AEPS-PINN: Adaptive Energy-Prior Scheduling with Superposed Multi-Harmonic Excitation for Physics-Informed Electrical Impedance Tomography

Dikky Juliyanto; Endah Rahmawati

doi:10.35882/jeeemi.v9i1.2012

Dikky Juliyanto Department of Physics, Universitas Negeri Surabaya, Surabaya, Indonesia https://orcid.org/0009-0006-5274-3043
Endah Rahmawati Department of Physics, Universitas Negeri Surabaya, Surabaya, Indonesia https://orcid.org/0000-0003-0102-4656

DOI: https://doi.org/10.35882/jeeemi.v9i1.2012

Keywords: Adaptive, Computation, Electricity, Medicine, Physics

Abstract

Background: Electrical Impedance Tomography (EIT) reconstructs internal conductivity distributions from boundary voltage measurements, but its ill-posed nature and limited sensitivity to interior structures remain major challenges.

Aims: This study develops and evaluates AEPS-PINN, a physics-informed reconstruction framework incorporating Adaptive Energy-Prior Scheduling to reduce the computational overhead of energy-based regularization.

Methods: The framework combines superposed multi-harmonic excitation, a dual-head Physics-Informed Neural Network (PINN) for electric potential and conductivity estimation, and an Energy-Based Model (EBM) prior activated selectively when the governing partial differential equation residual exhibits stagnation. Training employs Adam optimization followed by L-BFGS refinement.

Results: Performance was evaluated using a synthetic three-inclusion conductivity phantom under identical optimization budgets for Standard PINN, Static EBM-PINN, and AEPS-PINN configurations. AEPS-PINN achieved a mean squared error (MSE) of 0.9008 (n = 5), compared with 0.9127 (n = 4) for Standard PINN and 0.8967 (n = 5) for Static EBM-PINN, with no statistically significant improvement over Standard PINN under the Wilcoxon signed-rank test. The adaptive scheduler reduced EBM evaluations by approximately 99.8%, from 7,511 ± 353 to 15 ± 4 evaluations per run, without a measurable deterioration in reconstruction accuracy. However, Dice and Intersection-over-Union scores remained zero across all configurations, indicating unsuccessful spatial recovery of the conductivity inclusions. Furthermore, the superposed multi-harmonic excitation produced a rank-1 boundary-voltage response matrix, corresponding to a single independent current-injection pattern rather than four separately applied patterns.

Conclusion: These findings demonstrate that AEPS-PINN substantially reduces energy-prior evaluation requirements while maintaining reconstruction performance comparable to continuously regularized PINN. Nevertheless, reliable inclusion recovery requires more informative boundary measurements, particularly multiple independent current-injection patterns, followed by experimental validation.

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