| Abstract: |
| High-index saddle dynamics (HiSD) is a powerful instrument in finding multiple saddle points of complex systems. A critical point in designing numerical algorithms is to preserve the manifold properties of HiSD. We perform numerical analysis for manifold-preserving numerical approximation to HiSD, which not only gives error estimates but provides expatiation for manifold-preserving mechanisms of the continuous HiSD. Furthermore, a data-driven HiSD algorithm is presented and analyzed to improve the applicability of the HiSD. |
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