Neural Network Methods for Solving Differential Equations

Yadav, Neha; Yadav, Anupam; Kumar, Manoj

doi:10.1007/978-94-017-9816-7_4

Cited by 21 publications

(18 citation statements)

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“…( 2 ). It is well known that a neural network implementation of differential equation is possible 62 – 64 and efficient in terms of execution time, compared with classical method that do not exploit parallel computing 65 . In particular, a simple implementation of finite differences methods is presented by Lee and Kung 62 together with an explicit method for calculating a general continuous and discrete neural algorithms for solving a wide range of complex partial differential equations.…”

Section: Discussionmentioning

confidence: 99%

Gravitational models explain shifts on human visual attention

Zanca

Gori

Melacci

et al. 2020

Sci Rep

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Visual attention refers to the human brain’s ability to select relevant sensory information for preferential processing, improving performance in visual and cognitive tasks. It proceeds in two phases. One in which visual feature maps are acquired and processed in parallel. Another where the information from these maps is merged in order to select a single location to be attended for further and more complex computations and reasoning. Its computational description is challenging, especially if the temporal dynamics of the process are taken into account. Numerous methods to estimate saliency have been proposed in the last 3 decades. They achieve almost perfect performance in estimating saliency at the pixel level, but the way they generate shifts in visual attention fully depends on winner-take-all (WTA) circuitry. WTA is implemented by the biological hardware in order to select a location with maximum saliency, towards which to direct overt attention. In this paper we propose a gravitational model to describe the attentional shifts. Every single feature acts as an attractor and the shifts are the result of the joint effects of the attractors. In the current framework, the assumption of a single, centralized saliency map is no longer necessary, though still plausible. Quantitative results on two large image datasets show that this model predicts shifts more accurately than winner-take-all.

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Section: Discussionmentioning

confidence: 99%

Gravitational models explain shifts on human visual attention

Zanca

Gori

Melacci

et al. 2020

Sci Rep

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“…This allows a prediction of the output value with a certain probability. Further described is the use of neural networks to precisely determine the resulting values based on the input measurement data and cluster analysis method [ 9 , 12 ].…”

Section: Methodsmentioning

confidence: 99%

“…The suitability of using the perceptron neural networks with one hidden layer for this exact purpose will be described in the article. By creating a suitable file containing learning information for the neural network and finding a suitable number of neurons in a hidden layer, it is possible to apply it to solve the discriminatory task and, more precisely, find individual parameters [ 9 , 10 ].…”

Section: Introductionmentioning

confidence: 99%

Solving the Issue of Discriminant Roughness of Heterogeneous Surfaces Using Elements of Artificial Intelligence

et al. 2021

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This work deals with investigative methods used for evaluation of the surface quality of selected metallic materials’ cutting plane that was created by CO2 and fiber laser machining. The surface quality expressed by Rz and Ra roughness parameters is examined depending on the sample material and the machining technology. The next part deals with the use of neural networks in the evaluation of measured data. In the last part, the measured data were statistically evaluated. Based on the conclusions of this analysis, the possibilities of using neural networks to determine the material of a given sample while knowing the roughness parameters were evaluated. The main goal of the presented paper is to demonstrate a solution capable of finding characteristic roughness values for heterogeneous surfaces. These surfaces are common in scientific as well as technical practice, and measuring their quality is challenging. This difficulty lies mainly in the fact that it is not possible to express their quality by a single statistical parameter. Thus, this paper's main aim is to demonstrate solutions using the cluster analysis methods and the hidden layer, solving the problem of discriminant and dividing the heterogeneous surface into individual zones that have characteristic parameters.

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“…ivan Pavlov won the nobel Prize (1904) for 'conditional learning.' to capture the market of electronic computers "international Business Machines (iBM)" was established in 1914. in 1943, McCulloch and Pitts wrote a paper on "neuron structure with weighted inputs" (Yadav et al, 2015). Minsky and Papert (1969) published a book on Perceptions which mathematically prove that learning is impossible through weights.…”

Section: The History Of Neural Network In Businessmentioning

confidence: 99%

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Neural Network Methods for Solving Differential Equations

Cited by 21 publications

References 0 publications

Gravitational models explain shifts on human visual attention

Gravitational models explain shifts on human visual attention

Solving the Issue of Discriminant Roughness of Heterogeneous Surfaces Using Elements of Artificial Intelligence

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