Range-dynamical low-rank split-step Fourier method for the parabolic wave equation.

Numerical solutions to the parabolic wave equation are plagued by the curse of dimensionality coupled with the Nyquist criterion. As a remedy, a new range-dynamical low-rank split-step Fourier method is developed. The integration scheme scales sub-linearly with the number of classical degrees of freedom in the transverse directions.

Dynamically orthogonal narrow-angle parabolic equations for stochastic underwater sound propagation. Part II: Applications.

The stochastic dynamically orthogonal (DO) narrow-angle parabolic equations (NAPEs) are exemplified and their properties and capabilities are described using three new two-dimensional stochastic range-independent and range-dependent test cases with uncertain sound speed field, bathymetry, and source location. We validate results against ground-truth deterministic analytical solutions and direct Monte Carlo (MC) predictions of acoustic pressure and transmission loss fields. We verify the stochastic convergence and computational advantages of the DO-NAPEs and discuss the differences with normal mode approaches.

Dynamically orthogonal narrow-angle parabolic equations for stochastic underwater sound propagation. Part I: Theory and schemes.

Robust informative acoustic predictions require precise knowledge of ocean physics, bathymetry, seabed, and acoustic parameters. However, in realistic applications, this information is uncertain due to sparse and heterogeneous measurements and complex ocean physics. Efficient techniques are thus needed to quantify these uncertainties and predict the stochastic acoustic wave fields.

Generalized neural closure models with interpretability.

Improving the predictive capability and computational cost of dynamical models is often at the heart of augmenting computational physics with machine learning (ML). However, most learning results are limited in interpretability and generalization over different computational grid resolutions, initial and boundary conditions, domain geometries, and physical or problem-specific parameters. In the present study, we simultaneously address all these challenges by developing the novel and versatile methodology of unified neural partial delay differential equations.

Multiscale multiphysics data-informed modeling for three-dimensional ocean acoustic simulation and prediction.

Three-dimensional (3D) underwater sound field computations have been used for a few decades to understand sound propagation effects above sloped seabeds and in areas with strong 3D temperature and salinity variations. For an approximate simulation of effects in nature, the necessary 3D sound-speed field can be made from snapshots of temperature and salinity from an operational data-driven regional ocean model. However, these models invariably have resolution constraints and physics approximations that exclude features that can have strong effects on acoustics, example features being strong submesoscale fronts and nonhydrostatic nonlinear internal waves (NNIWs).