Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Learning emergent PDEs in a learned emergent space   We extract data-driven, intrinsic spatial coordinates from observations of
the dynamics of large systems of coupled heterogeneous agents. These
coordinates then serve as an emergent space in which to learn predictive models
in the form of partial differential equations (PDEs) for the collective
description of the coupled-agent system. They play the role of the independent
spatial variables in this PDE (as opposed to the dependent, possibly also
data-driven, state variables). This leads to an alternative description of the
dynamics, local in these emergent coordinates, thus facilitating an alternative
modeling path for complex coupled-agent systems. We illustrate this approach on
a system where each agent is a limit cycle oscillator (a so-called
Stuart-Landau oscillator); the agents are heterogeneous (they each have a
different intrinsic frequency $\omega$) and are coupled through the ensemble
average of their respective variables. After fast initial transients, we show
that the collective dynamics on a slow manifold can be approximated through a
learned model based on local "spatial" partial derivatives in the emergent
coordinates. The model is then used for prediction in time, as well as to
capture collective bifurcations when system parameters vary. The proposed
approach thus integrates the automatic, data-driven extraction of emergent
space coordinates parametrizing the agent dynamics, with machine-learning
assisted identification of an "emergent PDE" description of the dynamics in
this parametrization.

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The categories of this paper are: mtrl-th
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ph
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The categories of this paper are: eess
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The categories of this paper are: chao-dyn
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The categories of this paper are: supr-con
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The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-th
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The categories of this paper are: math
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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: comp-gas