Learning-based Physics-Constrained Neural Kernel for Sound Field Estimation With Source-Position-Dependent Directional Weighting

Physics-informed machine learning incorporates physical principles --often expressed via differential operators-- into data-driven models. While physics-informed neural networks (PINNs) dominate empirical applications, the complexity of neural network architectures and optimization landscapes hinders the development of a corresponding learning theory. In turn, kernel methods offer an appealing alternative with closed-form solutions and analytical tractability, yet existing guarantees primarily cover the well-specified setting where the target belongs to the native Reproducing Kernel Hilbert Space (RKHS). This imposes unrealistic regularity assumptions that physical targets often fail to satisfy. In this paper, we introduce and analyze Physics-Informed Kernel methodS (PIKS). We establish the universal consistency of PIKS for linear differential constraints, proving that for universal kernels (such as Gaussian or Matérn), the estimator asymptotically learns the target while satisfying physical constraints. We further derive finite-sample bounds under suitable source conditions. Our analysis is based on extending classical operator-theoretic analysis of kernel methods to physics-informed machine learning. Numerical experiments demonstrate that PIKS can be competitive with PINNs and traditional finite element methods.

Estimating a speaker's head orientation from audio can provide valuable information in smart environments, meetings, and driver monitoring. We propose a novel approach that leverages the phase component of the short-time Fourier transform from a single microphone array as input to a deep neural network combining convolutional, recurrent, and self-attention layers. Unlike prior methods that use physics-informed handcrafted features or raw waveform inputs, our approach enables robust learning from simulated and real data. Trained on a large-scale dataset generated with voice directivity patterns and fine-tuned on real recordings, our model achieves state-of-the-art accuracy, outperforming baselines under both clean and noisy conditions. Personalization experiments further demonstrate significant gains, reaching a mean angular error of 11.3 degrees when adapting to individual users and environments.

In this paper, we propose a reconstruction framework that leverages the Wavelet Scattering Transform (WST) as a multi-scale feature extractor to impose statistical priors under sparse observation conditions. The reconstruction problem is formulated as an optimization task and solved using a neural field, with the WST incorporated into the training loss function. As a proof of concept, we validate the proposed method on HRTF upsampling. A masking strategy is applied to the WST coefficients, resulting in a two-phase procedure. The first phase learns a binary mask from a small multi-subject dataset, while the second phase applies the learned mask to the WST coefficients of an individual HRTF to preserve informative statistical structures during reconstruction. Validation against baseline methods, which also serve as an ablation study of the different components of the framework, demonstrates the effectiveness of the proposed approach.