Related papers: Calibrated Physics-Informed Uncertainty Quantifica…
Physics-Informed Neural Networks (PINNs) are machine learning tools that approximate the solution of general partial differential equations (PDEs) by adding them in some form as terms of the loss/cost function of a Neural Network. Most…
In recent years, Physics-Informed Neural Networks (PINNs) have become a representative method for solving partial differential equations (PDEs) with neural networks. PINNs provide a novel approach to solving PDEs through optimization…
Conformal Prediction (CP) is a distribution-free method for constructing prediction sets with marginal finite-sample coverage guarantees, making it a suitable framework for reliable uncertainty quantification in safety-critical object…
Quantum algorithms for partial differential equations (PDEs) face severe practical constraints on near-term hardware: limited qubit counts restrict spatial resolution to coarse grids, while circuit depth limitations prevent accurate…
Motivated by recent research on Physics-Informed Neural Networks (PINNs), we make the first attempt to introduce the PINNs for numerical simulation of the elliptic Partial Differential Equations (PDEs) on 3D manifolds. PINNs are one of the…
Uncertainty quantification (UQ) for foundation models is essential to identify and mitigate potential hallucinations in automatically generated text. However, heuristic UQ approaches lack formal guarantees for key metrics such as the false…
Physics-informed neural networks have emerged as a prominent new method for solving differential equations. While conceptually straightforward, they often suffer training difficulties that lead to relatively large discretization errors or…
We address the problem of uncertainty quantification (UQ) in the localization of a sound source within adverse acoustic environments. Estimating the position of the source is influenced by various factors, such as noise and reverberation,…
The calibration of complex computer codes using uncertainty quantification (UQ) methods is a rich area of statistical methodological development. When applying these techniques to simulators with spatial output, it is now standard to use…
Computational molecular modeling and visualization has seen significant progress in recent years with sev- eral molecular modeling and visualization software systems in use today. Nevertheless the molecular biology community lacks…
Numerical discretisations of partial differential equations (PDEs) can be written as discrete convolutions, which, themselves, are a key tool in AI libraries and used in convolutional neural networks (CNNs). We therefore propose to…
Uncertainty Quantification (UQ) is crucial for deploying reliable Deep Learning (DL) models in high-stakes applications. Recently, General Type-2 Fuzzy Logic Systems (GT2-FLSs) have been proven to be effective for UQ, offering Prediction…
We analyze an ensemble-based approach for uncertainty quantification (UQ) in atomistic neural networks. This method generates an epistemic uncertainty signal without requiring changes to the underlying multi-headed regression neural network…
Planning energy production is a challenging task due to its cost-sensitivity, fast-moving energy markets, uncertainties in demand, and technical constraints of power plants. Thus, more complex models of this so-called \emph{unit commitment…
With the increased use of data-driven approaches and machine learning-based methods in material science, the importance of reliable uncertainty quantification (UQ) of the predicted variables for informed decision-making cannot be…
Quantum computing promises exponential improvements in solving large systems of partial differential equations (PDE), which forms a bottleneck in high-resolution computational fluid dynamics (CFD) simulations, in, among others, aerospace…
Uncertainty quantification (UQ) is a crucial but challenging task in many high-dimensional regression or learning problems to increase the confidence of a given predictor. We develop a new data-driven approach for UQ in regression that…
Predicting the behavior of complex systems in engineering often involves significant uncertainty about operating conditions, such as external loads, environmental effects, and manufacturing variability. As a result, uncertainty…
Estimates of predictive uncertainty are important for accurate model-based planning and reinforcement learning. However, predictive uncertainties---especially ones derived from modern deep learning systems---can be inaccurate and impose a…
We introduce a physics-informed Bayesian Neural Network (BNN) with flow approximated posteriors using multiplicative normalizing flows (MNF) for detailed uncertainty quantification (UQ) at the physics event-level. Our method is capable of…