ROCK: A variational formulation for occupation kernel methods in Reproducing Kernel Hilbert Spaces
This work provides a more efficient and performant method for learning dynamical systems, which is incremental but improves upon existing techniques in machine learning and numerical methods.
The authors tackled the problem of learning dynamical systems from data by generalizing the multivariate occupation kernel method with a new variational formulation, resulting in the ROCK method which is more computationally efficient and performs better on most benchmarks.
We present a Representer Theorem result for a large class of weak formulation problems. We provide examples of applications of our formulation both in traditional machine learning and numerical methods as well as in new and emerging techniques. Finally we apply our formulation to generalize the multivariate occupation kernel (MOCK) method for learning dynamical systems from data proposing the more general Riesz Occupation Kernel (ROCK) method. Our generalized methods are both more computationally efficient and performant on most of the benchmarks we test against.