  Conventional offline training of reduced-order bases in a predetermined
region of a parameter space leads to parametric reduced-order models that are
vulnerable to extrapolation. This vulnerability manifests itself whenever a
queried parameter point lies in an unexplored region of the parameter space.
This paper addresses this issue by presenting an in-situ, adaptive framework
for nonlinear model reduction where computations are performed by default
online, and shifted offline as needed. The framework is based on the concept of
a database of local Reduced-Order Bases (ROBs), where locality is defined in
the parameter space of interest. It achieves accuracy by updating on-the-fly a
pre-computed ROB, and approximating the solution of a dynamical system along
its trajectory using a sequence of most-appropriate local ROBs. It achieves
efficiency by managing the dimension of a local ROB, and incorporating
hyperreduction in the process. While sufficiently comprehensive, the framework
is described in the context of dynamic multiscale computations in solid
mechanics. In this context, even in a nonparametric setting of the macroscale
problem and when all offline, online, and adaptation overhead costs are
accounted for, the proposed computational framework can accelerate a single
three-dimensional, nonlinear, multiscale computation by an order of magnitude,
without compromising accuracy.
