Congratulations to Abhinav Gupta, a Ph.D candidate in the MSEAS group, for being awarded the 2020-2021 MathWorks Mechanical Engineering Fellowship! The MathWorks Engineering Fellowships are awarded to the top nominees from all of the academic departments in the School of Engineering, who are using MATLAB and/or Simulink to advance discovery and innovation across disciplines. All the best to Abhinav!

Developing accurate and computationally efficient models for ocean acoustics is inherently challenging due to several factors including the complex physical processes and the need to provide results on a large range of scales. Furthermore, the ocean itself is an inherently dynamic environment within the multiple scales. Even if we could measure the exact properties at a specific instant, the ocean will continue to change in the smallest temporal scales, ever increasing the uncertainty in the ocean prediction. In this work, we explore ocean acoustic prediction from the basics of the wave equation and its derivation. We then explain the deterministic implementations of the Parabolic Equation, Ray Theory, and Level Sets methods for ocean acoustic computation. We investigate methods for evolving stochastic fields using direct Monte Carlo, Empirical Orthogonal Functions, and adaptive Dynamically Orthogonal (DO) differential equations. As we evaluate the potential of Reduced-Order Models for stochastic ocean acoustics prediction, for the first time, we derive and implement the stochastic DO differential equations for Ray Tracing (DO-Ray), starting from the differential equations of Ray theory. With a stochastic DO-Ray implementation, we can start from non-Gaussian environmental uncertainties and compute the stochastic acoustic ray fields in a reduced order fashion, all while preserving the complex statistics of the ocean environment and the nonlinear relations with stochastic ray tracing. We outline a deterministic Ray-Tracing model, validate our implementation, and perform Monte Carlo stochastic computation as a basis for comparison. We then present the stochastic DO-Ray methodology with detailed derivations. We develop varied algorithms and discuss implementation challenges and solutions, using again direct Monte Carlo for comparison. We apply the stochastic DO-Ray methodology to three idealized cases of stochastic sound-speed profiles (SSPs): constant-gradients, uncertain deep-sound channel, and a varied sonic layer depth. Through this implementation with non-Gaussian examples, we observe the ability to represent the stochastic ray trace field in a reduced order fashion.

Time-optimal paths are evaluated by VISIR (“discoVerIng Safe and effIcient Routes”), a graph-search ship routing model, with respect to the solution of the fundamental differential equations governing optimal paths in a dynamic wind-wave environment. The evaluation exercise makes use of identical setups: topological constraints, dynamic wave environmental conditions, and vessel-ocean parametrizations, while advection by external currents is not considered. The emphasis is on predicting the time-optimal ship headings and Speeds Through Water constrained by dynamic ocean wave fields. VISIR upgrades regarding angular resolution, time-interpolation, and static navigational safety constraints are introduced. The deviations of the graph-search results relative to the solution of the exact differential equations in both the path duration and length are assessed. They are found to be of the order of the discretization errors, with VISIR’s solution converging to that of the differential equation for sufficient resolution.

Congratulations to Chinmay Kulkarni, a Ph.D candidate in the MSEAS group, for being awarded the 2020 MathWorks prize for outstanding doctoral research! The MathWorks prize is awarded by the MIT Center of Computational Science and Engineering. All the best to Chinmay!

Congratulations to Jing Lin on his graduation! Jing received an SM from Mechanical Engineering for his research on “Minimum-Correction Second-Moment Matching: Theory, Algorithms and Applications” with our MSEAS group at MIT.