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Updated: Jun 30, 2025

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OKRidge: Scalable Optimal k-Sparse Ridge Regression.

Jiachang Liu1, Sam Rosen1, Chudi Zhong1

  • 1Duke University.

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Summary
This summary is machine-generated.

We developed OKRidge, a fast algorithm for identifying sparse governing equations in nonlinear dynamical systems. This method efficiently solves sparse ridge regression problems to provable optimality, accelerating scientific discovery.

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Area of Science:

  • Scientific Discovery
  • Dynamical Systems Theory
  • Machine Learning

Background:

  • Identifying sparse governing equations is crucial for understanding nonlinear dynamical systems.
  • Existing methods for sparse ridge regression can be computationally intensive.

Purpose of the Study:

  • To propose a novel, fast algorithm for solving sparse ridge regression problems to provable optimality.
  • To accelerate the identification of sparse governing equations for nonlinear dynamical systems.

Main Methods:

  • Developed the OKRidge algorithm utilizing a novel lower bound calculation.
  • Employed a saddle point formulation leading to either linear system solution or an ADMM-based approach.
  • Incorporated a beam search method for warm-starting the solver.

Main Results:

  • OKRidge achieves provable optimality in sparse ridge regression.
  • Experimental results show run times orders of magnitude faster than existing Mixed-Integer Programming (MIP) formulations.
  • The algorithm efficiently identifies driving terms in nonlinear dynamics.

Conclusions:

  • OKRidge offers a significant speedup for identifying sparse governing equations.
  • The proposed method provides a computationally efficient and optimal solution for a key scientific discovery problem.