A future for intelligent autonomous ocean observing systems

Lermusiaux, Pierre F. J.; Subramani, Deepak N.; Lin, Jun; Kulkarni, Chinmay S.; Gupta, Abhinav; Dutt, Arkopal; Lolla, T.; Haley, Patrick J.; Ali, Wael H.; Mirabito, Chris; Jana, Sudip

doi:10.1357/002224017823524035

Cited by 59 publications

(30 citation statements)

References 93 publications

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“…In nature, these vessels are affected by environmental disturbances like wind, waves and ocean currents, often in competition, and often characterized by unpredictable (chaotic) evolutions. * article submitted to AIP Publishing Chaos, Focus Issue: When Machine Learning Meets Complex Systems: Networks, Chaos and Nonlinear Dynamics (2019) This is problematic when one wants to send probes to specific locations, for example when trying to optimize data-assimilation for environmental applications [7,[12][13][14][15]. Most of the times, a dense set of fixed platforms or manned vessels are not economically viable solutions.…”

Section: Introductionmentioning

confidence: 99%

Zermelo’s problem: Optimal point-to-point navigation in 2D turbulent flows using reinforcement learning

Biferale

Bonaccorso

Buzzicotti

et al. 2019

Chaos: An Interdisciplinary Journal of Nonlinear Science

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To find the path that minimizes the time to navigate between two given points in a fluid flow is known as Zermelo's problem. Here, we investigate it by using a Reinforcement Learning (RL) approach for the case of a vessel which has a slip velocity with fixed intensity, Vs, but variable direction and navigating in a 2D turbulent sea. We show that an Actor-Critic RL algorithm is able to find quasi-optimal solutions for both time-independent and chaotically evolving flow configurations. For the frozen case, we also compared the results with strategies obtained analytically from continuous Optimal Navigation (ON) protocols. We show that for our application, ON solutions are unstable for the typical duration of the navigation process, and are therefore not useful in practice. On the other hand, RL solutions are much more robust with respect to small changes in the initial conditions and to external noise, even when Vs is much smaller than the maximum flow velocity. Furthermore, we show how the RL approach is able to take advantage of the flow properties in order to reach the target, especially when the steering speed is small.Zermelo's point-to-point optimal navigation problem in the presence of a complex flow is key for a variety of geophysical and applied instances. In this work, we apply Reinforcement Learning to solve Zermelo's problem in a multi-scale 2d turbulent snapshot for both frozen-in-time velocity configurations and fully time-dependent flows. We show that our approach is able to find the quasi-optimal path to navigate from two distant points with high efficiency, even comparing with policies obtained from optimal control theory. Furthermore, we connect the learned policy with the topological flow structures that must be harnessed by the vessel to navigate fast. Our result can be seen as a first step towards more complicated applications to surface oceanographic problems and/or 3d chaotic and turbulent flows.

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Section: Introductionmentioning

confidence: 99%

Zermelo’s problem: Optimal point-to-point navigation in 2D turbulent flows using reinforcement learning

Biferale

Bonaccorso

Buzzicotti

et al. 2019

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…Their relevance and numerical implementations for tracking smooth decompositions was discussed. Possible future applications of the derived dynamic matrix equations abound over a rich spectrum of needs, from dynamic reduced-order modeling [57,22] and data sciences [41] to adaptive data assimilation [45,7,51] and adaptive path planning and sampling [50,63,46,47]. Downloaded 02/11/20 to 18.10.29.253.…”

Section: Discussionmentioning

confidence: 99%

The Extrinsic Geometry of Dynamical Systems Tracking Nonlinear Matrix Projections

Feppon¹,

Lermusiaux²

2019

SIAM J. Matrix Anal. Appl.

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A generalization of the concepts of extrinsic curvature and Weingarten endomorphism is introduced to study a class of nonlinear maps over embedded matrix manifolds. These (nonlinear) oblique projections generalize (nonlinear) orthogonal projections, i.e., applications mapping a point to its closest neighbor on a matrix manifold. Examples of such maps include the truncated SVD, the polar decomposition, and functions mapping symmetric and nonsymmetric matrices to their linear eigenprojectors. This paper specifically investigates how oblique projections provide their image manifolds with a canonical extrinsic differential structure, over which a generalization of the Weingarten identity is available. By diagonalization of the corresponding Weingarten endomorphism, the manifold principal curvatures are explicitly characterized, which then enables us to (i) derive explicit formulas for the differential of oblique projections and (ii) study the global stability of a governing generic ordinary differential equation (ODE) computing their values. This methodology, exploited for the truncated SVD in [Feppon and Lermusiaux, SIAM J. Matrix Anal. Appl., 39 (2018), pp. 510-538], is generalized to non-Euclidean settings and applied to the four other maps mentioned above and their image manifolds: respectively, the Stiefel, the isospectral, and the Grassmann manifolds and the manifold of fixed rank (nonorthogonal) linear projectors. In all cases studied, the oblique projection of a target matrix is surprisingly the unique stable equilibrium point of the above gradient flow. Three numerical applications concerned with ODEs tracking dominant eigenspaces involving possibly multiple eigenvalues finally showcase the results.

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“…The stochastic Dynamically Orthogonal differential equations have been derived to evolve stochastic fields while preserving its dominant statistics [78,97,25]. With such stochastic predictions, we can use our gained knowledge of the forecast probability distributions to complete non-Gaussian Bayesian data assimilation [80,58] and optimize the data collection using information-based adaptive sampling and principled model learning [44,50,48]. turing the stochastic variation in an ocean's acoustic propagation due to an uncertain SSP, using a dynamic reduced oder representation of the stochastic ray field.…”

Section: Some Of the Practical Acoustic Models And Computational Methmentioning

confidence: 99%

“…This transfer of uncertainty within the context of acoustic tracing is the subject of the present thesis. Once such non-Gaussian uncertainty quantification is for acoustic ray tracing is available, we would be able to complete Bayesian data assimilation [31,44,50] for the joint inversion of acoustic rays and ocean fields. We note that the goal of Bayesian estimation is to estimate the posterior probability of the state we estimate, best combining prior model predictions with observations.…”

Section: Coupled Stochastic Ocean Physics-acoustics Uncertainty Quantmentioning

confidence: 99%

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Stochastic acoustic ray tracing with dynamically orthogonal equations

Humara¹

2020

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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.

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A future for intelligent autonomous ocean observing systems

Cited by 59 publications

References 93 publications

Zermelo’s problem: Optimal point-to-point navigation in 2D turbulent flows using reinforcement learning

Zermelo’s problem: Optimal point-to-point navigation in 2D turbulent flows using reinforcement learning

The Extrinsic Geometry of Dynamical Systems Tracking Nonlinear Matrix Projections

Stochastic acoustic ray tracing with dynamically orthogonal equations

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