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Approaching a realistic force balance in geodynamo simulations.

ABSTRACT: Earth sustains its magnetic field by a dynamo process driven by convection in the liquid outer core. Geodynamo simulations have been successful in reproducing many observed properties of the geomagnetic field. However, although theoretical considerations suggest that flow in the core is governed by a balance between Lorentz force, rotational force, and buoyancy (called MAC balance for Magnetic, Archimedean, Coriolis) with only minute roles for viscous and inertial forces, dynamo simulations must use viscosity values that are many orders of magnitude larger than in the core, due to computational constraints. In typical geodynamo models, viscous and inertial forces are not much smaller than the Coriolis force, and the Lorentz force plays a subdominant role; this has led to conclusions that these simulations are viscously controlled and do not represent the physics of the geodynamo. Here we show, by a direct analysis of the relevant forces, that a MAC balance can be achieved when the viscosity is reduced to values close to the current practical limit. Lorentz force, buoyancy, and the uncompensated (by pressure) part of the Coriolis force are of very similar strength, whereas viscous and inertial forces are smaller by a factor of at least 20 in the bulk of the fluid volume. Compared with nonmagnetic convection at otherwise identical parameters, the dynamo flow is of larger scale and is less invariant parallel to the rotation axis (less geostrophic), and convection transports twice as much heat, all of which is expected when the Lorentz force strongly influences the convection properties.

SUBMITTER: Yadav RK

PROVIDER: S-EPMC5087023 | biostudies-literature | 2016 Oct

REPOSITORIES: biostudies-literature

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Approaching a realistic force balance in geodynamo simulations.

Yadav Rakesh K RK Gastine Thomas T Christensen Ulrich R UR Wolk Scott J SJ Poppenhaeger Katja K

Proceedings of the National Academy of Sciences of the United States of America 20161010 43

Earth sustains its magnetic field by a dynamo process driven by convection in the liquid outer core. Geodynamo simulations have been successful in reproducing many observed properties of the geomagnetic field. However, although theoretical considerations suggest that flow in the core is governed by a balance between Lorentz force, rotational force, and buoyancy (called MAC balance for Magnetic, Archimedean, Coriolis) with only minute roles for viscous and inertial forces, dynamo simulations must ...[more]

PMID: 27790991

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Project description:IntroductionThe value approximation bias is known to lead to suboptimal policies or catastrophic overestimation bias accumulation that prevent the agent from making the right decisions between exploration and exploitation. Algorithms have been proposed to mitigate the above contradiction. However, we still lack an understanding of how the value bias impact performance and a method for efficient exploration while keeping stable updates. This study aims to clarify the effect of the value bias and improve the reinforcement learning algorithms to enhance sample efficiency.MethodsThis study designs a simple episodic tabular MDP to research value underestimation and overestimation in actor-critic methods. This study proposes a unified framework called Realistic Actor-Critic (RAC), which employs Universal Value Function Approximators (UVFA) to simultaneously learn policies with different value confidence-bound with the same neural network, each with a different under overestimation trade-off.ResultsThis study highlights that agents could over-explore low-value states due to inflexible under-overestimation trade-off in the fixed hyperparameters setting, which is a particular form of the exploration-exploitation dilemma. And RAC performs directed exploration without over-exploration using the upper bounds while still avoiding overestimation using the lower bounds. Through carefully designed experiments, this study empirically verifies that RAC achieves 10x sample efficiency and 25% performance improvement compared to Soft Actor-Critic in the most challenging Humanoid environment. All the source codes are available at https://github.com/ihuhuhu/RAC.DiscussionThis research not only provides valuable insights for research on the exploration-exploitation trade-off by studying the frequency of policies access to low-value states under different value confidence-bounds guidance, but also proposes a new unified framework that can be combined with current actor-critic methods to improve sample efficiency in the continuous control domain.

Dataset Information

Approaching a realistic force balance in geodynamo simulations.

Publications

Approaching a realistic force balance in geodynamo simulations.

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