Work

Quantitative Analysis of the Fractional Fokker–Planck–Levy Equation via a Modified Physics-Informed Neural Network Architecture

Year: 2024

Type: article

Abstract: An innovative approach is utilized in this paper to solve the Fractional Fokker–Planck–Levy (FFPL) equation. A hybrid technique is designed by combining the finite difference method (FDM), Adams numerical technique, and physics-informed neural network (PINN) architecture, namely, the FDM-APINN, to solve the fractional Fokker‒Planck‒Levy (FFPL) equation numerically. Two scenarios of the FFPL equation are considered by varying the value of α (i.e., 1.75,1.85). Moreover, three cases of each scenario are numerically studied for different discretized domains with 100,200 and 500 points in x∈[-1,1] and t∈[0,1]. For the FFPL equation, solutions are obtained via the FDM-APINN technique via 1000,2000, and 5000 iterations. The errors, loss function graphs, and statistical tables are presented to validate our claim that the FDM-APINN is a better alternative intelligent technique for handling fractional-order partial differential equations with complex terms. FDM-APINN can be extended by using nongradient-based bioinspired computing for higher-order fractional partial differential equations.

Source: Fractal and Fractional

DOI: 10.3390/fractalfract8110671

Authors: Fazlullah Fazal, Muhammad Sulaiman, David Bassir, Fahad Sameer Alshammari, Ghaylen Laouini