Related papers: Uncertainty quantification for noisy inputs-output…
When does a large language model (LLM) know what it does not know? Uncertainty quantification (UQ) provides measures of uncertainty, such as an estimate of the confidence in an LLM's generated output, and is therefore increasingly…
A key factor in ensuring the accuracy of computer simulations that model physical systems is the proper calibration of their parameters based on real-world observations or experimental data. Inevitably, uncertainties arise, and Bayesian…
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…
Machine learning methods are increasingly widely used in high-risk settings such as healthcare, transportation, and finance. In these settings, it is important that a model produces calibrated uncertainty to reflect its own confidence and…
In current noisy intermediate-scale quantum (NISQ) devices, hybrid quantum neural networks (HQNNs) offer a promising solution, combining the strengths of classical machine learning with quantum computing capabilities. However, the…
This paper introduces for the first time, to the best of our knowledge, the Bayesian Physics-Informed Neural Networks for applications in power systems. Bayesian Physics-Informed Neural Networks (BPINNs) combine the advantages of…
While the uncertainty in generation and demand increases, accurately estimating the dynamic characteristics of power systems becomes crucial for employing the appropriate control actions to maintain their stability. In our previous work, we…
In a world where more decisions are made using artificial intelligence, it is of utmost importance to ensure these decisions are well-grounded. Neural networks are the modern building blocks for artificial intelligence. Modern neural…
Uncertainty quantification (UQ) is essential for deploying machine learning models in safety-critical physical systems, yet classical Bayesian approaches incur substantial computational overhead. We establish a formal connection between…
Neural networks (NNs) can achieved high performance in various fields such as computer vision, and natural language processing. However, deploying NNs in resource-constrained safety-critical systems has challenges due to uncertainty in the…
This paper explores Uncertainty Quantification (UQ) in SVM predictions, particularly for regression and forecasting tasks. Unlike the Neural Network, the SVM solutions are typically more stable, sparse, optimal and interpretable. However,…
We present a deep learning framework for quantifying and propagating uncertainty in systems governed by non-linear differential equations using physics-informed neural networks. Specifically, we employ latent variable models to construct…
This paper introduces a novel approach to solve inverse problems by leveraging deep learning techniques. The objective is to infer unknown parameters that govern a physical system based on observed data. We focus on scenarios where the…
Physics-Informed Neural Networks (PINNs) have emerged as a promising approach for solving partial differential equations (PDEs) by embedding the governing physics into the loss function associated with a deep neural network. In this work, a…
We present a "module-based hybrid" Uncertainty Quantification (UQ) framework for general nonlinear multi-physics simulation. The proposed methodology, introduced in [\hyperlink{ref1}{1}], supports the independent development of each…
Temporally and spatially dependent uncertain parameters are regularly encountered in engineering applications. Commonly these uncertainties are accounted for using random fields and processes, which require knowledge about the appearing…
Quantifying uncertainty is important for actionable predictions in real-world applications. A crucial part of predictive uncertainty quantification is the estimation of epistemic uncertainty, which is defined as an integral of the product…
We study methods for estimating model uncertainty for neural networks (NNs) in regression. To isolate the effect of model uncertainty, we focus on a noiseless setting with scarce training data. We introduce five important desiderata…
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…
Data-driven discovery of governing equations in computational science has emerged as a new paradigm for obtaining accurate physical models and as a possible alternative to theoretical derivations. The recently developed physics-informed…