Related papers: Constructive Approximation of Random Process via S…
Artificial neural network operators (ANNOs) have been widely used for approximating deterministic input-output functions; however, their extension to random dynamics remains comparatively unexplored. In this paper, we construct a new class…
In the present article, we introduce and study the behaviour of the new family of exponential type neural network operators activated by the sigmoidal functions. We establish the point-wise and uniform approximation theorems for these NN…
In this paper, we prove the rate of approximation for the Neural Network Sampling Operators activated by sigmoidal functions with mixed Lebesgue norm in terms of averaged modulus of smoothness for a bounded measurable functions on bounded…
In this paper, we considered the problem of the simultaneous approximation of a function and its derivatives by means of the well-known neural network (NN) operators activated by sigmoidal function. Other than a uniform convergence theorem…
This paper considers binomial approximation of continuous time stochastic processes. It is shown that, under some mild integrability conditions, a process can be approximated in mean square sense and in other strong metrics by binomial…
In this work, we introduce a new class of neural network operators designed to handle problems where memory effects and randomness play a central role. In this work, we introduce a new class of neural network operators designed to handle…
In this paper we present a class of convolutional neural networks (CNNs) called non-overlapping CNNs in the study of approximation capabilities of CNNs. We prove that such networks with sigmoidal activation function are capable of…
In this paper, a new class of \emph{Taylor-accelerated neural network interpolation operators} is introduced on quasi-uniform irregular grids. These operators improve existing neural network interpolation operators by incorporating Taylor…
This paper introduces an operator-based neural network, the mirror-padded Fourier neural operator (MFNO), designed to learn the dynamics of stochastic systems. MFNO extends the standard Fourier neural operator (FNO) by incorporating mirror…
The stochastic rounding (SR) function is proposed to evaluate and demonstrate the effects of stochastically rounding row and column subscripts in image interpolation and scan conversion. The proposed SR function is based on a pseudorandom…
This paper presents a new approach of constructing $\alpha$-fractal interpolation functions (FIFs) using neural network operators, integrating concepts from approximation theory. Initially, we construct $\alpha$-fractals utilizing neural…
Stationary stochastic processes (SPs) are a key component of many probabilistic models, such as those for off-the-grid spatio-temporal data. They enable the statistical symmetry of underlying physical phenomena to be leveraged, thereby…
In the present paper, we introduce three neural network operators of convolution type activated by symmetrized, deformed and parametrized B-generalized logistic function. We deal with the approximation properties of these operators to the…
The primary objective of this study is to develop novel interpolation operators that interpolate the boundary values of a function defined on a triangle. This is accomplished by constructing New Generalized Boolean sum neural network…
Deep neural networks is a branch in machine learning that has seen a meteoric rise in popularity due to its powerful abilities to represent and model high-level abstractions in highly complex data. One area in deep neural networks that is…
This paper contributes to a development of randomized methods for neural networks. The proposed learner model is generated incrementally by stochastic configuration (SC) algorithms, termed as Stochastic Configuration Networks (SCNs). In…
Neural operators have achieved significant success in modern scientific computing due to their flexibility and strong generalization capabilities. Existing models, however, primarily rely on first-order kernel integral approximations, which…
We establish in this work approximation results of deep neural networks for smooth functions measured in Sobolev norms, motivated by recent development of numerical solvers for partial differential equations using deep neural networks. {Our…
On the one hand, the framework of mixed norm spaces has potential applications in different areas of mathematics. On the other hand, neural network (NN) operators are well established as approximators, attracting significant attention in…
We introduce a machine-learning framework named statistics-informed neural network (SINN) for learning stochastic dynamics from data. This new architecture was theoretically inspired by a universal approximation theorem for stochastic…