A Physics-Guided Probabilistic Surrogate Modeling Framework for Digital Twins of Underwater Radiated Noise

TL;DR

The paper addresses real-time prediction of underwater radiated noise in coastal environments by developing a physics-guided probabilistic digital twin for 3D transmission loss. It combines a physics-informed mean for spreading and absorption with learned bathymetry and geometry encoders and a sparse variational Gaussian process residual to provide calibrated uncertainty. Trained on over 30 million Bellhop3D simulations across seasonal sound-speed profiles and 12.5 Hz–8 kHz, the surrogate delivers sub-second predictions and uncertainty quantification, enabling near real-time operational decision support. Case studies in the Salish Sea demonstrate fast 3D TL mapping, dynamic ship speed optimization to reduce marine mammal exposure, and sensor data assimilation to improve reliability, highlighting the framework’s potential for sustainable and uncertainty-aware maritime operations.

Abstract

Ship traffic is an increasing source of underwater radiated noise in coastal waters, motivating real-time digital twins of ocean acoustics for operational noise mitigation. We present a physics-guided probabilistic framework to predict three-dimensional transmission loss in realistic ocean environments. As a case study, we consider the Salish Sea along shipping routes from the Pacific Ocean to the Port of Vancouver. A dataset of over 30 million source-receiver pairs was generated with a Gaussian beam solver across seasonal sound speed profiles and one-third-octave frequency bands spanning 12.5 Hz to 8 kHz. We first assess sparse variational Gaussian processes (SVGP) and then incorporate physics-based mean functions combining spherical spreading with frequency-dependent absorption. To capture nonlinear effects, we examine deep sigma-point processes and stochastic variational deep kernel learning. The final framework integrates four components: (i) a learnable physics-informed mean that represents dominant propagation trends, (ii) a convolutional encoder for bathymetry along the source-receiver track, (iii) a neural encoder for source, receiver, and frequency coordinates, and (iv) a residual SVGP layer that provides calibrated predictive uncertainty. This probabilistic digital twin facilitates the construction of sound-exposure bounds and worst-case scenarios for received levels. We further demonstrate the application of the framework to ship speed optimization, where predicted transmission loss combined with near-field source models provides sound exposure level estimates for minimizing acoustic impacts on marine mammals. The proposed framework advances uncertainty-aware digital twins for ocean acoustics and illustrates how physics-guided machine learning can support sustainable maritime operations.

Figures (13)

• Figure 1: Illustration of the digital twin framework for ocean soundscape modeling, integrating ship tracks and hydrophone data with physics-based and machine learning solvers for real time acoustic prediction.
• Figure 2: Digital twin framework for real-time voyage optimization, integrating uncertainty-aware acoustic field prediction with vessel routing and speed control.
• Figure 3: Architecture of the probabilistic digital twin. The model integrates a physics-informed mean with neural encoders for bathymetry and geometry, followed by an SVGP residual head for uncertainty-aware prediction.
• Figure 4: Pipeline of the bathymetry encoder. The 128-point bathymetric profile $\Omega$ is processed through convolutional layers, pooling, flattening, and fully connected layers to produce the embedding vector $\mathbf{z}_\Omega$.
• Figure 5: Architecture of the feature encoder. The input vector $\mathbf{x}_g=[\mathbf{X_s},\mathbf{X_r},f]$ is processed through a stack of fully connected layers with batch normalization and GELU activations to produce the latent embedding $\mathbf{z}_g$, which is concatenated with the bathymetry embedding $\mathbf{z}_\Omega$ to form $\mathbf{z}_{\text{lat}}$.