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.

翻译：我们针对一大类弱形式化问题提出了一个表示定理结果。我们展示了该公式在传统机器学习与数值方法以及新兴技术中的应用实例。最后，我们应用该公式推广了从数据中学习动力系统的多元占据核（MOCK）方法，提出了更一般的里斯占据核（ROCK）方法。我们推广的方法在测试的大多数基准上均具有更高的计算效率和更好的性能表现。