arXiv subjects

Marcial Sanchis-Agudo

Publications and source records attributed to Marcial Sanchis-Agudo.

5 recordsLinked to original sources

arXiv2026

A Hybrid Generative Reduced-Order Model for the Minimal Flow Unit

A data-driven reduced-order modelling framework is proposed for wall-bounded turbulent flows to forecast the intermittent near-wall dynamics over extended time horizons from sparse sensor measurements. The approach combines a $β$-VAE-GAN, which compresses high-dimensional flow fields into a low-dimensional latent space, with a sensor-conditioned Transformer that forecasts the evolution of the latent variables. The temporal module employs Easy Attention, a static time-mixing operator that replaces the learnable query-key mechanism of standard self-attention at reduced computational cost, combined with an adapted AdaLN-Zero modulation mechanism for sensor-based conditioning. Evaluated on the Minimal Flow Unit ($Re_τ= 200$) at $y^+ = 14$, the compression stage recovers $87\%$ of the turbulent kinetic energy within a four-dimensional latent space, exceeding the standard $β$-VAE baseline by more than $10\%$. The latent dimensions autonomously encode the characteristic timescales of the flow, with specific coordinates capturing the low-frequency signature of the near-wall regeneration cycle ($T^+ \approx 1724$), establishing the physical interpretability of the learnt representation. The sensor-conditioned Transformer maintains accurate forecasts over $17{,}288\,t^+$ from an initialisation window of only $128\,t^+$, whilst end-to-end inference reconstructs $82\%$ of the turbulent kinetic energy. The principal limitation is the attenuation of rare, extreme-amplitude events, a consequence of the encoder prioritising the most statistically recurrent flow states within the low-dimensional bottleneck. Nevertheless, the framework accurately reproduces the alternating active and quiescent phases of the regeneration cycle, demonstrating its suitability as a surrogate model for the intermittent dynamics of wall-bounded turbulence.

physics.flu-dyn↗

arXiv2026

X-CAL: Explaining latent causality in physical space for fluid mechanics

We present X-CAL, a pipeline that combines a $β$-variational autoencoder ($β$-VAE) with the synergistic-unique-redundant decomposition (SURD)~\cite{surd} approach for causality analysis to interpret low-dimensional latent representations of turbulent fluid flows. Combining $β$-VAE compression with SURD and SHAP (SHapley Additive exPlanations) yields interpretable latent representations and structure-level attributions in physical space, offering a general methodology for causal analysis of high-dimensional flows. Using direct numerical simulation (DNS) data of the flow around a wall-mounted square cylinder at $Re_h=2000$, we (i) learn a compact latent space with near-orthogonal variables, (ii) quantify directed information flows among these variables via the SURD approach, and (iii) map latent-space causality back to physical space through gradient-SHAP fields . By means of percolation analysis of the SHAP fields, we extract the coherent, time-resolved structures that most influence each latent variable. The analysis connects coherent structures with latent variables which are in turn associated with wake-boundary-layer interactions. This method enables translating the insight obtained through causal analysis in the latent space into interpretable phenomena in physical space.

physics.flu-dyn↗

arXiv2026

A Mixed-Metric Two-Field Framework for Turbulence: Emergent Stress Anisotropy and Wall Asymptotics from a Single Scalar

In our previous work~\cite{SanchisAgudoVinuesa2025PRL}, we argued that viscous dissipation in turbulence can be understood as the macroscopic imprint of microscopic path uncertainty, and showed that a kernel variance field $s(y)$ constrained by a balance condition yields both the Kolmogorov scales and the logarithmic law of the wall from a single stochastic principle. In the present work we promote $s$ to a dynamical field $s(\bm{x},t)$ with units of kinematic viscosity and develop a two-field framework in which the velocity $\ve$ and an \emph{intermittency} (or stochastic diffusivity) field $s$ evolve in a coupled way. The effective viscosity is $ν_{\mathrm{eff}}=ν_0+s$, but the stress tensor is generalized to include a non-linear closure driven by the commutator of strain and rotation, $[\bm{S}, \bmΩ]$, capturing emergent anisotropy. The evolution of $s$ is defined as a mixed-metric gradient flow: a Wasserstein-2 gradient flow for morphology, $\Div(s\grad s)$, combined with a local $L^2$ gradient flow driven by an objective coupling term $q$. The coupling is decomposed as $q=q_{\mathrm{prod}}-q_{\mathrm{relax}}$, where production is driven by a vortex-stretching invariant, $\mathcal{I} = \|\bm{S}\boldsymbolω\|^2$. This choice ensures that production vanishes identically in strictly two-dimensional flows. We show that, under standard assumptions of constant stress, high Reynolds number and overlap-layer scale invariance, the only scale-invariant overlap-layer solution of the mixed-metric equation is $s(y)\propto y$, which recovers the logarithmic velocity profile. Thus the same mixed-metric equation organizes both wall-resolved and wall-modeled asymptotics within a single, energetically constrained framework.

physics.flu-dyn↗

arXiv2025

A Geometric Foundation for the Universal Laws of Turbulence

We propose a theoretical framework where the dissipative structures of turbulence emerge from microscopic path uncertainty. By modeling fluid parcels as stochastic tracers governed by the Schrödinger Bridge (SB) variational principle, we demonstrate that the Navier--Stokes viscous term is a natural linear, second-order macroscopic operator consistent with isotropic microscopic diffusion. We derive two foundational pillars of turbulence from this single principle. First, we show that the Kolmogorov scale $η\sim (ν^3/ε)^{1/4}$ is not merely a dimensional necessity but a geometric diffusion horizon: it is the scale at which the kinetic energy of a fractal trajectory, scaling as $k \sim ν/τ$, balances the macroscopic dissipation rate. Second, we show that the universal law of the wall is the stationary solution to this stochastic process under no-slip constraints. The logarithmic mean profile arises from the scale invariance of the turbulent diffusivity, while finite-Reynolds-number corrections emerge as controlled asymptotic expansions of the stochastic variance. This framework offers a physically grounded derivation of turbulent scaling laws that complements and extends purely phenomenological dimensional analysis.

physics.flu-dyn↗

arXiv2025

Easy attention: A simple attention mechanism for temporal predictions with transformers

To improve the robustness of transformer neural networks used for temporal-dynamics prediction of chaotic systems, we propose a novel attention mechanism called easy attention which we demonstrate in time-series reconstruction and prediction. While the standard self attention only makes use of the inner product of queries and keys, it is demonstrated that the keys, queries and softmax are not necessary for obtaining the attention score required to capture long-term dependencies in temporal sequences. Through the singular-value decomposition (SVD) on the softmax attention score, we further observe that self attention compresses the contributions from both queries and keys in the space spanned by the attention score. Therefore, our proposed easy-attention method directly treats the attention scores as learnable parameters. This approach produces excellent results when reconstructing and predicting the temporal dynamics of chaotic systems exhibiting more robustness and less complexity than self attention or the widely-used long short-term memory (LSTM) network. We show the improved performance of the easy-attention method in the Lorenz system, a turbulence shear flow and a model of a nuclear reactor.

cs.LG↗