For non-convex objectives satisfying the Łojasiewicz inequality of order 2, the DIN continuous-time dynamics converge in function value at a rate arbitrarily close to e^{-2√µ t}, which is worst-case optimal within this dynamics family.
Anitescu, Degenerate nonlinear programming with a quadratic growth condition, SIAM Journal on Optimization, 10 (2000), pp
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Heavy-ball dynamics with Hessian-driven damping for non-convex optimization under the {\L}ojasiewicz condition
For non-convex objectives satisfying the Łojasiewicz inequality of order 2, the DIN continuous-time dynamics converge in function value at a rate arbitrarily close to e^{-2√µ t}, which is worst-case optimal within this dynamics family.