Scalable Framework for hierarchical design and planning under uncertainty with application to marine vehicles – DARPA/SNWSC

We will develop an information-driven, learning-based mathematical framework for uncertainty quantification (UQ), design, and optimal operation of ultra-high-speed marine vessels, doubling the speed of existing vessels for US Navy special operations. The framework will be scalable with respect to the high number of decision variables and uncertain parameters required by such systems.  It will integrate the design of physical components with control algorithms, and hence it will achieve a holistic design that will replace traditional fragmented processes by a set-based design, i.e., focusing on eliminating poor designs at an early stage and rapidly generating feasibility regions in the design space. This framework will be demonstrated in the context of design and operation of an unconventional Hybrid Hydrofoil H2-SWATH – a concept first proposed by MIT team member S. Brizollara. In foil-borne mode, the vessel reaches 120 knots maximum speed while in extreme sea states it achieves speeds over 60 knots through real-time path planning to avoid excessive waves.

The integrated framework we propose is founded upon the concept of deep networks, and enables simultaneously multi-fidelity modeling, information fusion, scalable learning, and uncertainty quantification. In particular, deep networks offer a general setting under which we can model non-Gaussian response surfaces for quantities of interest (QoI) as a hierarchical composition of nonlinear random maps, which we can learn from diverse data sources. We propose to learn such maps using epi-splines estimates guided by Mori-Zwanzig (MZ) probability density function equations. A major contribution of this proposal is the development of fast parallel solvers that scale linearly with the data and are immune to high dimensionality. Our framework is based on different and complementary scalable UQ methods we propose, starting with uncertainty sets, which are independent of dimensionality, during the early and intermediate design stages, and progressing to probabilistic approaches as we refine the feasibility regions of the design space. We will also address information-driven optimization under uncertainty, and will develop new algorithms for controlling nonlinear systems under uncertainty. We aim to develop methods that simultaneously optimize decisions, accounting for decision maker’s risk averseness, and learn levels of uncertainty and errors for a given design. Motivated by the specific application, i.e., maintaining high speeds at extreme sea states, we will develop optimal path planning algorithms based on Pontryagin’s stochastic maximum principle and also on the stochastic Hamilton-Jacobi-Bellman equation, taking advantage again of our scalable UQ methods.

The proposed project will set the stage for the next generation of design and decision making principles in the Navy, among naval architects, and the broader engineering community. At the methodological level, the project will provide fundamental advances in the areas of multi-fidelity UQ analyses, information fusion and learning, extreme event estimation, large-scale optimization under uncertainty, and multi-stage and risk-averse decision making. More generally, by combining the integrated framework with measures of risk observation models based on MZ/epi-splines or functional series expansions (deep learning stage), and infinite-dimensional optimization we can overcome the long standing “big n” problem. We are already in discussions with the Navatek company and with the Navy (NAVSEA HQ) on the proposed work, and we plan to invite technical representatives from these organizations to our meetings at MIT to receive input from them but also to update them on our progress.