TY - JOUR

T1 - Physics-Informed Neural Networks for 1-D Steady-State Diffusion-Advection-Reaction Equations

AU - Laghi, Laura

AU - Schiassi, Enrico

AU - De Florio, Mario

AU - Furfaro, Roberto

AU - Mostacci, Domiziano

N1 - Publisher Copyright:
© 2023 American Nuclear Society.

PY - 2023

Y1 - 2023

N2 - 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.

AB - 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.

KW - Extreme Learning Machine

KW - functional interpolation

KW - Physics-Informed Neural Networks

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U2 - 10.1080/00295639.2022.2160604

DO - 10.1080/00295639.2022.2160604

M3 - Article

AN - SCOPUS:85147774094

SN - 0029-5639

JO - Nuclear Science and Engineering

JF - Nuclear Science and Engineering

ER -