arXiv subjects

Alfredo Pinelli

Publications and source records attributed to Alfredo Pinelli.

13 recordsLinked to original sources

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

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 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.

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

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

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↗

arXiv2025

Walsh-Hadamard Neural Operators for Solving PDEs with Discontinuous Coefficients

Neural operators have emerged as powerful tools for learning solution operators of partial differential equations (PDEs). However, standard spectral methods based on Fourier transforms struggle with problems involving discontinuous coefficients due to the Gibbs phenomenon and poor representation of sharp interfaces. We introduce the Walsh-Hadamard Neural Operator (WHNO), which leverages Walsh-Hadamard transforms-a spectral basis of rectangular wave functions naturally suited for piecewise constant fields-combined with learnable spectral weights that transform low-sequency Walsh coefficients to capture global dependencies efficiently. We validate WHNO on three problems: steady-state Darcy flow (preliminary validation), heat conduction with discontinuous thermal conductivity, and the 2D Burgers equation with discontinuous initial conditions. In controlled comparisons with Fourier Neural Operators (FNO) under identical conditions, WHNO demonstrates superior accuracy with better preservation of sharp solution features at material interfaces. Critically, we discover that weighted ensemble combinations of WHNO and FNO achieve substantial improvements over either model alone: for both heat conduction and Burgers equation, optimal ensembles reduce mean squared error by 35-40 percent and maximum error by up to 25 percent compared to individual models. This demonstrates that Walsh-Hadamard and Fourier representations capture complementary aspects of discontinuous PDE solutions, with WHNO excelling at sharp interfaces while FNO captures smooth features effectively.

physics.comp-ph↗

arXiv2025

Filament inclination effect on turbulent canopy flows

Inspired by the spontaneous behaviour observed in filamentous layers -- where the balance between flow-induced drag and structural elasticity dictates the filaments' equilibrium streamlined posture -- we perform a series of large-eddy simulations to investigate how filament inclination affects turbulent shear flows developing both above and within a canopy of filaments. We examine six distinct filament inclination angles ranging from 0\deg to 90\deg. The in-plane solid fraction and filament length are chosen to achieve a fully dense canopy at zero inclination, and these parameters remain constant throughout our study. By setting a nominal bulk Reynolds number of 6000, we provide a detailed statistical characterisation of the turbulent flow. Our findings illustrate distinct changes in the flow regime with varying filament inclination. At lower angles, the canopy remains dense and significantly influences the flow, conforming to a classical canopy-flow regime. However, as the inclination approaches 90\deg, the intra-canopy region progressively becomes shielded from the outer flow. Remarkably, at 90\deg inclination, the flow drag reduces significantly, and the total drag becomes lower than that typically seen in an open, filament-free flow. We document this transition from a canopy-dominated regime to a scenario where the canopy becomes largely sheltered from the outer turbulent flow, highlighting key alterations in intra-canopy dynamics as filament inclination increases. Our observations are substantiated by an analysis of the velocity spectra, providing deeper insight into the interactions between the canopy and the developing turbulent boundary layer.

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↗

arXiv2022

On the solidity parameter in canopy flows

We have performed high-fidelity simulations of turbulent open-channel flows over submerged rigid canopies made of cylindrical filaments of fixed length $l=0.25H$ ($H$ being the domain depth) mounted on the wall with an angle of inclination $θ$. The inclination is the free parameter that sets the density of the canopy by varying its frontal area. The density of the canopy, based on the solidity parameter $λ$, is a widely accepted criterion defining the ongoing canopy flow regime, with low values ($λ\ll 0.1$) indicating the sparse regime, and higher values ($λ> 0.1$) the dense regime. All the numerical predictions have been obtained considering the same nominal bulk Reynolds number (i.e. $Re_b=U_b H/ν= 6000$). We consider nine configurations of canopies, with $θ$ varying symmetrically around $0°$ in the range $θ\in [\pm 78.5°]$, where positive angles define canopies inclined in the flow direction (with the grain) and $θ=0°$ corresponds to the wall-normally mounted canopy. The study compares canopies with identical solidity obtained inclining the filaments in opposite angles and assesses the efficacy of the solidity as a representative parameter. It is found that when the canopy is inclined, the actual flow regime differs substantially from the one of a straight canopy that shares the same solidity indicating that criteria solely based on this parameter are not robust. Finally, a new phenomenological model describing the interaction between the coherent structures populating the canopy region and the outer flow is given.

physics.flu-dyn↗

arXiv2018

Turbulent channel flow over an anisotropic porous wall - Drag increase and reduction

The effect of the variations of the permeability tensor on the close-to-the-wall behaviour of a turbulent channel flow bounded by porous walls is explored using a set of direct numerical simulations. It is found that the total drag can be either reduced or increased by more than $20\%$ by adjusting the permeability directional properties. Drag reduction is achieved for the case of materials with permeability in the vertical direction lower than the one in the wall-parallel planes. This configuration limits the wall normal velocity at the interface while promoting an increase of the tangential slip velocity leading to an almost "one-component" turbulence where the low- and high-speed streaks coherence is strongly enhanced. On the other hand, strong drag increase is found when a high wall-normal and low wall-parallel permeabilities are prescribed. In this condition, the enhancement of the wall-normal fluctuations due to the reduced wall-blocking effect triggers the onset of structures which are strongly correlated in the spanwise direction, a phenomenon observed by other authors in flows over isotropic porous layers or over ribletted walls with large protrusion heights. The use of anisotropic porous walls for drag reduction is particularly attractive since equal gains can be achieved at different Reynolds numbers by rescaling the magnitude of the permeability only.

physics.flu-dyn↗

arXiv2010

Travelling-waves consistent with turbulence-driven secondary flow in a square duct

We present numerically determined travelling-wave solutions for pressure-driven flow through a straight duct with a square cross-section. This family of solutions represents typical coherent structures (a staggered array of counter-rotating streamwise vortices and an associated low-speed streak) on each wall. Their streamwise average flow in the cross-sectional plane corresponds to an eight vortex pattern much alike the secondary flow found in the turbulent regime.

physics.flu-dyn↗