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Spatial Interpolation of Room Impulse Responses based on Deeper Physics-Informed Neural Networks with Residual Connections

Ken Kurata, Gen Sato, Izumi Tsunokuni, Yusuke Ikeda

TL;DR

A deeper PINN architecture with residual connections is developed and how network depth affects estimation performance is analyzed, indicating that the residual PINN with sinusoidal activations achieves the highest accuracy for both interpolation and extrapolation of RIRs.

Abstract

The room impulse response (RIR) characterizes sound propagation in a room from a loudspeaker to a microphone under the linear time-invariant assumption. Estimating RIRs from a limited number of measurement points is crucial for sound propagation analysis and visualization. Physics-informed neural networks (PINNs) have recently been introduced for accurate RIR estimation by embedding governing physical laws into deep learning models; however, the role of network depth has not been systematically investigated. In this study, we developed a deeper PINN architecture with residual connections and analyzed how network depth affects estimation performance. We further compared activation functions, including tanh and sinusoidal activations. Our results indicate that the residual PINN with sinusoidal activations achieves the highest accuracy for both interpolation and extrapolation of RIRs. Moreover, the proposed architecture enables stable training as the depth increases and yields notable improvements in estimating reflection components. These results provide practical guidelines for designing deep and stable PINNs for acoustic-inverse problems.

Spatial Interpolation of Room Impulse Responses based on Deeper Physics-Informed Neural Networks with Residual Connections

TL;DR

A deeper PINN architecture with residual connections is developed and how network depth affects estimation performance is analyzed, indicating that the residual PINN with sinusoidal activations achieves the highest accuracy for both interpolation and extrapolation of RIRs.

Abstract

The room impulse response (RIR) characterizes sound propagation in a room from a loudspeaker to a microphone under the linear time-invariant assumption. Estimating RIRs from a limited number of measurement points is crucial for sound propagation analysis and visualization. Physics-informed neural networks (PINNs) have recently been introduced for accurate RIR estimation by embedding governing physical laws into deep learning models; however, the role of network depth has not been systematically investigated. In this study, we developed a deeper PINN architecture with residual connections and analyzed how network depth affects estimation performance. We further compared activation functions, including tanh and sinusoidal activations. Our results indicate that the residual PINN with sinusoidal activations achieves the highest accuracy for both interpolation and extrapolation of RIRs. Moreover, the proposed architecture enables stable training as the depth increases and yields notable improvements in estimating reflection components. These results provide practical guidelines for designing deep and stable PINNs for acoustic-inverse problems.
Paper Structure (21 sections, 14 equations, 7 figures, 4 tables)

This paper contains 21 sections, 14 equations, 7 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. method
  4. Physics-informed neural networks (Conventional Method)
  5. Loss Functions
  6. Network Architecture
  7. PINNs with residual connections (Proposed Method)
  8. Training Processes
  9. Experimental Setup
  10. Simulation Setup
  11. Network parameters
  12. evaluation method
  13. Results
  14. Evaluation of overall estimation accuracy
  15. Training Stability and Convergence
  16. ...and 6 more sections

Figures (7)

  • Figure 1: Problem of RIR estimation from a limited number of microphones
  • Figure 2: (a) Conventional hidden layers architecture. (b) Proposed hidden layers architecture. (c) Network architecture. Inputs are coordinates $(x,y,z)$ and time $t$. The network is composed of $N$ hidden layers. The loss function is calculated by the output RIRs ${{\boldsymbol{\hat{h}}_m}}(m\in\mathcal{M})$ and measured RIRs ${\boldsymbol{h}_m}$. The network parameters ($\mathbf{w}$ and $\mathbf{b}$) are then optimized by minimizing this total loss function, Eq. (\ref{['PI-SIREN_loss']}), via backpropagation. $\mathcal{M}$ is the set of indices for the estimation points.
  • Figure 3: (a) Room geometry. (b) Magnified view of the estimation region and source position within the room. The sound source is positioned $1.5$ m from the room's center in the positive y-direction. The estimation region is a $0.3$ m cube, centered in the room. Microphones are placed within this estimation region, and the RIRs for this entire region are estimated from the measured signals. The evaluation points are defined by discretizing the estimation region into a $14 \times 14 \times 14$ grid.
  • Figure 4: Arrangement of the measurement points. The points are positioned equidistantly with a $0.05$ m spacing on a sphere with a radius of $0.15$ m. The center of the sphere coincides with the center of the room.
  • Figure 5: The trajectory of the loss function and estimation accuracy of evaluation and measured points. The trajectory of the loss function $\mathcal{L}$ over iterations for models with (a) $N=6$ and (b) $N=18$ hidden layers. (c) NMSE of evaluation points versus the number of hidden layers. (d) NMSE of measurement points versus the number of hidden layers. (e) Frequency-domain NMSE for the best-performing model of each method, where the network depth is selected to maximize performance.
  • ...and 2 more figures