Related papers: Comments on "Bayesian Solution Uncertainty Quantif…
This is an open letter that we sent to S. Ilie, G. Soederlind and R.M. Corless in August 2008.
In this paper, we study the higher-order uncertain differential equations (UDEs) as defined by Kaixi Zhang (https://doi.org/10.1007/s10700-024-09422-0), mainly focus on the second-order case. We propose a pivotal condition (monotonicity in…
This paper introduces Bayesian frameworks for tackling various aspects of multi-criteria decision-making (MCDM) problems, leveraging a probabilistic interpretation of MCDM methods and challenges. By harnessing the flexibility of Bayesian…
We analyze in great detail the mathematical derivations from the article "Doppler signature in electrodynamic retarded potentials" by Giovanni Perosa, Simone Di Mitri, William A. Barletta, and Fulvio Parmigiani, published in Physics Open…
Probabilistic numerical solvers for ordinary differential equations (ODEs) treat the numerical simulation of dynamical systems as problems of Bayesian state estimation. Aside from producing posterior distributions over ODE solutions and…
Solving partial differential equations (PDEs) is the canonical approach for understanding the behavior of physical systems. However, large scale solutions of PDEs using state of the art discretization techniques remains an expensive…
The authors give a detailed information about symmetry (Lie, non-Lie, conditional) of nonlinear PDEs for spinor, vector and scalar fields; using advanced methods of group-theoretical, symmetry analysis construct wide families of classical…
A statistical learning approach for parametric PDEs related to Uncertainty Quantification is derived. The method is based on the minimization of an empirical risk on a selected model class and it is shown to be applicable to a broad range…
This short, self-contained article seeks to introduce and survey continuous-time deep learning approaches that are based on neural ordinary differential equations (neural ODEs). It primarily targets readers familiar with ordinary and…
High-dimensional partial differential equations (PDEs) pose significant challenges for numerical computation due to the curse of dimensionality, which limits the applicability of traditional mesh-based methods. Since 2017, the Deep BSDE…
This paper advocates the usefulness of new theories of uncertainty for the purpose of modeling some facets of uncertain knowledge, especially vagueness, in AI. It can be viewed as a partial reply to Cheeseman's (among others) defense of…
In this paper we consider the estimation of unknown parameters in Bayesian inverse problems. In most cases of practical interest, there are several barriers to performing such estimation, This includes a numerical approximation of a…
Some of the conclusions of an improved JWKB method by Eleuch H., Rostovtsev Y. V. and Scully M. O., EPL, 89 (2010) 50004 are clarified. The degree of approximation to exact solutions is quantitatively assessed. The improved JWKB method is…
We discuss the relation between entropic uncertainty relations by Buscemi et al. and by Barchielli et al.
Partial differential equation (PDE) models with multiple temporal/spatial scales are prevalent in several disciplines such as physics, engineering, and many others. These models are of great practical importance but notoriously difficult to…
Recently, the non-linear Changhee differential equations were introduced in [5] and these differential equations turned out to be very useful for studying special polynomials and mathematical physics. Some interesting identities and…
This paper collects into one place (most of) my answers to the questions Maximilian Schlosshauer posed in his interview volume, "Elegance and Enigma: The Quantum Interviews" (Springer, Frontiers Collection, 2011).
This is a comment on the recent paper by Soumitra Nandi1 and Ulrich Nierste ``Resolving the sign ambiguity in $\Delta \Gamma_s$ with $B_s \to D_s K$'', arXiv:0801.0143 [hep-ph].
Solving partial differential equations (PDEs) within the framework of probabilistic numerics offers a principled approach to quantifying epistemic uncertainty arising from discretization. By leveraging Gaussian process regression and…
Several recent works have developed a new, probabilistic interpretation for numerical algorithms solving linear systems in which the solution is inferred in a Bayesian framework, either directly or by inferring the unknown action of the…