Optimal experimental design (OED) refers to a class of methods for selecting new data collection conditions that minimize the statistical uncertainty in the inferred parameter values of a model. The Fisher information matrix (FIM) gives an estimate of the relative uncertainty in and correlation among the model parameters based on the local curvature of the cost function. FIM-based approaches to OED allow for rapid assessment of many different experimental conditions (e.g., input data type, parameterizations, etc.). In machine learning models, accurate parameter estimates are often not a priority (nor even desirable) as they have no direct physical meaning. Instead, one would like to minimize the uncertainty in the model predictions for several quantities of interest. FIM approaches to OED can be generalized to minimize statistical variance, not in parameters, but in predictions of the quantities of interest. This approach has been applied, for example, to systems biology models of biochemical reaction networks [Transtrum and Qiu, BMC Bioinformatics 13(1), 181 (2012)]. Preliminary application of the FIM to optimize experimental design for source localization in an uncertain ocean environment is a first step towards an efficient machine learning algorithm that produces results with the least uncertainty in the quantities of interest.

In ocean acoustics, many types of optimizations have been employed to locate acoustic sources and estimate the properties of the seabed. How these tasks can take advantage of recent advances in deep learning remains as open questions, especially due to the lack of labeled field data. In this work, a Convolutional Neural Network (CNN) is used to find seabed type and source range simultaneously from 1 s pressure time series from impulsive sounds. Simulated data are used to train the CNN before application to signals from a single hydrophone signal during the 2017 Seabed Characterization Experiment. The training data includes four seabeds representing deep mud, mud over sand, sandy silt, and sand, and a wide range of source parameters. When applied to measured data, the trained CNN predicts expected seabed types and obtains ranges within 0.5 km when the source-receiver range is greater than 5 km, showing the potential for such algorithms to address these problems.

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Broadband spectrograms from surface ships are employed in convolutional neural networks (CNNs) to predict the seabed type, ship speed, and closest point of approach (CPA) range. Three CNN architectures of differing size and depth are trained on different representations of the spectrograms. Multitask learning is employed; the seabed type prediction comes from classification, and the ship speed and CPA range are estimated via regression. Due to the lack of labeled field data, the CNNs are trained on synthetic data generated using measured sound speed profiles, four seabed types, and a random distribution of source parameters. Additional synthetic datasets are used to evaluate the ability of the trained CNNs to interpolate and extrapolate source parameters. The trained models are then applied to a measured data sample from the 2017 Seabed Characterization Experiment (SBCEX 2017). While the largest network provides slightly more accurate predictions on tests with synthetic data, the smallest network generalized better to the measured data sample. With regard to the input data type, complex pressure spectral values gave the most accurate and consistent results for the ship speed and CPA predictions with the smallest network, whereas using absolute values of the pressure provided more accurate results compared to the expected seabed types.

In ocean acoustics, simultaneous estimation of both source-receiver range and environment are complicated by low signal-to-noise ratio (SNR). Range and environment class can be found with a convolutional neural network (CNN), which is chosen because of its ability to find patterns in grid-structured data. The CNN acts on synthetic pressure time series data from a single receiver generated for four canonical environments: deep mud, mud over sand, sandy silt, and sand. Data were split into training and validation sets. The CNN is trained to identify source range and environmental class. The change in performance for different SNR values is evaluated by adding Gaussian-distributed noise. A study is done regarding the impact of having different SNR values for the training and validation datasets. The trained CNN is applied to pressure time series data measured on the APL-UW Intensity Vector Autonomous Receiver system at SBCEX. This study shows that performance depends more on the suitability of the training dataset than on the SNR value, implying that a CNN has potential to both estimate range and environmental class, even when there is low SNR. [Work supported from Office of Naval Research.]