Abstract
In this research, a soft computing approach based on a Nature-inspired technique, the Fractional-Order Darwinian Particle Swarm Optimization (FO-DPSO) algorithm, is hybridized with feed-forward artificial neural network (FF-ANN) to suggest and calculate better solutions for non-linear second-order ordinary differential equation (ODE) representing the corneal shape model (CSM). The unknown weights involved in approximate solutions obtained through ANN are tuned with the help of FO-DPSO. To test the robustness of our approach and conditionality of CSM, we have considered several cases of CSM with different aspects of the problem. Solutions obtained by Adam's method are used as a reference point for the sake of comparison. We establish it that FO-DPSO is a suitable technique for tuning the unknown weights involved in the solution designed with ANNs. Our results suggest that the proposed approach is a suitable candidate for solving real-world problems involving differential equations.
Highlights
The transparent front part of the eye known as corneal is represented by its curvature model
The research done in this paper is concluded by the following remarks, 1) We have designed a new soft computing procedure, by which we have calculated solutions for the corneal shape model
Feed-Forward ANNs are used to approximate the general solutions for the corneal shape model (CSM) model
Summary
The transparent front part of the eye known as corneal is represented by its curvature model. Problems arising in the fields of oscillation theory, ignition, and electro-analytical chemistry are solved with the help of a coupled Green’s function together with an iterative technique. These problems include Bratu differential equations [17]–[19]. In [20]–[22], they combine ANNs with random search techniques to tackle biological models represented through differential equations These artificial intelligence schemes are suitable to calculate solutions for the CSM. Our approach is based on a single optimization technique which is effective in term of computational cost like execution time, function evaluation and number of iteration as compared to PSO-ASA which is the combination of two algorithms.
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