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

arXiv: https://arxiv.org/abs/2509.25730 · HTML: https://mlsanity.com/paper/2509.25730/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 58 references that are in the map.
- First posted on arXiv 30 Sep 2025.

## Builds on (most cited first, 14 of 14)

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- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [Deep Kernel Learning](https://mlsanity.com/paper/1511.02222/) (2015)
- [Scalable Variational Gaussian Process Classification](https://mlsanity.com/paper/1411.2005/) (2014)
- [Stochastic Variational Deep Kernel Learning](https://mlsanity.com/paper/1611.00336/) (2016)
- [Deep Sigma Point Processes](https://mlsanity.com/paper/2002.09112/) (2020)
- [How to Evaluate Uncertainty Estimates in Machine Learning for Regression?](https://mlsanity.com/paper/2106.03395/) (2021)
- [Predicting waves in fluids with deep neural network](https://mlsanity.com/paper/2201.06628/) (2022)
- [A multi-objective optimization framework for reducing the impact of ship noise on marine mammals](https://mlsanity.com/paper/2402.02647/) (2024)
- [Continual Learning of Range-Dependent Transmission Loss for Underwater Acoustic using Conditional Convolutional Neural Net](https://mlsanity.com/paper/2404.08091/) (2024)
- [MUTE-DSS: A Digital-Twin-Based Decision Support System for Minimizing Underwater Radiated Noise in Ship Voyage Planning](https://mlsanity.com/paper/2508.01907/) (2025)

## Abstract (arXiv)

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.