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We develop a novel deep learning method for uncertainty quantification in stochastic partial differential equations based on Bayesian neural network (BNN) and Hamiltonian Monte Carlo (HMC). A BNN efficiently learns the posterior…
State-of-the-art computer codes for simulating real physical systems are often characterized by a vast number of input parameters. Performing uncertainty quantification (UQ) tasks with Monte Carlo (MC) methods is almost always infeasible…
Effective quantification of uncertainty is an essential and still missing step towards a greater adoption of deep-learning approaches in different applications, including mission-critical ones. In particular, investigations on the…
Bayesian Neural Networks (BNNs) offer a principled and natural framework for proper uncertainty quantification in the context of deep learning. They address the typical challenges associated with conventional deep learning methods, such as…
Machine learning methods for the construction of data-driven reduced order model models are used in an increasing variety of engineering domains, especially as a supplement to expensive computational fluid dynamics for design problems. An…
Uncertainty quantification (UQ) is essential for assessing the reliability of Earth observation (EO) products. However, the extensive use of machine learning models in EO introduces an additional layer of complexity, as those models…
Understanding the uncertainty of a neural network's (NN) predictions is essential for many purposes. The Bayesian framework provides a principled approach to this, however applying it to NNs is challenging due to large numbers of parameters…
Effective Uncertainty Quantification (UQ) represents a key aspect for reliable deployment of Large Language Models (LLMs) in automated decision-making and beyond. Yet, for LLM generation with multiple choice structure, the state-of-the-art…
Physics-Informed Neural Networks (PINNs) have emerged as a powerful framework for solving PDEs, yet existing uncertainty quantification (UQ) approaches for PINNs generally lack rigorous statistical guarantees. In this work, we bridge this…
Coherent anti-Stokes Raman scattering (CARS) spectroscopy is a powerful and rapid technique widely used in medicine, material science, and chemical analyses. However, its effectiveness is hindered by the presence of a non-resonant…
Uncertainty quantification (UQ) is crucial in machine learning, yet most (axiomatic) studies of uncertainty measures focus on classification, leaving a gap in regression settings with limited formal justification and evaluations. In this…
The practice of uncertainty quantification (UQ) validation, notably in machine learning for the physico-chemical sciences, rests on several graphical methods (scattering plots, calibration curves, reliability diagrams and confidence curves)…
Machine learning (ML) offers promising new approaches to tackle complex problems and has been increasingly adopted in chemical and materials sciences. Broadly speaking, ML models employ generic mathematical functions and attempt to learn…
Modern convolutional neural networks (CNNs) are known to be overconfident in terms of their calibration on unseen input data. That is to say, they are more confident than they are accurate. This is undesirable if the probabilities predicted…
Kernel methods are widely used in causal inference for tasks such as treatment effect estimation, policy evaluation, and policy learning. The bootstrap is a standard tool for uncertainty quantification because of its broad applicability. As…
In this paper, we adopt conformal prediction, a distribution-free uncertainty quantification (UQ) framework, to obtain confidence prediction intervals with coverage guarantees for Deep Operator Network (DeepONet) regression. Initially, we…
The role of uncertainty quantification (UQ) in deep learning has become crucial with growing use of predictive models in high-risk applications. Though a large class of methods exists for measuring deep uncertainties, in practice, the…
Advances in deep neural network (DNN) based molecular property prediction have recently led to the development of models of remarkable accuracy and generalization ability, with graph convolution neural networks (GCNNs) reporting…
Assessing the predictive uncertainty of deep neural networks is crucial for safety-related applications of deep learning. Although Bayesian deep learning offers a principled framework for estimating model uncertainty, the common approaches…
Uncertainty Quantification (UQ) is widely regarded as the primary safeguard for deploying Large Language Models (LLMs) in high-stakes domains. However, we argue that the field suffers from a category error: mainstream UQ methods for LLMs…