A method for the nonintrusive and structure-preserving model reduction of canonical and noncanonical Hamiltonian systems is presented. Based on the idea of operator inference, this technique is provably convergent and reduces to a straightforward linear solve given snapshot data and gray-box knowledge of the system Hamiltonian. Examples involving several hyperbolic partial differential equations show that the proposed method yields reduced models which, in addition to being accurate and stable with respect to the addition of basis modes, preserve conserved quantities well outside the range of their training data.

Despite heavy investment in data management and monitoring platforms, the financial services industry still lacks real-time operational intelligence to enable better business decision-making and prevent systems and service failures and catastrophic trading errors. These outages expose institutions to undue risk and compliance violations that can cost organizations millions of dollars in financial losses and regulatory fines. They also undermine investor confidence and damage firm reputation. Modern financial markets have become more complex that ever fueled by the globalization of capital markets, including a variety of new securities, derivatives and indexes, the evolution of high-frequency trading platforms with millisecond execution windows, more stringent regulations and higher levels of interconnection among different players. This increased complexity is overwhelming legacy systems, resulting in overlooked information and missed opportunities to uncover hidden patterns, relationships and dependencies.