  Discovering the governing laws underpinning physical and chemical phenomena
is a key step towards understanding and ultimately controlling systems in
science and engineering. We introduce Discovery of Dynamical Systems via Moving
Horizon Optimization (DySMHO), a scalable machine learning framework for
identifying governing laws in the form of differential equations from
large-scale noisy experimental data sets. DySMHO consists of a novel moving
horizon dynamic optimization strategy that sequentially learns the underlying
governing equations from a large dictionary of basis functions. The sequential
nature of DySMHO allows leveraging statistical arguments for eliminating
irrelevant basis functions, avoiding overfitting to recover accurate and
parsimonious forms of the governing equations. Canonical nonlinear dynamical
system examples are used to demonstrate that DySMHO can accurately recover the
governing laws, is robust to high levels of measurement noise and that it can
handle challenges such as multiple time scale dynamics.
