistencies. We then provide a comprehensive and statistically consistent framework…
Machine learning (ML) has been leveraged to tackle a diverse range of tasks in almost all branches of nuclear engineering. Many of the successes in ML applications can be attributed to the recent performance breakthroughs in deep learning,…
We propose a rigorous framework for Uncertainty Quantification (UQ) in which the UQ objectives and the assumptions/information set are brought to the forefront. This framework, which we call \emph{Optimal Uncertainty Quantification} (OUQ),…
In recent years, operator learning, particularly the DeepONet, has received much attention for efficiently learning complex mappings between input and output functions across diverse fields. However, in practical scenarios with limited and…
Large language models (LLMs) excel in many tasks but struggle to accurately quantify uncertainty in their generated responses. This limitation makes it challenging to detect misinformation and ensure reliable decision-making. Existing…
Reliable uncertainty quantification (UQ) is essential for deploying large language models (LLMs) in safety-critical scenarios, as it enables them to abstain from responding when uncertain, thereby avoiding hallucinations, i.e., plausible…
The high dynamics and heterogeneous interactions in the complicated urban systems have raised the issue of uncertainty quantification in spatiotemporal human mobility, to support critical decision-makings in risk-aware web applications such…
The Bayesian uncertainty quantification technique has become well established in turbulence modeling over the past few years. However, it is computationally expensive to construct a globally accurate surrogate model for Bayesian inference…
The rapid proliferation of large language models (LLMs) has stimulated researchers to seek effective and efficient approaches to deal with LLM hallucinations and low-quality outputs. Uncertainty quantification (UQ) is a key element of…
In this work we introduce a manifold learning-based method for uncertainty quantification (UQ) in systems describing complex spatiotemporal processes. Our first objective is to identify the embedding of a set of high-dimensional data…
This paper provides a comparative study of modern uncertainty quantification (UQ) methods. To greatly enhance real-time performance, both differential algebra (DA) and a directional differential algebra (DDA) approach are employed. This can…
AI Uncertainty Quantification (UQ) has the potential to improve human decision-making beyond AI predictions alone by providing additional probabilistic information to users. The majority of past research on AI and human decision-making has…
A problem of considerable importance within the field of uncertainty quantification (UQ) is the development of efficient methods for the construction of accurate surrogate models. Such efforts are particularly important to applications…
Large language models (LLMs) have transformed natural language processing, but their reliable deployment requires effective uncertainty quantification (UQ). Existing UQ methods are often heuristic and lack a probabilistic interpretation.…
Uncertainty estimation is important for deploying LLMs in high-stakes applications such as healthcare and finance, where hallucinations can appear fluent and plausible while being factually incorrect, making it difficult for users to judge…
We present a simple and effective approach for posterior uncertainty quantification in deep operator networks (DeepONets); an emerging paradigm for supervised learning in function spaces. We adopt a frequentist approach based on randomized…