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PHYSICS-INFORMED DEEP AI SIMULATION FOR FRACTAL INTEGRO-DIFFERENTIAL EQUATION.
- Source :
-
Fractals . 2024, Vol. 32 Issue 1, p1-8. 8p. - Publication Year :
- 2024
-
Abstract
- Fractal integro-differential equations (IDEs) can describe the effect of local microstructure on a complex physical problem, however, the traditional numerical methods are not suitable for solving the new-born models with the fractal integral and fractal derivative. Here we show that deep learning can be used to solve the bottleneck. By the two-scale transformation, the fractal IDE is first approximately converted to its traditional integro-differential partner, which is further converted to a differential equation system by introducing an auxiliary variable to remove the integral operation. Moreover, a flexible adaptive technology is adopted to deal with the loss weights of a deep learning neural network. A fractal Volterra IDE is used to show the effectiveness and simplicity of this new physics-informed deep AI simulation model. All results indicate the AI simulation model has good robustness and convergence, and the fractal Volterra IDE might explore the different properties of viscoelasticity for a porous medium. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0218348X
- Volume :
- 32
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Fractals
- Publication Type :
- Academic Journal
- Accession number :
- 175445537
- Full Text :
- https://doi.org/10.1142/S0218348X24500221