arXiv subjects

Miguel Pérez Cuadrado

Publications and source records attributed to Miguel Pérez Cuadrado.

5 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

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↗

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↗