A Three-Dimensional Fourier Neural Operator Surrogate with a Laplace-Residual Regularizer for the Electric Potential Field in Reinforced-Concrete Corrosion
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1
Master of Mechanical Engineering, Universitas Syiah Kuala, Jln. Syech Abdurrauf 7, Darussalam, Banda Aceh 23111, Indonesia
2
Department of Mechanical Engineering, Universitas Syiah Kuala, Jl. Tgk. Syech Abdul Rauf No. 7, Banda Aceh, 23111, Indonesia
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akhyar Akhyar
Department of Mechanical Engineering, Universitas Syiah Kuala, Jl. Tgk. Syech Abdul Rauf No. 7, Banda Aceh, 23111, Indonesia
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Corrosion of the steel reinforcement is the main cause of deterioration in concrete infrastructure, and it is usually assessed through the electric potential field around the corroding rebar. Finite-element modeling of this field is accurate, but it has to be repeated for every anode configuration. This study develops a three-dimensional Fourier Neural Operator, trained with a finite-difference Laplace-residual regularizer, that maps anode geometry to the potential field in a single forward pass. The network was trained on 979 FEniCSx solutions spanning a combinatorial grid of anode position and axial length. On 195 held-out configurations it reproduced the finite-element field with a mean relative error of 0.61% (median 0.48%, 99.5% of samples below 5%), and on 40 configurations off the training grid with 0.77%; two further random splits gave 0.81% and 0.52%. The error is concentrated near the rebar, where the reference field contains discretization artifacts of the finite-element mesh. Inference takes about 90 ms per configuration on a GPU at batch size 8, against 15.6 s for the finite-element solve on a CPU; on identical CPU hardware the gain is only 3.5-fold, so most of the speed-up comes from hardware parallelism. The Laplace-residual term made the bulk field smoother but did not improve accuracy. The neural operator also did not outperform simpler surrogates: averaged over three splits its error was 0.02 percentage points lower than that of proper orthogonal decomposition with Gaussian-process regression, and it extrapolated worse when the longest anodes were withheld (1.9 to 2.8% against 1.2%). Over two decades of conductivity, the unchanged surrogate stayed within 0.65 to 1.3% of the finite-element field. Within the sampled range, the surrogate reproduces the finite-element solver to engineering accuracy at much lower inference cost, although for this two-parameter problem it is not more accurate than simpler alternatives.