Dynamically Orthogonal Differential Equations for Stochastic and Deterministic Reduced-Order Modeling of Ocean Acoustic Wave Propagation

Accurate and computationally efficient acoustic models are needed for varied marine applications. In this paper, we focus our attention on forward models, which are essential to inverse problems such as imaging and mapping. First, we introduce new dynamically orthogonal (DO) equations for the acoustic wave equation in full generality, allowing for stochastic and spatially heterogeneous parameters. These equations may be spatially discretized and integrated in time numerically. Alternatively, the DO equations may be discretized themselves, admitting a non-intrusive reduced-order approach to solve the stochastic wave equation. We demonstrate the latter with a test case of an acoustic pulse traveling through the ocean with an uncertain sound speed. Second, we adapt the spatially discrete DO approach, typically used to reduce the stochastic dimension, to efficient reduced-order modeling of deterministic 3D acoustic propagation. We solve the 3D parabolic wave equation and show that low-rank solutions rapidly converge to the full-rank solution. Together, these approaches offer novel ways to solve stochastic and deterministic problems with strong or weak scattering at a reduced computational cost.