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Updated: May 29, 2025

Reservoir Condition Pore-scale Imaging of Multiple Fluid Phases Using X-ray Microtomography
Published on: February 25, 2015
Contraction and synchronization in reservoir systems
Adrian S Wong1, Robert S Martin2, Daniel Q Eckhardt3
1Edwards AFB, Air Force Research Laboratory, Jacobs, Technology Inc. and In-Space Propulsion Branch, California 93524, USA.
Abstract:
This paper explores the conditions under which global contraction manifests in the leaky continuous time reservoirs, thus guaranteeing generalized synchronization. Results on continuous time reservoirs make use of the logarithmic norm of the connectivity matrix. Further analysis yields some simple guidelines on how to better construct the connectivity matrix in these systems. Additionally, we outline how the universal approximation property of discrete time reservoirs is readily satisfied by virtue of the activation function being contracting, and how continuous time reservoirs may inherit a limited form of universal approximation by virtue of them overlapping with neural ordinary differential equations. The ability of the reservoir computing framework to universally approximate topological conjugates, along with their fast training, make them a compelling data-driven, black-box surrogate of dynamical systems and a potential candidate for a component of digital twins.
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