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

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

YOU? · · 2024 · Open Access · · DOI: https://doi.org/10.20944/preprints202410.0525.v1

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.

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Partial Differential Equation

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Type: preprint
Language: en
Landing Page: https://doi.org/10.20944/preprints202410.0525.v1
PDF: https://www.preprints.org/manuscript/202410.0525/v1/download
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Cited By: 1
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DOI: https://doi.org/10.20944/preprints202410.0525.v1

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

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Type: preprint

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Language: en

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Publication year: 2024

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Publication date: 2024-10-08

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

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Landing page: https://doi.org/10.20944/preprints202410.0525.v1

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Concepts: Fokker–Planck equation, Architecture, Artificial neural network, Physics, Statistical physics, Mathematical physics, Applied mathematics, Artificial intelligence, Computer science, Mathematics, Quantum mechanics, Partial differential equation, Art, Visual arts

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