Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exact Recovery of Chaotic Systems from Highly Corrupted Data   Learning the governing equations in dynamical systems from time-varying
measurements is of great interest across different scientific fields. This task
becomes prohibitive when such data is moreover highly corrupted, for example,
due to the recording mechanism failing over unknown intervals of time. When the
underlying system exhibits chaotic behavior, such as sensitivity to initial
conditions, it is crucial to recover the governing equations with high
precision. In this work, we consider continuous time dynamical systems $\dot{x}
= f(x)$ where each component of $f: \mathbb{R}^{d} \rightarrow \mathbb{R}^d$ is
a multivariate polynomial of maximal degree $p$; we aim to identify $f$ exactly
from possibly highly corrupted measurements $x(t_1), x(t_2), \dots, x(t_m)$. As
our main theoretical result, we show that if the system is sufficiently ergodic
that this data satisfies a strong central limit theorem (as is known to hold
for chaotic Lorenz systems), then the governing equations $f$ can be exactly
recovered as the solution to an $\ell_1$ minimization problem -- even if a
large percentage of the data is corrupted by outliers. Numerically, we apply
the alternating minimization method to solve the corresponding constrained
optimization problem. Through several examples of 3D chaotic systems and higher
dimensional hyperchaotic systems, we illustrate the power, generality, and
efficiency of the algorithm for recovering governing equations from noisy and
highly corrupted measurement data.

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The categories of this paper are: chem-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
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The categories of this paper are: quant-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ex
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The categories of this paper are: stat
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ph