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Numerical Methods for Engineering An introduction using MATLAB® and computational electromagnetics examples, 2019 1 Rectangle rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1 Order . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Error bounds for the rectangle rules . . . . . . . . . . . . . . . . . .
Gernot Beer +2 more
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Tensor Neural Network and Its Numerical Integration [PDF]
Journal of Computational Mathematics, 2022 In this paper, we introduce a type of tensor neural network. For the first time, we propose its numerical integration scheme and prove the computational complexity to be the polynomial scale of the dimension.
Yifan Wang, Pengzhan Jin, Hehu Xie
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On Numerical Integration in Neural Ordinary Differential Equations [PDF]
International Conference on Machine Learning, 2022 The combination of ordinary differential equations and neural networks, i.e., neural ordinary differential equations (Neural ODE), has been widely studied from various angles.
Aiqing Zhu +3 more
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Geometric Numerical Integration
Oberwolfach Reports, 2022 The subject of this workshop was numerical methods that preserve geometric properties of the flow of an ordinary or partial differential equation. This was complemented by the question as to how structure preservation affects the long-time behaviour of ...
E. Faou +3 more
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Loop-Tree Duality for Multiloop Numerical Integration. [PDF]
Physical Review Letters, 2019 Loop-tree duality (LTD) offers a promising avenue to numerically integrate multiloop integrals directly in momentum space. It is well established at one loop, but there have been only sparse numerical results at two loops.
Zeno Capatti +3 more
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Numerical Integration in Multiple Dimensions with Designed Quadrature [PDF]
SIAM Journal on Scientific Computing, 2018 We present a systematic computational framework for generating positive quadrature rules in multiple dimensions on general geometries. A direct moment-matching formulation that enforces exact integration on polynomial subspaces yields nonlinear ...
Vahid Keshavarzzadeh +2 more
semanticscholar +1 more source
Numerical integration and FE implementation of a hypoplastic constitutive model
Acta Geotechnica, 2018 Hypoplastic constitutive equation based on nonlinear tensor functions possesses a failure surface but no yield surface. In this paper, we consider the numerical integration and FE implementation of a simple hypoplastic constitutive equation. The accuracy
Shun Wang +4 more
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Numerical integration of bivariate fractal interpolation functions on rectangular domains. [PDF]
Eur Phys J Spec Top, 2023 Aparna MP, Paramanathan P.
europepmc +1 more source
Evaluating statistical significance in a meta-analysis by using numerical integration. [PDF]
Comput Struct Biotechnol J, 2022 Lin YC, Liang YJ, Yang HC.
europepmc +1 more source
Benchmarking of numerical integration methods for ODE models of biological systems. [PDF]
Sci Rep, 2021 Städter P +4 more
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