Results 21 to 30 of about 785 (250)
Numerical identification of forcing terms by discrete mollification [PDF]
Computers & Mathematics with Applications, 1989 AbstractA new and totally automated technique for the approximate reconstruction of the unknown forcing terms in a system of ordinary differential equations when the experimental information is obtained through measured data, on a discrete set of points, is presented.
Murio, D.A., Hinestroza, D.
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A Truncated-Kernel Mollification Method for the Cauchy Problem of the Modified Helmholtz Equation
AxiomsThis paper addresses the Cauchy problem for the multi-dimensional modified Helmholtz equation, a classical and severely ill-posed problem. A truncated-kernel mollification method is proposed as an effective regularization approach.
Huilin Xu, Fanli Xu, Baoxia Wang
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Numerical solution of generalized IHCP by discrete mollification [PDF]
Computers & Mathematics with Applications, 1996 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mejía, C.E., Murio, D.A.
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Regularization of the inverse Laplace transform by mollification
Inverse ProblemsAbstract In this paper we study the inverse Laplace transform. We first derive a new global logarithmic stability estimate that shows that the inversion is severely ill-posed. Then we propose a regularization method to compute the inverse Laplace transform using the concept of mollification.
Pierre Maréchal +2 more
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A General Framework for Activation Function Optimization Based on Mollification Theory
MathematicsThe deep learning paradigm is progressively shifting from non-smooth activation functions, exemplified by ReLU, to smoother alternatives such as GELU and SiLU.
Wentao Zhang +3 more
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Robust Classification by Coupling Data Mollification with Label Smoothing
CoRRIntroducing training-time augmentations is a key technique to enhance generalization and prepare deep neural networks against test-time corruptions. Inspired by the success of generative diffusion models, we propose a novel approach of coupling data mollification, in the form of image noising and blurring, with label smoothing to align predicted label ...
Heinonen, Markus +3 more
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One-Line-of-Code Data Mollification Improves Optimization of Likelihood-based Generative Models [PDF]
, 2023 Generative Models (GMs) have attracted considerable attention due to their tremendous success in various domains, such as computer vision where they are capable to generate impressive realistic-looking images.
Filippone, Maurizio +3 more
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Mollification formulas and implicit smoothing [PDF]
Advances in Computational Mathematics, 2006 The authors develop some mollification formulas involving convolutions between popular radial basis function \(f\), and suitable mollifiers \(k\). Polyharmonic splines, scaled Bessel kernels and compactly supported basic functions are considered. An application which motivated the development of the formulas is a technique called implicit smoothing ...
Richard K. Beatson, H.-Q. Bui
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Mathematics, 2023 This paper is focused on the inverse problem of identifying the space-dependent source function and initial value of the time fractional nonhomogeneous diffusion-wave equation from noisy final time measured data in a multi-dimensional case.
Xianli Lv, Xiufang Feng
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Mathematics, 2023 This study examined a Cauchy problem for a multi-dimensional Laplace equation with mixed boundary. This problem is severely ill-posed in the sense of Hadamard.
Xianli Lv, Xiufang Feng
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