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Acoustic Field Reconstruction in Tubes via Physics-Informed Neural Networks

Xinmeng Luan, Kazuya Yokota, Gary Scavone

TL;DR

This paper tackles reconstructing the time-domain acoustic field in a tube with an unknown radiation model, using pressure observations at the tube open end. It employs physics-informed neural networks to enforce the time-domain horn equation for the velocity potential $\phi$, along with boundary, periodicity, and observation constraints, and introduces two approaches for estimating the radiation coefficients $\alpha$ and $\beta$: PINN-FTM and TOM. Results show that PINN can recover the space-time field under 40 dB SNR noise and unknown radiative parameters, with PINN-FTM delivering balanced and robust predictions of the radiation model, outperforming TOM in noisy settings. This work demonstrates the practicality of PINN-based inverse problems in acoustic tubes and suggests potential extensions to impedance-tube measurements, duct acoustics, and room acoustics.

Abstract

This study investigates the application of Physics-Informed Neural Networks (PINNs) to inverse problems in acoustic tube analysis, focusing on reconstructing acoustic fields from noisy and limited observation data. Specifically, we address scenarios where the radiation model is unknown, and pressure data is only available at the tube's radiation end. A PINNs framework is proposed to reconstruct the acoustic field, along with the PINN Fine-Tuning Method (PINN-FTM) and a traditional optimization method (TOM) for predicting radiation model coefficients. The results demonstrate that PINNs can effectively reconstruct the tube's acoustic field under noisy conditions, even with unknown radiation parameters. PINN-FTM outperforms TOM by delivering balanced and reliable predictions and exhibiting robust noise-tolerance capabilities.

Acoustic Field Reconstruction in Tubes via Physics-Informed Neural Networks

TL;DR

This paper tackles reconstructing the time-domain acoustic field in a tube with an unknown radiation model, using pressure observations at the tube open end. It employs physics-informed neural networks to enforce the time-domain horn equation for the velocity potential , along with boundary, periodicity, and observation constraints, and introduces two approaches for estimating the radiation coefficients and : PINN-FTM and TOM. Results show that PINN can recover the space-time field under 40 dB SNR noise and unknown radiative parameters, with PINN-FTM delivering balanced and robust predictions of the radiation model, outperforming TOM in noisy settings. This work demonstrates the practicality of PINN-based inverse problems in acoustic tubes and suggests potential extensions to impedance-tube measurements, duct acoustics, and room acoustics.

Abstract

This study investigates the application of Physics-Informed Neural Networks (PINNs) to inverse problems in acoustic tube analysis, focusing on reconstructing acoustic fields from noisy and limited observation data. Specifically, we address scenarios where the radiation model is unknown, and pressure data is only available at the tube's radiation end. A PINNs framework is proposed to reconstruct the acoustic field, along with the PINN Fine-Tuning Method (PINN-FTM) and a traditional optimization method (TOM) for predicting radiation model coefficients. The results demonstrate that PINNs can effectively reconstruct the tube's acoustic field under noisy conditions, even with unknown radiation parameters. PINN-FTM outperforms TOM by delivering balanced and reliable predictions and exhibiting robust noise-tolerance capabilities.
Paper Structure (14 sections, 18 equations, 5 figures, 2 tables)

This paper contains 14 sections, 18 equations, 5 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Problem formulation
  3. Governing equation and conditions
  4. Inverse problem statement
  5. Proposed Method
  6. Acoustic field reconstruction via PINNs
  7. Radiation model reconstruction
  8. Validation of the proposed method
  9. Implementation
  10. Results
  11. Acoustic field reconstruction: $\Gamma$
  12. Radiation model reconstruction: $\Lambda$
  13. Discussion
  14. Conclusion

Figures (5)

  • Figure 1: Schematic diagram of acoustic field reconstruction in a tube.
  • Figure 2: PINN architecture.
  • Figure 3: Time-space pressure field along the tube: results from PINN ($\Gamma$) (left), FDM (middle), and the error (absolute difference) between PINN and FDM (right).
  • Figure 4: $p$, $p_t$ and $u_t$ at $x=L$, from PINN ($\Gamma$).
  • Figure 5: The PINN-FTM ($\Lambda$) training progress of $\alpha$ and $\beta$ over epochs.