# Gaussian Process Regression of Steering Vectors With Physics-Aware Deep Composite Kernels for Augmented Listening

arXiv: https://arxiv.org/abs/2509.02571 · HTML: https://mlsanity.com/paper/2509.02571/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 31 of its 101 references that are in the map.
- First posted on arXiv 20 Aug 2025.

## Builds on (most cited first, 30 of 31)

- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks](https://mlsanity.com/paper/2207.10289/) (2022)
- [An Expert's Guide to Training Physics-informed Neural Networks](https://mlsanity.com/paper/2308.08468/) (2023)
- [Learning in Sinusoidal Spaces with Physics-Informed Neural Networks](https://mlsanity.com/paper/2109.09338/) (2021)
- [EasyCom: An Augmented Reality Dataset to Support Algorithms for Easy Communication in Noisy Environments](https://mlsanity.com/paper/2107.04174/) (2021)
- [Data vs. Physics: The Apparent Pareto Front of Physics-Informed Neural Networks](https://mlsanity.com/paper/2105.00862/) (2021)
- [Differentiable Artificial Reverberation](https://mlsanity.com/paper/2105.13940/) (2021)
- [Sound field reconstruction in rooms: inpainting meets super-resolution](https://mlsanity.com/paper/2001.11263/) (2020)
- [Room impulse response reconstruction with physics-informed deep learning](https://mlsanity.com/paper/2401.01206/) (2024)
- [Implicit neural representation with physics-informed neural networks for the reconstruction of the early part of room impulse responses](https://mlsanity.com/paper/2306.11509/) (2023)
- [Reconstruction of Sound Field through Diffusion Models](https://mlsanity.com/paper/2312.08821/) (2023)
- [Fast evaluation of spherical harmonics with sphericart](https://mlsanity.com/paper/2302.08381/) (2023)
- [HRTF upsampling with a generative adversarial network using a gnomonic equiangular projection](https://mlsanity.com/paper/2306.05812/) (2023)
- [NIIRF: Neural IIR Filter Field for HRTF Upsampling and Personalization](https://mlsanity.com/paper/2402.17907/) (2024)
- [Acoustic Space Learning for Sound Source Separation and Localization on Binaural Manifolds](https://mlsanity.com/paper/1402.2683/) (2014)
- [FRA-RIR: Fast Random Approximation of the Image-source Method](https://mlsanity.com/paper/2208.04101/) (2022)
- [Head-Related Transfer Function Interpolation from Spatially Sparse Measurements Using Autoencoder with Source Position Conditioning](https://mlsanity.com/paper/2207.10967/) (2022)
- [HRTF Field: Unifying Measured HRTF Magnitude Representation with Neural Fields](https://mlsanity.com/paper/2210.15196/) (2022)
- [Generative adversarial networks with physical sound field priors](https://mlsanity.com/paper/2308.00426/) (2023)
- [Deep Sound Field Reconstruction in Real Rooms: Introducing the ISOBEL Sound Field Dataset](https://mlsanity.com/paper/2102.06455/) (2021)
- [Neural Fourier Shift for Binaural Speech Rendering](https://mlsanity.com/paper/2211.00878/) (2022)
- [Speech dereverberation constrained on room impulse response characteristics](https://mlsanity.com/paper/2407.08657/) (2024)
- [Neural Steerer: Novel Steering Vector Synthesis with a Causal Neural Field over Frequency and Source Positions](https://mlsanity.com/paper/2305.04447/) (2023)
- [HRTF Interpolation using a Spherical Neural Process Meta-Learner](https://mlsanity.com/paper/2310.13430/) (2023)
- [Sound field reconstruction using neural processes with dynamic kernels](https://mlsanity.com/paper/2311.05188/) (2023)
- [Sound Field Reconstruction Using a Compact Acoustics-informed Neural Network](https://mlsanity.com/paper/2402.08904/) (2024)
- [Point Neuron Learning: A New Physics-Informed Neural Network Architecture](https://mlsanity.com/paper/2408.16969/) (2024)
- [Subspace Hybrid Beamforming for Head-worn Microphone Arrays](https://mlsanity.com/paper/2303.08967/) (2023)

## Abstract (arXiv)

This paper investigates continuous representations of steering vectors over frequency and microphone/source positions for augmented listening (e.g., spatial filtering and binaural rendering), enabling user-parameterized control of the reproduced sound field. Steering vectors have typically been used for representing the spatial response of a microphone array as a function of the look-up direction. The basic algebraic representation of these quantities assuming an idealized environment cannot deal with the scattering effect of the sound field. One may thus collect a discrete set of real steering vectors measured in dedicated facilities and super-resolve (i.e., upsample) them. Recently, physics-aware deep learning methods have been effectively used for this purpose. Such deterministic super-resolution, however, suffers from the overfitting problem due to the non-uniform uncertainty over the measurement space. To solve this problem, we integrate an expressive representation based on the neural field (NF) into the principled probabilistic framework based on the Gaussian process (GP). Specifically, we propose a physics-aware composite kernel that models the directional incoming waves and the subsequent scattering effect. Our comprehensive comparative experiment showed the effectiveness of the proposed method under data insufficiency conditions. In downstream tasks such as speech enhancement and binaural rendering using the simulated data of the SPEAR challenge, the oracle performances were attained with less than ten times fewer measurements.