This talk addresses the problem of robust identification and (in)validation of hybrid models from noisy data. Given some input/output data the goal is to infer the underlying dynamical system that can interpolate the data within a given noise bound or to check whether there is a model within a model family that can interpolate the data. We define suitable a priori model sets and objective functions that seek "simple" models which can capture the information sparsely encoded in the data streams. Although this leads to generically hard to solve, nonconvex problems, as we show, computationally tractable relaxations can be obtained by exploiting a combination of elements from convex analysis and the classical theory of moments. Moreover, dynamics induce a structure on these optimization problems that can be leveraged to improve efficiency. Finally we make connections between anomaly detection and model invalidation and show how dynamic invariants can be used to algorithmically determine how much data is "enough" for detection.