Related papers: Sensitivity Analysis and Uncertainty Quantificatio…
Turning pass-through network architectures into iterative ones, which use their own output as input, is a well-known approach for boosting performance. In this paper, we argue that such architectures offer an additional benefit: The…
Rapidity divergences occur when parton densities in a gauge theory are defined in the most natural way, as expectation values of partonic number operators in light-front quantization. I review these and other related divergences, and show…
The widespread adoption of machine learning surrogate models has significantly improved the scale and complexity of systems and processes that can be explored accurately and efficiently using atomistic modeling. However, the inherently…
We present theoretical thermally-averaged rate constants for vibrational and rotational (de-)excitation of the H3+ ion by electron impact. The constants are calculated using the multi-channel quantum-defect approach. The calculation…
Atomic radii and charges are two major parameters used in implicit solvent electrostatics and energy calculations. The optimization problem for charges and radii is under-determined, leading to uncertainty in the values of these parameters…
The mean-field rate equations have proven to be a versatile method in simulating defect dynamics and temporal changes in the micro-structure of materials. However, the reliability and usefulness of the method depends critically on the…
We consider the problem of detecting abrupt changes (i.e., large jump discontinuities) in the rate function of a point process. The rate function is assumed to be fully unknown, non-stationary, and may itself be a random process that…
Point defects have a strong influence on the physical properties of materials, often dominating the electronic and optical behavior in semiconductors and insulators. The simulation and analysis of point defects is therefore crucial for…
Uncertainty quantification for Particle Image Velocimetry (PIV) is critical for comparing flow fields with Computational Fluid Dynamics (CFD) results, and model design and validation. However, PIV features a complex measurement chain with…
We present a simple regularization of adversarial perturbations based upon the perceptual loss. While the resulting perturbations remain imperceptible to the human eye, they differ from existing adversarial perturbations in that they are…
Perturbation-based explanations are widely utilized to enhance the transparency of machine-learning models in practice. However, their reliability is often compromised by the unknown model behavior under the specific perturbations used.…
Generalized polynomial chaos (gPC) method has been extensively used in uncertainty quantification problems where equations contain random variables. For gPC to achieve high accuracy, PDE solutions need to have high regularity in the random…
We devise a {\sl non--perturbative} method, called {\sl Parametric Perturbation Theory} (PPT), which is alternative to the ordinary perturbation theory. The method relies on a principle of simplicity for the observable solutions, which are…
We apply random matrix theory to study the impact of measurement uncertainty on dynamic mode decomposition. Specifically, when the measurements follow a normal probability density function, we show how the moments of that density propagate…
We consider the linearized BGK equation and want to quantify uncertainties in the case of modelling errors. More specifically, we want to quantify the error produced if the pre-determined equilibrium function is chosen inaccurately. In this…
Bayesian inference is a popular approach to calibrating uncertainties, but it can underpredict such uncertainties when model misspecification is present, impacting its reliability to inform decision making. Recently, the statistics and…
In this work, we investigate the convergence of numerical approximations to coercivity constants of variational problems. These constants are essential components of rigorous error bounds for reduced-order modeling; extension of these…
Reparametrization-invariant theories of point relativistic particle interaction with fields of arbitrary tensor dimension are considered. It has been shown that the equations of motion obtained by Kalman [G. Kalman, Phys. Rev. vol.123,…
We discuss a general setup which allows the study of the perturbation theory of an arbitrary, locally harmonic 1D quantum mechanical potential as well as its multi-variable (many-body) generalization. The latter may form a prototype for…
The foundations of irradiation damage theory were laid in the 1950s and 60s within the framework of chemical reaction kinetics. While helpful to analyze qualitative aspects of irradiation damage, the theory contained gaps that delayed its…