Solving Time-Fractional reaction–diffusion systems through a tensor-based parallel algorithm

Machine Learning (ML) approach is a discussed research topic because of its benefit in several research fields. The most important issues in the training process of ML are accuracy and speed: a suitable mathematical model is critical and a fast data processing is mandatory. Fractional Calculus is in...

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Veröffentlicht in:Physica A Jg. 611; S. 128472
Hauptverfasser: Cardone, Angelamaria, De Luca, Pasquale, Galletti, Ardelio, Marcellino, Livia
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 01.02.2023
Schlagworte:
GPU computing
Machine Learning
Numerical methods
Parallel algorithm
Reaction–diffusion systems
Parallel algorithm
Reaction–diffusion systems
65M70
65M06
Numerical methods
35R11
65Y05
Machine Learning
GPU computing
ISSN:0378-4371, 1873-2119
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Zusammenfassung:Machine Learning (ML) approach is a discussed research topic because of its benefit in several research fields. The most important issues in the training process of ML are accuracy and speed: a suitable mathematical model is critical and a fast data processing is mandatory. Fractional Calculus is involved in a large number of important applications and, recently, many ML algorithms, in order to improve accuracy of results when performing training in solving optimization problems, are based on decision and control performed by means of time-fractional models to better understand complex systems. However, the high computational cost, which characterizes the numerical solution, of this approach might be a problem for large scale Machine Learning systems. High Performance Computing (HPC) is the way of addressing the need of real time computation. In fact, through tensor-based parallel strategies designed for modern parallel architectures, Fractional Calculus tools are very helpful for the ML training step. In this contest, we consider a time-fractional diffusion system and, after introducing a suitable modification of a numerical model to solve it, we propose a related and novel parallel implementation on GPUs (Graphics Processing Units). Experiments show the gain of performance in terms of execution time and accuracy of our parallel implementation. •A Time-fractional reaction–diffusion system is considered, focusing attention on the Sylvester equation system arising of discretization process.•A new tensor-based equivalent form for the Sylvester problem formulation is proposed.•A parallel algorithm which use this new formulation to provide fast results, exploiting the advanced GPU environment, has been implemented.
ISSN:0378-4371
1873-2119
DOI:10.1016/j.physa.2023.128472