Related papers: High-order Uncertain Differential Equation and Its…
This paper introduces a novel approach to uncertainty quantification for radiance fields by leveraging higher-order moments of the rendering equation. Uncertainty quantification is crucial for downstream tasks including view planning and…
Finite element analysis (FEA) has been widely used to generate simulations of complex and nonlinear systems. Despite its strength and accuracy, the limitations of FEA can be summarized into two aspects: a) running high-fidelity FEA often…
In this work we investigate the existence of solutions, their uniqueness and finally dependence on parameters for solutions of second order neutral nonlinear difference equations. The main tool which we apply is Darbo fixed point theorem.
From neural ODEs to continuous-time machine learning, differentiable solvers allow physics, optimization, and simulation to become trainable components within deep learning systems. This has opened the path to a new generation of deep…
When the cost of misclassifying a sample is high, it is useful to have an accurate estimate of uncertainty in the prediction for that sample. There are also multiple types of uncertainty which are best estimated in different ways, for…
In this article, we design and analyze a hybrid high-order (HHO) finite element approximation for the solution of a nonlocal nonlinear problem of Kirchhoff type. The HHO method involves arbitrary-order polynomial approximations on…
This paper presents a high-accuracy higher-order multiscale method for solving multi-continuum problems in in highly heterogeneous media. First, microscopic unit cell functions are defined, leading to the derivation of macroscopic…
The evolution of the system created in a high energy nuclear collision is very sensitive to the fluctuations in the initial geometry of the system. In this letter we show how one can utilize these large fluctuations to select events…
Definite integrals with parameters of holonomic functions satisfy holonomic systems of linear partial differential equations. When we restrict parameters to a one dimensional curve, the system becomes a linear ordinary differential equation…
These days, as high energy particle colliders become unavailable for testing speculative theoretical ideas, physicists are looking to other environments that may provide extreme conditions where theory confronts physical reality. One such…
Recent years have witnessed a growth in mathematics for deep learning--which seeks a deeper understanding of the concepts of deep learning with mathematics and explores how to make it more robust--and deep learning for mathematics, where…
Exponential time differencing methods is a power tool for high-performance numerical simulation of computationally challenging problems in condensed matter physics, fluid dynamics, chemical and biological physics, where mathematical models…
We provide of a method to integrate first order non-linear systems of differential equations with variable coefficients. It determines approximate solutions given initial or boundary conditions or even for Sturm-Liouville problems. This…
A unified approach, for solving a wide class of single and many-body quantum problems, commonly encountered in literature is developed based on a recently proposed method for finding solutions of linear differential equations. Apart from…
We describe a way of solving a partial differential equation using the differential invariants of its point symmetries. By first solving its quotient PDE, which is given by the differential syzygies in the algebra of differential…
Estimating uncertainty in deep learning models is critical for reliable decision-making in high-stakes applications such as medical imaging. Prior research has established that the difference between an input sample and its reconstructed…
In this paper, we present a deep learning-based numerical method for approximating high dimensional stochastic partial differential equations (SPDEs). At each time step, our method relies on a predictor-corrector procedure. More precisely,…
In this work we propose and analyze a novel Hybrid High-Order discretization of a class of (linear and) nonlinear elasticity models in the small deformation regime which are of common use in solid mechanics. The proposed method is valid in…
In this paper, a class of high order numerical schemes is proposed to solve the nonlinear parabolic equations with variable coefficients. This method is based on our previous work [10] for convection-diffusion equations, which relies on a…
Quantitative calculations of the properties of hadrons and nuclei, with assessed uncertainties, have emerged as competitive with experimental measurements in a number of major cases. We may well be entering an era where theoretical…