Related papers: Beyond Scale Variations: Perturbative Theory Uncer…
A key issue in making precise predictions in perturbative QCD is the uncertainty in setting the renormalization scale. If in principle, the entire perturbative series is void of this issue, in practice the perturbative corrections are known…
We propose a novel iterative algorithm for estimating a deterministic but unknown parameter vector in the presence of model uncertainties. This iterative algorithm is based on a system model where an overall noise term describes both, the…
Inverse problems and, in particular, inferring unknown or latent parameters from data are ubiquitous in engineering simulations. A predominant viewpoint in identifying unknown parameters is Bayesian inference where both prior information…
We report lowest-order series expansions for primary matrix functions of quantum states based on a perturbation theory for functions of linear operators. Our theory enables efficient computation of functions of perturbed quantum states that…
We investigate the role played by symmetries in the perturbative expansion of the large-scale structure. In particular, we establish which of the coefficients of the perturbation theory kernels are dictated by symmetries and which not. Up…
Large language models (LLMs) often generate fluent but factually incorrect outputs, known as hallucinations, which undermine their reliability in real-world applications. While uncertainty estimation has emerged as a promising strategy for…
This is one of the two papers where the optimized perturbation theory was first formulated. The other paper is published in Theor. Math. Phys. 28, 652--660 (1976). The main idea of the theory is to reorganize the perturbative sequence by…
We compare the non-linear matter power spectrum in real space calculated analytically from 3rd-order perturbation theory with N-body simulations at 1<z<6. We find that the perturbation theory prediction agrees with the simulations to better…
The next generation of cosmological surveys will operate over unprecedented scales, and will therefore provide exciting new opportunities for testing general relativity. The standard method for modelling the structures that these surveys…
Neural networks (NNs) are currently changing the computational paradigm on how to combine data with mathematical laws in physics and engineering in a profound way, tackling challenging inverse and ill-posed problems not solvable with…
We consider the inference problem for parameters in stochastic differential equation models from discrete time observations (e.g. experimental or simulation data). Specifically, we study the case where one does not have access to…
Obtaining reliable uncertainty estimates of neural network predictions is a long standing challenge. Bayesian neural networks have been proposed as a solution, but it remains open how to specify their prior. In particular, the common…
A variety of techniques have been proposed to train machine learning classifiers that are independent of a given feature. While this can be an essential technique for enabling background estimation, it may also be useful for reducing…
The setting of the renormalization scale ($\mu_r$) in the perturbative QCD (pQCD) is one of the crucial problems for achieving precise fixed-order pQCD predictions. The conventional prescription is to take its value as the typical momentum…
In its original formulation, Heisenberg's uncertainty principle describes a trade-off relation between the error of a quantum measurement and the thereby induced disturbance on the measured object. However, this relation is not valid in…
A mathematical framework for information-theoretic analysis is established, with a new viewpoint of describing transmitted messages and communication channels by the nonlinear expectation theory, beyond the framework of classical…
The review presents general methods for treating complicated problems that cannot be solved exactly and whose solution encounters two major difficulties. First, there are no small parameters allowing for the safe use of perturbation theory…
In this article a novel approach for training deep neural networks using Bayesian techniques is presented. The Bayesian methodology allows for an easy evaluation of model uncertainty and additionally is robust to overfitting. These are…
There has been some recent activity in trying to understand the dark matter clustering properties in the quasilinear regime, through resummation of perturbative terms, otherwise known as the renormalized perturbation theory…
Model-free adaptive optimization methods are capable of optimizing unknown, time-varying processes even when other optimization methods are not. However, their practical application is often limited by perturbations that are used to gather…