mlsanityData to 14 Oct 2026

ROCK: A variational formulation for occupation kernel methods in Reproducing Kernel Hilbert Spaces

arXiv 2503.13791 ↗First posted 18 Mar 2025stat.ML cs.LGcited by 1

Not on the map. Why?

Abstract (arXiv)

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.

Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 12 of its 33 references that are in the map. First posted on arXiv 18 Mar 2025.

Builds on

12 of 33 references.

References · 12

  1. 2015Deep Residual Learning for Image Recognitioncited by 52,096
  2. 2018Neural Ordinary Differential Equationscited by 3,779
  3. 2019DeepXDE: A deep learning library for solving differential equationscited by 619
  4. 2017Deep learning for universal linear embeddings of nonlinear dynamicscited by 494
  5. 2021Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and controlcited by 137
  6. 2017Learning Deep Neural Network Representations for Koopman Operators of Nonlinear Dynamical Systemscited by 127
  7. 2020SINDy-PI: A Robust Algorithm for Parallel Implicit Sparse Identification of Nonlinear Dynamicscited by 125
  8. 2019Learning Compositional Koopman Operators for Model-Based Controlcited by 67
  9. 2022Discovering Governing Equations from Partial Measurements with Deep Delay Autoencoderscited by 58
  10. 2014A Unifying Framework in Vector-valued Reproducing Kernel Hilbert Spaces for Manifold Regularization and Co-Regularized Multi-view Learningcited by 12
  11. 2022A Kernel Approach for PDE Discovery and Operator Learningcited by 7
  12. 2023MOCK: an Algorithm for Learning Nonparametric Differential Equations via Multivariate Occupation Kernel Functionscited by 2

Built on by

Cited by year

Citing papers per year: 2025: 1.

1 paper.

  1. 2025The Stochastic Occupation Kernel (SOCK) Method for Learning Stochastic Differential Equationscited by 0