Chaotic systems often evolve on a low-dimensional attractor whose geometry varies from one region to another. We propose a non-intrusive reduced-order model that reads this local geometry by clustering and uses it to shape a radial basis library whose kernels adapt to each region. Fitting the reduced velocity onto this library by one global regularised least-squares solve gives an explicit, differentiable vector field that reproduces the long-term statistics, that is, the invariant measure, without any use of the governing equations. Since a radial basis field decays away from the data and cannot by itself return an escaped state, the integration is stabilised by a kinematic corrector whose magnitude is reported as a measure of how far each result rests on the learned field rather than on the corrector. On Lorenz-63 the model recovers the attractor, its marginal densities, and the positive and neutral Lyapunov exponents, while under-recovering the strong transverse contraction. On Lorenz-96 its valid prediction time is competitive with tuned neural-network and reservoir-computing forecasters, and the invariant measure is reproduced on both the full state and a reduced observable. On the Kuramoto--Sivashinsky equation and the quasiperiodic Kolmogorov flow the model matches the energy distribution and spectrum of an intrusive quantised-local Galerkin model, and improves on a global Galerkin projection of the same dimension, without ever projecting the governing equations.
Miguel Pérez Cuadrado, Giorgio Maria Cavallazzi, Alfredo Pinelli· 0 citations
Closed-loop wall controllers learnt by multi-agent reinforcement learning are usually trained on periodic boxes far smaller than the flows they are meant to drive, and a large part of their drag reduction is lost when they are carried across. Retraining on the target domain is not an affordable remedy: the centralised critic that assigns credit to each wall patch degrades as patches are added, the zero-net-mass constraint couples the patches it is asked to separate, and the episodes must be collected in sequence at a cost that grows with the domain. We propose instead a short gradient-free refinement stage, applied to the transferred policy on the domain it will drive. An evolution strategy scores whole flow episodes against a regularised objective, so no credit has to be assigned to individual patches, and the candidates in a generation are independent and run in parallel. Applied to a recurrent multi-agent policy trained on a minimal flow unit at $\Retau\simeq180$ and evaluated on a channel sixteen times larger in wall-parallel area, a few generations raise the drag reduction from $19.0\%$ to $25.7\%$, above the $22.5\%$ of opposition control. Because the policies before and after refinement share an architecture and a training history, the difference between the controlled flows follows from the refinement alone. It shows in the friction decomposition, in the Reynolds stresses and in the near-wall spectra, and the actuation moves from a weak coupling to the wall-normal velocity towards a strong coupling to the streamwise fluctuation.
Giorgio Maria Cavallazzi, Miguel Pérez Cuadrado, Alfredo Pinelli· 0 citations