  Enhancing the sparsity of data-driven reduced-order models (ROMs) has gained
increasing attention in recent years. In this work, we analyze an efficient
approach to identifying skillful ROMs with a sparse structure using an
information-theoretic indicator called causation entropy. The causation entropy
quantifies in a statistical way the additional contribution of each term to the
underlying dynamics beyond the information already captured by all the other
terms in the ansatz. By doing so, the causation entropy assesses the importance
of each term to the dynamics before a parameter estimation procedure is
performed. Thus, the approach can be utilized to eliminate terms with little
dynamic impact, leading to a parsimonious structure that retains the essential
physics. To circumvent the difficulty of estimating high-dimensional
probability density functions (PDFs) involved in the causation entropy
computation, we leverage Gaussian approximations for such PDFs, which are
demonstrated to be sufficient even in the presence of highly non-Gaussian
dynamics. The effectiveness of the approach is illustrated by the
Kuramoto-Sivashinsky equation by building sparse causation-based ROMs for
various purposes, such as recovering long-term statistics and inferring
unobserved dynamics via data assimilation with partial observations.
