This work aims to solve six problems with four different physics-informed machine learning frameworks and compare the results in terms of accuracy and computational cost. First, we considered the diffusion-advection-reaction equations, which are second-order linear differential equations with two boundary conditions. The first algorithm is the classic Physics-Informed Neural Networks. The second one is Physics-Informed Extreme Learning Machine. The third framework is Deep Theory of Functional Connections, a multilayer neural network based on the solution approximation via a constrained expression that always analytically satisfies the boundary conditions. The last algorithm is the Extreme Theory of Functional Connections (X-TFC), which combines Theory of Functional Connections and shallow neural network with random features [e.g., Extreme Learning Machine (ELM)]. The results show that for these kinds of problems, ELM-based frameworks, especially X-TFC, overcome those using deep neural networks both in terms of accuracy and computational time.

Physics-Informed Neural Networks for 1-D Steady-State Diffusion-Advection-Reaction Equations / Laghi, L; Schiassi, E; De Florio, M; Furfaro, R; Mostacci, D. - In: NUCLEAR SCIENCE AND ENGINEERING. - ISSN 0029-5639. - STAMPA. - 197:9(2023), pp. 2373-2403. [10.1080/00295639.2022.2160604]

Physics-Informed Neural Networks for 1-D Steady-State Diffusion-Advection-Reaction Equations

Laghi, L
;
Mostacci, D
2023

Abstract

This work aims to solve six problems with four different physics-informed machine learning frameworks and compare the results in terms of accuracy and computational cost. First, we considered the diffusion-advection-reaction equations, which are second-order linear differential equations with two boundary conditions. The first algorithm is the classic Physics-Informed Neural Networks. The second one is Physics-Informed Extreme Learning Machine. The third framework is Deep Theory of Functional Connections, a multilayer neural network based on the solution approximation via a constrained expression that always analytically satisfies the boundary conditions. The last algorithm is the Extreme Theory of Functional Connections (X-TFC), which combines Theory of Functional Connections and shallow neural network with random features [e.g., Extreme Learning Machine (ELM)]. The results show that for these kinds of problems, ELM-based frameworks, especially X-TFC, overcome those using deep neural networks both in terms of accuracy and computational time.
2023
Physics-Informed Neural Networks for 1-D Steady-State Diffusion-Advection-Reaction Equations / Laghi, L; Schiassi, E; De Florio, M; Furfaro, R; Mostacci, D. - In: NUCLEAR SCIENCE AND ENGINEERING. - ISSN 0029-5639. - STAMPA. - 197:9(2023), pp. 2373-2403. [10.1080/00295639.2022.2160604]
Laghi, L; Schiassi, E; De Florio, M; Furfaro, R; Mostacci, D
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/938693
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