arXiv subjects

Giorgio Maria Cavallazzi

Publications and source records attributed to Giorgio Maria Cavallazzi.

8 recordsLinked to original sources

arXiv2026

Manifold-adapted radial basis functions for reduced-order modelling of chaotic flows

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 least-squares solve gives an explicit, differentiable vector field that reproduces the long-term statistics without any use of the governing equations. A radial basis field decays away from the data and cannot by itself return an escaped state. The integration is therefore stabilised by a kinematic corrector, whose reported magnitude measures how far each result rests on the learned field. On Lorenz-63 the model recovers the attractor, its marginal densities and its Lyapunov spectrum. On Lorenz-96 its valid prediction time matches typical configurations of neural-network and reservoir-computing forecasters and trails their best-tuned ones, and the invariant measure is reproduced on both the full state and on 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 reduced dimension. The recovery is dictated by the distance from a state to its nearest kernels, not by the one-step regression error.

physics.flu-dyn↗

arXiv2026

Gradient-free learning of a closed-loop wall controller for turbulent drag reduction

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.

physics.flu-dyn↗

arXiv2026

Deep reinforcement learning with spatial and temporal awareness for active boundary control of buoyancy-driven convection

Deep reinforcement learning (DRL) applied to thermal convection control consistently produces degenerate actuation: wall-temperature policies whose outputs are saturated, pseudo-random, or spatially incoherent. Two compounding deficiencies are responsible: multilayer-perceptron policies that discard spatial flow structure, and memoryless policies that cannot distinguish self-induced flow changes from background evolution. Together they degrade the actuation into forms whose relation to the convective topology cannot be read off and which are not realisable at the actuator, even when cell coalescence (the merging of convection rolls into fewer, larger structures), which would reduce Nu, is accessible to boundary actuation. The present framework addresses both causes through four targeted design choices: convolutional policy networks, Gated Recurrent Unit (GRU) memory, off-policy training (TD3/MADDPG), and action-smoothness constraints. A systematic 2x2 factorial design isolates the contribution of each component. On Rayleigh-Benard convection at Ra = 10,000, all four configurations achieve cell coalescence and reduce Nu to as low as 1.83 (26% below the uncontrolled baseline) in 350 episodes, without the full-field data augmentation required by prior work. Crucially, coalescence is achieved even by the single-agent configuration, demonstrating that the multi-agent formulation is not a prerequisite once the policy architecture is sufficiently expressive. Applied to double-diffusive convection in the salt-finger regime, the framework spontaneously discovers a travelling-wave actuation whose phase speed adapts to the evolving mixing state of the flow, enhancing heat transfer by 19.1% and reducing salinity variance by 21.0%.

physics.flu-dyn↗

arXiv2026

Reward hacking in physical reinforcement learning revealed by turbulent drag reduction

Reinforcement-learning controllers optimise specified rewards, but in physical systems those rewards often capture only part of the true control objective. Three mechanisms through which this mismatch can produce apparent success without physical improvement are identified: incomplete accounting that omits relevant costs, constraint enforcement outside the policy that corrupts credit assignment, and observations that fail to resolve the relevant dynamics. All three are demonstrated in active drag reduction of wall-bounded turbulence, where the conservation constraint and full energy budget can be measured directly. A memoryless learnt policy reports drag reduction while raising total dissipation, collapsing to non-physical flow configurations. A recurrent multi-agent controller with the zero-mean projection embedded in the actor, temporal memory matched to the relevant timescales, and an actuation cost that bounds the wall power delivers a physically consistent control. Progress in physical reinforcement learning requires the reward, constraints, observations and evaluation metrics to represent unequivocally the physical objective.

physics.flu-dyn↗

arXiv2026

Offline accuracy is not enough: closed-loop instability and stabilisation of a wall-sensor neural estimator in opposition control

Opposition control reduces skin-friction drag by opposing the wall-normal velocity on a near-wall detection plane, but the detection-plane velocity it requires is not available from wall-mounted sensors. Wall data can reconstruct inner-flow quantities accurately when assessed offline on a fixed flow state, and we ask whether such a reconstructed field can instead serve as a live surrogate sensor inside the feedback loop. We train a recurrent estimator to infer the detection-plane velocity from the two wall-shear-stress components in opposition-controlled turbulence. Offline it performs extremely well, reaching a correlation of 0.99 and near-unity coherence across the energetic scales; yet the same estimator fails in closed loop, decorrelating from the true field within a few viscous time units as the control collapses. The failure is not one of accuracy but of distribution shift induced by the controller itself: small closed-loop errors carry the flow off the attractor represented in the training data, while unresolved high-wavenumber errors enter through the wall boundary condition and return as out-of-distribution inputs. Standard remedies such as low-pass filtering and exponential averaging only delay numerical breakdown while accelerating decorrelation. Stable wall-only control is recovered by imposing spectral consistency on the deployed actuation and retraining the estimator on its own closed-loop data, giving a controller that holds much of the drag reduction of ideal opposition control from wall quantities alone. The obstacle is not whether the near-wall flow can be reconstructed offline, but whether that reconstruction stays dynamically consistent when allowed to modify the flow it senses.

physics.flu-dyn↗

arXiv2026

Restoring Convergence Order in Explicit Runge-Kutta Integration of Hyperbolic PDE with Time-Dependent Boundary Conditions

Explicit Runge-Kutta (RK) integration of hyperbolic initial-boundary value problems with time-dependent Dirichlet data often displays order reduction: the observed convergence order falls below the nominal order because the stage structure interacts with asymmetric near-boundary spatial closures. This paper develops a purely spatial remedy that preserves the time integrator while redesigning only the first two boundary-adjacent derivative operators. For an arbitrary explicit $s$-stage RK method applied to linear advection, the one-step truncation error at the boundary-adjacent nodes is shown to admit a tableau-dependent decomposition whose cancellation yields explicit algebraic conditions on the boundary weights. A solvability coefficient $R(\mathbf{b},\mathbf{c},A)$ determines whether a spatial compensation mechanism exists; the result is specialised to SSP-RK3, for which closed-form conditions are derived. Constrained differential evolution then identifies 5-point closures that, coupled to a 5th-order upwind interior stencil, recover third-order convergence from the degraded second-order behaviour of classical Taylor closures. A stability-aware variant augments the optimisation with an eigenvalue penalty, exposing the trade-off between order recovery and CFL robustness. Validation covers linear advection, manufactured-solution Burgers flow, and dimensionally split two-dimensional advection. The analysis clarifies why weak-stage-order temporal fixes do not resolve the finite-difference boundary problem, and indicates how the framework extends to non-uniform meshes.

math.NA↗

arXiv2026

Manifold-Adapted Sparse RBF-SINDy: Unbiased Library Construction and Unsupervised Discovery of Dynamical States in Turbulent Wall Flows

The turbulent attractor of wall bounded flows is not a structureless strange set but contains a skeleton of dynamically distinct states connected by rare directed transitions whose geometry is reflected in the invariant measure of the phase space trajectory. We show that this skeleton can be recovered from wall measurements alone, namely wall pressure and wall shear stress, without physical labels or prior knowledge, provided that the data driven function library used to identify the dynamics respects the intrinsic geometry of the attractor rather than the variance hierarchy of the POD representation. Standard sparse identification approaches introduce two structural biases during library construction. First, the steep decay of POD spectra causes Euclidean distances in k means clustering to be dominated by leading modes, collapsing basis function centres into a low dimensional subspace and leaving transitional dynamics poorly represented. Second, turbulent trajectories slow near quasi invariant states, so uniform time sampling over represents these regions and under samples rapid transitions. Both biases are corrected by resampling the trajectory uniformly in arc length and replacing the Euclidean metric with a Mahalanobis metric derived from the local cluster covariance. A single sparse regression on this corrected library yields a reduced model. Applied to a minimal turbulent channel at low Reynolds number, unsupervised clustering reveals two phases of the near wall cycle: stable streak states and burst initiating instabilities corresponding to the coherent structure skeleton of the flow. The model reproduces the invariant measure, reaches the Lyapunov predictability horizon and provides a differentiable vector field on which invariant solutions can be located by Newton iteration.

physics.flu-dyn↗

arXiv2024

Deep reinforcement learning for the management of the wall regeneration cycle in wall-bounded turbulent flows

The wall cycle in wall-bounded turbulent flows is a complex turbulence regeneration mechanism that remains not fully understood. This study explores the potential of deep reinforcement learning (DRL) for managing the wall regeneration cycle to achieve desired flow dynamics. We integrate the StableBaselines3 DRL libraries with the open-source DNS solver CaNS to create a robust platform for dynamic flow control. The DRL agent interacts with the DNS environment, learning policies that modify wall boundary conditions to optimize objectives such as the reduction of the skin-friction coefficient or the enhancement of certain coherent structures features. Initial experiments demonstrate the capability of DRL to achieve drag-reduction rates comparable with those achieved via traditional methods, though limited to short time periods. We also propose a strategy to enhance the coherence of velocity streaks, assuming that maintaining straight streaks can inhibit instability and further reduce skin friction. The implementation makes use of the message-passing-interface (MPI) wrappers for efficient communication between the Python-based DRL agent and the DNS solver, ensuring scalability on high-performance computing architectures. Our results highlight the promise of DRL in flow control applications and underscore the need for more advanced control laws and objective functions. Future work will focus on optimizing actuation periods and exploring new computational architectures to extend the applicability and the efficiency of DRL in turbulent flow management.

physics.flu-dyn↗