Spatial acoustic properties recovery with deep learning.

The physics-informed neural network (PINN) can recover partial differential equation (PDE) coefficients that remain constant throughout the spatial domain directly from measurements. We propose a spatially dependent physics-informed neural network (SD-PINN), which enables recovering coefficients in spatially dependent PDEs using one neural network, eliminating the requirement for domain-specific physical expertise. The network is trained by minimizing a combination of loss functions involving data-fitting and physical constraints, in which the requirement for satisfying the assumed governing PDE is encoded. For the recovery of spatially two-dimensional (2D) PDEs, we store the PDE coefficients at all locations in the 2D region of interest into a matrix and incorporate a low-rank assumption for this matrix to recover the coefficients at locations without measurements. We apply the SD-PINN to recovering spatially dependent coefficients of the wave equation to reveal the spatial distribution of acoustic properties in the inhomogeneous medium.

Eigenvalues of the noise covariance matrix in ocean waveguides.

The eigenvalue (EV) spectra of the theoretical noise covariance matrix (CM) and observed sample CM provide information about the environment, source, and noise generation. This paper investigates these spectra for vertical line arrays (VLAs) and horizontal line arrays (HLAs) in deep and shallow water numerically. Empirically, the spectra are related to the width of the conventional beamforming output in angle space. In deep water, the HLA noise CM tends to be isotropic regardless of the sound speed profile. Thus, the EV spectrum approaches a step function. In contrast, the VLA noise CM is non-isotropic, and the EVs of the CM jump in two steps. The EVs before the first jump are due to sea surface noise, while those between the first and second jump are due to bottom-reflected noise. In shallow water, the VLA noise CM is affected by the environment (sound speed profile and seabed density, sound speed, attenuation, and layers) and array depth, the EVs have a more complicated structure. For Noise09 VLA experimental data, the noise sample CM EVs match the waveguide noise model better than the three-dimensional isotropic noise model.

Geoacoustic inversion using Bayesian optimization with a Gaussian process surrogate model.

Geoacoustic inversion can be a computationally expensive task in high-dimensional parameter spaces, typically requiring thousands of forward model evaluations to estimate the geoacoustic environment. We demonstrate Bayesian optimization (BO), an efficient global optimization method capable of estimating geoacoustic parameters in seven-dimensional space within 100 evaluations instead of thousands. BO iteratively searches parameter space for the global optimum of an objective function, defined in this study as the Bartlett power. Each step consists of fitting a Gaussian process surrogate model to observed data and then choosing a new point to evaluate using a heuristic acquisition function. The ideal acquisition function balances exploration of the parameter space in regions with high uncertainty with exploitation of high-performing regions. Three acquisition functions are evaluated: upper confidence bound, expected improvement (EI), and logarithmically transformed EI. BO is demonstrated for both simulated and experimental data from a shallow-water environment and rapidly estimates optimal parameters while yielding results comparable to differential evolution optimization.

Predicting ocean pressure field with a physics-informed neural network.

Ocean sound pressure field prediction, based on partially measured pressure magnitudes at different range-depths, is presented. Our proposed machine learning strategy employs a trained neural network with range-depth as input and outputs complex acoustic pressure at the location. We utilize a physics-informed neural network (PINN), fitting sampled data while considering the additional information provided by the partial differential equation (PDE) governing the ocean sound pressure field. In vast ocean environments with kilometer-scale ranges, pressure fields exhibit rapidly fluctuating phases, even at frequencies below 100 Hz, posing a challenge for neural networks to converge to accurate solutions. To address this, we utilize the envelope function from the parabolic-equation technique, fundamental in ocean sound propagation modeling. The envelope function shows slower variations across ranges, enabling PINNs to predict sound pressure in an ocean waveguide more effectively. Additional PDE information allows PINNs to capture PDE solutions even with a limited amount of training data, distinguishing them from purely data-driven machine learning approaches that require extensive datasets. Our approach is validated through simulations and using data from the SWellEx-96 experiment.

Uncertainty quantification for direction-of-arrival estimation with conformal prediction.

Uncertainty quantification (UQ) of deep learning (DL)-based acoustic estimation methods is useful for establishing confidence in the predictions. This is crucial to enable the real-world applicability of DL-based systems for acoustic tasks. Specifically, it is proposed to use conformal prediction (CP) for UQ in direction-of-arrival (DOA) estimation. CP is a statistically rigorous method to provide confidence intervals for an estimated quantity without making distributional assumptions. With CP, confidence intervals are computed via quantiles of user-defined scores. This easy-to-use method can be applied to any trained classification/regression model if an appropriate score function is chosen. The proposed approach shows the potential to enhance the real-time applicability of DL methods for DOA estimation. The advantages of CP are illustrated for different DL methods for DOA estimation in the presence of commonly occurring environmental uncertainty. Codes are available online (https://github.com/NoiseLabUCSD/ConformalPrediction).

Graph-based sequential beamforming.

This paper presents a Bayesian estimation method for sequential direction finding. The proposed method estimates the number of directions of arrivals (DOAs) and their DOAs performing operations on the factor graph. The graph represents a statistical model for sequential beamforming. At each time step, belief propagation predicts the number of DOAs and their DOAs using posterior probability density functions (pdfs) from the previous time and a different Bernoulli-von Mises state transition model. Variational Bayesian inference then updates the number of DOAs and their DOAs. The method promotes sparse solutions through a Bernoulli-Gaussian amplitude model, is gridless, and provides marginal posterior pdfs from which DOA estimates and their uncertainties can be extracted. Compared to nonsequential approaches, the method can reduce DOA estimation errors in scenarios involving multiple time steps and time-varying DOAs. Simulation results demonstrate performance improvements compared to state-of-the-art methods. The proposed method is evaluated using ocean acoustic experimental data.

Inversion in an uncertain ocean using Gaussian processes.

Gaussian processes (GPs) can capture correlation of the acoustic field at different depths in the ocean. This feature is exploited in this work for pre-processing acoustic data before these are employed for source localization and environmental inversion using matched field inversion (MFI) in an underwater waveguide. Via the application of GPs, the data are denoised and interpolated, generating densely populated acoustic fields at virtual arrays, which are then used as data in MFI. Replicas are also computed at the virtual receivers at which field predictions are made. The correlations among field measurements at distinct spatial points are manifested through the selection of kernel functions. These rely on hyperparameters, that are estimated through a maximum likelihood process for optimal denoising and interpolation. The approach, employing Gaussian and Matérn kernels, is tested on synthetic and real data with both an exhaustive search and genetic algorithms and is found to be superior to conventional beamformer MFI. It is also shown that the Matérn kernel, providing more degrees of freedom because of an increased number of hyperparameters, is preferable over the frequently used Gaussian kernel.

Bayesian optimization with Gaussian process surrogate model for source localization.

Source localization with a geoacoustic model requires optimizing the model over a parameter space of range and depth with the objective of matching a predicted sound field to a field measured on an array. We propose a sample-efficient sequential Bayesian optimization strategy that models the objective function as a Gaussian process (GP) surrogate model conditioned on observed data. Using the mean and covariance functions of the GP, a heuristic acquisition function proposes a candidate in parameter space to sample, balancing exploitation (sampling around the best observed objective function value) and exploration (sampling in regions of high variance in the GP). The candidate sample is evaluated, and the GP conditioned on the updated data. Optimization proceeds sequentially until a fixed budget of evaluations is expended. We demonstrate source localization for a shallow-water waveguide using Monte Carlo simulations and experimental data from an acoustic source tow. Compared to grid search and quasi-random sampling strategies, simulations and experimental results indicate the Bayesian optimization strategy converges on optimal solutions rapidly.

Compressive frequency-difference direction-of-arrival estimation.

Direction-of-arrival estimation is difficult for signals spatially undersampled by more than half the wavelength. Frequency-difference beamforming [Abadi, Song, and Dowling (2012). J. Acoust. Soc. Am. 132, 3018-3029] offers an alternative approach to avoid such spatial aliasing by using multifrequency signals and processing them at a lower frequency, the difference-frequency. As with the conventional beamforming method, lowering the processing frequency sacrifices spatial resolution due to a beam broadening. Thus, unconventional beamforming is detrimental to the ability to distinguish between closely spaced targets. To overcome spatial resolution deterioration, we propose a simple yet effective method by formulating the frequency-difference beamforming as a sparse signal reconstruction problem. Similar to compressive beamforming, the improvement (compressive frequency-difference beamforming) promotes sparse nonzero elements to obtain a sharp estimate of the spatial direction-of-arrival spectrum. Analysis of the resolution limit demonstrates that the proposed method outperforms the conventional frequency-difference beamforming in terms of separation if the signal-to-noise ratio exceeds 4 dB. Ocean data from the FAF06 experiment support the validity.

Recovery of spatially varying acoustical properties via automated partial differential equation identification.

Observable dynamics, such as waves propagating on a surface, are generally governed by partial differential equations (PDEs), which are determined by the physical properties of the propagation media. The spatial variations of these properties lead to spatially dependent PDEs. It is useful in many fields to recover the variations from the observations of dynamical behaviors on the material. A method is proposed to form a map of the physical properties' spatial variations for a material via data-driven spatially dependent PDE identification and applied to recover acoustical properties (viscosity, attenuation, and phase speeds) for propagating waves. The proposed data-driven PDE identification scheme is based on ℓ1-norm minimization. It does not require any PDE term that is assumed active from the prior knowledge and is the first approach that is capable of identifying spatially dependent PDEs from measurements of phenomena. In addition, the method is efficient as a result of its non-iterative nature and can be robust against noise if used with an integration transformation technique. It is demonstrated in multiple experimental settings, including real laser measurements of a vibrating aluminum plate. Codes and data are available online at https://tinyurl.com/4wza8vxs.

Blind source separation by long-term monitoring: A variational autoencoder to validate the clustering analysis.

Noise exposure influences the comfort and well-being of people in several contexts, such as work or learning environments. For instance, in offices, different kind of noises can increase or drop the employees' productivity. Thus, the ability of separating sound sources in real contexts plays a key role in assessing sound environments. Long-term monitoring provide large amounts of data that can be analyzed through machine and deep learning algorithms. Based on previous works, an entire working day was recorded through a sound level meter. Both sound pressure levels and the digital audio recording were collected. Then, a dual clustering analysis was carried out to separate the two main sound sources experienced by workers: traffic and speech noises. The first method exploited the occurrences of sound pressure levels via Gaussian mixture model and K-means clustering. The second analysis performed a semi-supervised deep clustering analyzing the latent space of a variational autoencoder. Results show that both approaches were able to separate the sound sources. Spectral matching and the latent space of the variational autoencoder validated the assumptions underlying the proposed clustering methods.

Generative models for sound field reconstruction.

This work examines the use of generative adversarial networks for reconstructing sound fields from experimental data. It is investigated whether generative models, which learn the underlying statistics of a given signal or process, can improve the spatio-temporal reconstruction of a sound field by extending its bandwidth. The problem is significant as acoustic array processing is naturally band limited by the spatial sampling of the sound field (due to the difficulty to satisfy the Nyquist criterion in space domain at high frequencies). In this study, the reconstruction of spatial room impulse responses in a conventional room is tested based on three different generative adversarial models. The results indicate that the models can improve the reconstruction, mostly by recovering some of the sound field energy that would otherwise be lost at high frequencies. There is an encouraging outlook in the use of statistical learning models to overcome the bandwidth limitations of acoustic sensor arrays. The approach can be of interest in other areas, such as computational acoustics, to alleviate the classical computational burden at high frequencies.

Deep transfer learning-based variable Doppler underwater acoustic communications.

This paper proposes a deep transfer learning (DTL)-based variable Doppler frequency-hopping binary frequency-shift keying underwater acoustic communication system. The system uses a convolutional neural network (CNN) as the demodulation module of the receiver. This approach directly demodulates the received signal without estimating the Doppler. The DTL first uses the simulated communication signal data to complete the CNN training. It then copies a part of the convolution layers from the pre-trained CNN to the target CNN. After randomly initializing the remaining layers for the target CNN, it is trained by the data samples from the specific communication scenarios. During the training process, the CNN learns the corresponding frequency from each symbol in the selected frequency-hopping group through the Mel-spectrograms. Simulation and experimental data processing results show that the performance of the proposed system is better than conventional systems, especially when the transmitter and receiver of the communication system are in variable speed motion in shallow water acoustic channels.

Reducing echo state network size with controllability matrices.

Echo state networks are a fast training variant of recurrent neural networks excelling at approximating nonlinear dynamical systems and time series prediction. These machine learning models act as nonlinear fading memory filters. While these models benefit from quick training and low complexity, computation demands from a large reservoir matrix are a bottleneck. Using control theory, a reduced size replacement reservoir matrix is found. Starting from a large, task-effective reservoir matrix, we form a controllability matrix whose rank indicates the active sub-manifold and candidate replacement reservoir size. Resulting time speed-ups and reduced memory usage come with minimal error increase to chaotic climate reconstruction or short term prediction. Experiments are performed on simple time series signals and the Lorenz-1963 and Mackey-Glass complex chaotic signals. Observing low error models shows variation of active rank and memory along a sequence of predictions.

Gridless sparse covariance-based beamforming via alternating projections including co-prime arrays.

This paper presents gridless sparse processing for direction-of-arrival (DOA) estimation. The method solves a gridless version of sparse covariance-based estimation using alternating projections. Gridless sparse DOA estimation is represented by the reconstruction of Toeplitz-structured low-rank matrices, which our method recovers by alternatively projecting a solution matrix. Compared to the existing gridless sparse methods, our method improves speed and accuracy and considers non-uniformly configured linear arrays. High-resolution and reliable DOA estimation are achieved even with single-snapshot data, coherent sources, and non-uniform arrays. Simulation results demonstrate performance improvements compared to the existing DOA estimators, including gridless sparse methods. The method is illustrated using experimental data from a real ocean experiment.

Conditional Wasserstein generative adversarial networks applied to acoustic metamaterial design.

This work presents a method for the reduction of the total scattering cross section (TSCS) for a planar configuration of cylinders by means of generative modeling and deep learning. Currently, the minimization of TSCS requires repeated forward modelling at considerable computer resources, whereas deep learning can do this more efficiently. The conditional Wasserstein generative adversarial networks (cWGANs) model is proposed for minimization of TSCS in two dimensions by combining Wasserstein generative adversarial networks with convolutional neural networks to simulate TSCS of configuration of rigid scatterers. The proposed cWGAN model is enhanced by adding to it a coordinate convolution (CoordConv) layer. For a given number of cylinders, the cWGAN model generates images of 2D configurations of cylinders that minimize the TSCS. The proposed generative model is illustrated with examples for planar uniform configurations of rigid cylinders.

Automated partial differential equation identification.

Inspired by recent developments in data-driven methods for partial differential equation (PDE) estimation, we use sparse modeling techniques to automatically estimate PDEs from data. A dictionary consisting of hypothetical PDE terms is constructed using numerical differentiation. Given data, PDE terms are selected assuming a parsimonious representation, which is enforced using a sparsity constraint. Unlike previous PDE identification schemes, we make no assumptions about which PDE terms are responsible for a given field. The approach is demonstrated on synthetic and real video data, with physical phenomena governed by wave, Burgers, and Helmholtz equations. Codes are available at https://github.com/NoiseLab-RLiu/Automate-PDE-identification.

Sequential sparse Bayesian learning for time-varying direction of arrival.

This paper presents methods for the estimation of the time-varying directions of arrival (DOAs) of signals emitted by moving sources. Following the sparse Bayesian learning (SBL) framework, prior information of unknown source amplitudes is modeled as a multi-variate Gaussian distribution with zero-mean and time-varying variance parameters. For sequential estimation of the unknown variance, we present two sequential SBL-based methods that propagate statistical information across time to improve DOA estimation performance. The first method heuristically calculates the parameters of an inverse-gamma hyperprior based on the source signal estimate from the previous time step. In addition, a second sequential SBL method is proposed, which performs a prediction step to calculate the prior distribution of the current variance parameter from the variance parameter estimated at the previous time step. The SBL-based sequential processing provides high-resolution DOA tracking capabilities. Performance improvements are demonstrated by using simulated data as well as real data from the SWellEx-96 experiment.

Sparse planar arrays for azimuth and elevation using experimental data.

Sparse arrays are special geometrical arrangements of sensors which overcome some of the drawbacks associated with dense uniform arrays and require fewer sensors. For direction finding applications, sparse arrays with the same number of sensors can resolve more sources while providing higher resolution than a dense uniform array. This has been verified numerically and with real data for one-dimensional microphone arrays. In this study the use of nested and co-prime arrays is examined with sparse Bayesian learning (SBL), which is a compressive sensing algorithm, for estimating sparse vectors and support. SBL is an iterative parameter estimation method and can process multiple snapshots as well as multiple frequency data within its Bayesian framework. A multi-frequency variant of SBL is proposed, which accounts for non-flat frequency spectra of the sources. Experimental validation of azimuth and elevation [two-dimensional (2D)] direction-of-arrival (DOA)estimation are provided using sparse arrays and real data acquired in an anechoic chamber with a rectangular array. Both co-prime and nested arrays are obtained by sampling this rectangular array. The SBL method is compared with conventional beamforming and multiple signal classification for 2D DOA estimation of experimental data.

Mode separation with one hydrophone in shallow water: A sparse Bayesian learning approach based on phase speed.

An approach of broadband mode separation in shallow water is proposed using phase speed extracted from one hydrophone and solved with sparse Bayesian learning (SBL). The approximate modal dispersion relation, connecting the horizontal wavenumbers (phase velocities) for multiple frequencies, is used to build the dictionary matrix for SBL. Given a multi-frequency pressure vector on one hydrophone, SBL estimates a set of sparse coefficients for a large number of atoms in the dictionary. With the estimated coefficients and corresponding atoms, the separated normal modes are retrieved. The presented method can be used for impulsive or known-form signals in a shallow-water environment while no bottom information is required. The simulation results demonstrate that the proposed approach is adapted to the environment where both the reflected and refracted modes coexist, whereas the performance of the time warping transformation degrades significantly in this scenario.