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Pré-Publication, Document De Travail (Preprint/Prepublication) Année : 2024

Parallel Solution of Nonlinear Projection Equations in a Multi-Task Learning Framework

Résumé

Nonlinear projection equations (NPEs) provide a unified framework for addressing various constrained nonlinear optimization and engineering problems. However, when it comes to solving multiple NPEs, traditional numerical integration methods are not efficient enough. This is because traditional methods solve each NPE iteratively and independently. In this paper, we propose a novel approach based on Multi-Task Learning (MTL) for solving multiple NPEs. The solution procedure is outlined as follows. First, we model each NPE as a system of ordinary differential equations (ODEs) using neurodynamic optimization. Second, for each ODE system, we use a Physics-Informed Neural Network (PINN) as the solution. Third, we use a multi-branch MTL framework, where each branch corresponds to a PINN model. This allows us to solve multiple NPEs in parallel by training a single neural network model. Experimental results show that our approach has superior computational performance, especially when the number of NPEs to be solved is large.
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Dates et versions

hal-04371001 , version 1 (03-01-2024)

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  • HAL Id : hal-04371001 , version 1

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Dawen Wu, Abdel Lisser. Parallel Solution of Nonlinear Projection Equations in a Multi-Task Learning Framework. 2024. ⟨hal-04371001⟩
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