Related papers: Calibrated Physics-Informed Uncertainty Quantifica…
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…
Partial differential equations (PDEs) are fundamental for theoretically describing numerous physical processes that are based on some input fields in spatial configurations. Understanding the physical process, in general, requires…
The accessibility of spatially distributed data, enabled by affordable sensors, field, and numerical experiments, has facilitated the development of data-driven solutions for scientific problems, including climate change, weather…
The integration of Scientific Machine Learning (SciML) techniques with uncertainty quantification (UQ) represents a rapidly evolving frontier in computational science. This work advances Physics-Informed Neural Networks (PINNs) by…
Uncertainty quantification (UQ) helps to make trustworthy predictions based on collected observations and uncertain domain knowledge. With increased usage of deep learning in various applications, the need for efficient UQ methods that can…
Uncertainty quantification (UQ) is important to machine learning (ML) force fields to assess the level of confidence during prediction, as ML models are not inherently physical and can therefore yield catastrophically incorrect predictions.…
Inverse design is a central goal in much of science and engineering, including frequency-selective surfaces (FSS) that are critical to microelectronics for telecommunications and optical metamaterials. Traditional surrogate-assisted…
Reliable uncertainty quantification (UQ) is essential for developing machine-learned interatomic potentials (MLIPs) in predictive atomistic simulations. Conformal prediction (CP) is a statistical framework that constructs prediction…
The Best Estimate plus Uncertainty (BEPU) approach for nuclear systems modeling and simulation requires that the prediction uncertainty must be quantified in order to prove that the investigated design stays within acceptance criteria. A…
Data-driven surrogate models offer quick approximations to complex numerical and experimental systems but typically lack uncertainty quantification, limiting their reliability in safety-critical applications. While Bayesian methods provide…
Conformal prediction (CP), a distribution-free uncertainty quantification (UQ) framework, reliably provides valid predictive inference for black-box models. CP constructs prediction sets that contain the true output with a specified…
Physics Informed Neural Networks is a numerical method which uses neural networks to approximate solutions of partial differential equations. It has received a lot of attention and is currently used in numerous physical and engineering…
Physics-Informed Neural Networks (PINNs) are gaining popularity as a method for solving differential equations. While being more feasible in some contexts than the classical numerical techniques, PINNs still lack credibility. A remedy for…
As machine learning (ML) models are increasingly deployed in high-stakes domains, trustworthy uncertainty quantification (UQ) is critical for ensuring the safety and reliability of these models. Traditional UQ methods rely on specifying a…
Uncertainty quantification (UQ) is the process of systematically determining and characterizing the degree of confidence in computational model predictions. In the context of systems biology, especially with dynamic models, UQ is crucial…
Partial differential equations (PDEs) form the backbone of simulations of many natural phenomena, for example in climate modeling, material science, and even financial markets. The application of physics-informed neural networks to…
We describe a computational framework linking Uncertainty Quantification (UQ) methods for continuum problems depending on random parameters with Equation-Free (EF) methods for performing continuum deterministic numerics by acting directly…
The hybrid neural differentiable models mark a significant advancement in the field of scientific machine learning. These models, integrating numerical representations of known physics into deep neural networks, offer enhanced predictive…
Physics-informed neural networks (PINNs) have recently emerged as an alternative way of solving partial differential equations (PDEs) without the need of building elaborate grids, instead, using a straightforward implementation. In…
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…