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Boundary-Decoder network for inverse prediction of capacitor electrostatic analysis

Kart-Leong Lim, Rahul Dutta, Mihai Rotaru

TL;DR

The paper tackles the inefficiency of traditional and PINN-based electrostatic simulations under changing boundary conditions for a Laplace-Equation problem in a long air-filled capacitor. It introduces an end-to-end boundary-decoder network that directly maps boundary parameters, such as $d$, to the voltage distribution $V(x,y)$, bypassing separate latent-space regression and inverse-search steps. The approach uses semi-supervised training to jointly learn latent representations via an encoder-decoder and a supervised boundary-decoder objective, enabling rapid, accurate reconstructions under dynamic boundaries. Results show significant performance gains over baseline encoder-decoder, NN, and PINN methods, with no need for an initial estimate and preserved forward-model capability, suggesting practical speedups for boundary-variant electrostatic analyses.

Abstract

Traditional electrostatic simulation are meshed-based methods which convert partial differential equations into an algebraic system of equations and their solutions are approximated through numerical methods. These methods are time consuming and any changes in their initial or boundary conditions will require solving the numerical problem again. Newer computational methods such as the physics informed neural net (PINN) similarly require re-training when boundary conditions changes. In this work, we propose an end-to-end deep learning approach to model parameter changes to the boundary conditions. The proposed method is demonstrated on the test problem of a long air-filled capacitor structure. The proposed approach is compared to plain vanilla deep learning (NN) and PINN. It is shown that our method can significantly outperform both NN and PINN under dynamic boundary condition as well as retaining its full capability as a forward model.

Boundary-Decoder network for inverse prediction of capacitor electrostatic analysis

TL;DR

The paper tackles the inefficiency of traditional and PINN-based electrostatic simulations under changing boundary conditions for a Laplace-Equation problem in a long air-filled capacitor. It introduces an end-to-end boundary-decoder network that directly maps boundary parameters, such as , to the voltage distribution , bypassing separate latent-space regression and inverse-search steps. The approach uses semi-supervised training to jointly learn latent representations via an encoder-decoder and a supervised boundary-decoder objective, enabling rapid, accurate reconstructions under dynamic boundaries. Results show significant performance gains over baseline encoder-decoder, NN, and PINN methods, with no need for an initial estimate and preserved forward-model capability, suggesting practical speedups for boundary-variant electrostatic analyses.

Abstract

Traditional electrostatic simulation are meshed-based methods which convert partial differential equations into an algebraic system of equations and their solutions are approximated through numerical methods. These methods are time consuming and any changes in their initial or boundary conditions will require solving the numerical problem again. Newer computational methods such as the physics informed neural net (PINN) similarly require re-training when boundary conditions changes. In this work, we propose an end-to-end deep learning approach to model parameter changes to the boundary conditions. The proposed method is demonstrated on the test problem of a long air-filled capacitor structure. The proposed approach is compared to plain vanilla deep learning (NN) and PINN. It is shown that our method can significantly outperform both NN and PINN under dynamic boundary condition as well as retaining its full capability as a forward model.

Paper Structure

This paper contains 5 sections, 1 equation, 2 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Problem Statement
  3. Proposed Method
  4. Experiments
  5. Conclusion

Figures (2)

  • Figure 1: Boundary conditions of an air-filled capacitor. Parameter 'd' is allowed to vary. Only the first quadrant (shaded red) of the distribution $V(x,y)$ needs to be solved due to symmetry.
  • Figure 2: (Top) $V'$ plots at decoder corresponding to varying $d$. (Lower left) Inverse prediction using proposed method. (Lower right) Reconstructed $V'$ vs groundtruth (SOR) and the sum of squared error.