  Many-query computations, in which a computational model for an engineering
system must be evaluated many times, are crucial in design and control. For
systems governed by partial differential equations (PDEs), typical
high-fidelity numerical models are high-dimensional and too computationally
expensive for the many-query setting. Thus, efficient surrogate models are
required to enable low-cost computations in design and control. This work
presents a physics-preserving reduced model learning approach that targets PDEs
whose quadratic operators preserve energy, such as those arising in governing
equations in many fluids problems. The approach is based on the Operator
Inference method, which fits reduced model operators to state snapshot and time
derivative data in a least-squares sense. However, Operator Inference does not
generally learn a reduced quadratic operator with the energy-preserving
property of the original PDE. Thus, we propose a new energy-preserving Operator
Inference (EP-OpInf) approach, which imposes this structure on the learned
reduced model via constrained optimization. Numerical results using the viscous
Burgers' and Kuramoto-Sivashinksy equation (KSE) demonstrate that EP-OpInf
learns efficient and accurate reduced models that retain this energy-preserving
structure.
