Weak Dominant Balance for Robust Identification of Dynamically Consistent Fluid Flow Structure

Extracting interpretable, localized physical mechanisms from complex spatiotemporal data is a foundational challenge across physics, biology, and engineering, but has remained out of reach on real measurements. The central obstacle is obtaining high-quality gradients of data via numerical differentiation, which amplifies noise, diverges for high-order equations, and falters on irregular geometries, limiting the scope of existing approaches to clean simulations of low-order systems. Here, we present weak dominant balance, a derivative-free framework that projects governing equations into a weak (integral) formulation, offloading differentiation onto smooth analytical test functions and leaving the data untouched. The method sustains accurate regime identification under severe noise where existing approaches categorically fail, delivers the first data-driven decomposition of a third-order partial differential equation applied to turbulent duct flow, and produces matching decompositions across direct numerical simulation and particle-image velocimetry measurements of a wavy channel flow, uncovering a previously uncharacterized dynamical regime. Weak dominant balance brings mechanism-level analysis out of simulation and onto measured data, and opens complex physical systems to direct, equation-grounded interpretation.

Low-Cost High-Order Singular Value Decomposition for Tensor-Based Reconstruction from Sparse Sensor Measurements: Urban Flow and Air-Quality Applications

Urban flow and air-quality simulations generate high-dimensional datasets describing velocity and pollutant transport across multiple spatial, temporal, and physical-variable dimensions. Reconstructing these fields from sparse sensor measurements is a fundamental challenge in environmental monitoring, digital twins, forecasting, and data assimilation. Existing low-cost reconstruction approaches are commonly based on matrix decompositions, which require multidimensional datasets to be flattened into two-dimensional snapshot matrices, thereby discarding important structural information. This work introduces the low-cost High-Order Singular Value Decomposition (lcHOSVD), a novel tensor-based sparse-sensing reconstruction framework for high-dimensional environmental fields. To the authors' knowledge, this is the first methodology that combines sparse sensing and HOSVD for field reconstruction. Unlike matrix-based approaches, lcHOSVD preserves the natural tensor structure of the data, enabling the exploitation of correlations across spatial, temporal, and physical-variable dimensions while substantially reducing the computational requirements of conventional HOSVD. The methodology is applied to urban flow and air-quality datasets, where three-dimensional velocity and pollutant concentration fields are reconstructed using only 1-4% of the available spatial locations. While lcSVD provides larger computational speed-ups, lcHOSVD consistently achieves lower reconstruction errors in configurations characterized by strong multidimensional coupling and heterogeneous dynamics across dimensions. Additional sensor-anisotropy analyses demonstrate that the tensor formulation is significantly more robust to uneven sensor distributions, a common situation in practical environmental monitoring networks.

Explainable deep reinforcement learning reveals energy-efficient control strategies for turbulent drag reduction

We propose a method combining Multi-Agent Deep Reinforcement Learning (MARL) and eXplainable Deep Learning (XDL) to reduce drag in wall-bounded turbulent flows. Taking as a baseline the results of training agents directly targeting wall-shear stress and opposition control, three SHAP-guided approaches are compared. In the first, the reward is computed from SHAP attributions of a U-net predicting the future velocity field; in the second, from SHAP attributions of a U-net predicting the skin-friction coefficient; in the third, from a combination of SHAP attributions of two U-nets predicting the skin-friction coefficient and the wall pressure fluctuations, respectively. The combined SHAP strategy based on skin-friction coefficient and wall-pressure fluctuations achieves the best overall performance, achieving a DR of 34.44% and a NES of 34.01% with only 0.43% normalized input power. Relative to opposition control, drag reduction and net energy saving increase by 49.41% and 48.52%, respectively. Compared with the direct wall-shear-stress baseline, the proposed strategy simultaneously improves performance while reducing the normalized actuation cost from 5.90% to 0.43%. Analysis of the results reveals that the energetically efficient policy is consistent with pressure-gated actuation, activating predominantly at near-zero wall pressure, and operates on a temporal timescale comparable to the lifetime of the near-wall turbulent structures.

High-lift Wing Separation Control via Bayesian Optimization and Deep Reinforcement Learning

This study investigates active flow control (AFC) of a 30P30N high-lift wing at a Reynolds number Re$_c$ = 450,000 and angle of attack $α$ = 23$^\circ$ using wallresolved large-eddy simulations (LES). Two optimization strategies are explored: open-loop Bayesian optimization (BO) and closed-loop deep reinforcement learning (DRL), both targeting the mitigation of stall and the improvement of aerodynamic efficiency via synthetic jets on the slat, main, and flap elements. The uncontrolled configuration was validated against literature data, confirming the reliability of the LES setup. The BO framework successfully identified steady jet velocities that increased efficiency by +10.9% through a -9.7% drag reduction while maintaining lift. In contrast, the DRL agent, despite leveraging instantaneous flow information from distributed sensors, achieved only minor improvements in lift and drag, with negligible efficiency gain. Training analysis indicated that the penalty-dominated reward constrained exploration. These results highlight the need for carefully designed rewards and computational acceleration strategies in DRL-based flow control at high Reynolds numbers.

AeroJEPA: Learning Semantic Latent Representations for Scalable 3D Aerodynamic Field Modeling

Aerodynamic surrogate models are increasingly used to replace repeated high-fidelity CFD evaluations in many-query design settings, but current approaches still face two important limitations: they often scale poorly to the very large fields arising in realistic 3D aerodynamics, and they rarely produce latent representations that are directly useful for analysis and design. We introduce AeroJEPA, a Joint-Embedding Predictive Architecture for aerodynamic field modeling that addresses both issues. Rather than predicting the full flow field directly from geometry, AeroJEPA predicts a target latent representation of the flow from a context latent representation of the geometry and operating conditions, and optionally reconstructs the field through a continuous implicit decoder. This formulation decouples latent prediction from field resolution while encouraging the latent space to organize semantically. We evaluate AeroJEPA on two complementary datasets: HiLiftAeroML, which stresses the method in a high-fidelity regime with extremely large boundary-layer fields, and SuperWing, which tests large-scale generalization and latent-space optimization over a broad family of transonic wings. Across these benchmarks, AeroJEPA is competitive as a continuous surrogate for aerodynamic fields, scales naturally to high-resolution outputs, and learns context and predicted latents that encode geometry and aerodynamic quantities not used directly as supervision. We further show that the resulting latent space supports controlled interpolation, linear probing, concept-vector arithmetic, and a constrained design latent-optimization experiment. These results suggest that predictive latent learning is a promising direction for scalable and design-meaningful aerodynamic surrogate modeling.

Timescale Separation Enables Deep Reinforcement Learning Control of Rotating Detonation Engine Mode Transitions

Rotating detonation engines (RDEs) are a promising propulsion concept that may offer higher thermodynamic efficiency and specific impulse than conventional systems, but nonlinear phenomena, including transitions to oscillatory or chaotic propagation modes, can hinder practical operation. Deep Reinforcement Learning (DRL) has emerged as a promising method for controlling complex nonlinear dynamics such as those observed in RDEs. However, the multi-timescale nature of the RDE system makes direct application of DRL challenging. We address this challenge by reformulating the DRL problem in a moving reference frame that follows the detonation-wave pattern, making the wave structure appear quasi-steady to the agent. This reformulation enables scale separation between fast detonation propagation and slower operating-mode dynamics. We train DRL controllers to modulate spatially segmented injection pressure in a one-dimensional reduced-order RDE model and induce rapid transitions between different mode-locked states. Across a range of actuation periods, initial states, and target modes, controllers trained in the moving frame learn more reliably than those trained in a stationary frame and remain effective over a broader range of actuation periods. These results suggest that symmetry-aware moving reference frame formulations may be useful for related multiscale flow-control problems and that scale separation should be exploited whenever possible to enable DRL control of multi-timescale systems.

Physics-guided surrogate learning enables zero-shot control of turbulent wings

Turbulent boundary layers over aerodynamic surfaces are a major source of aircraft drag, yet their control remains challenging due to multiscale dynamics and spatial variability, particularly under adverse pressure gradients. Reinforcement learning has outperformed state-of-the-art strategies in canonical flows, but its application to realistic geometries is limited by computational cost and transferability. Here we show that these limitations can be overcome by exploiting local structures of wall-bounded turbulence. Policies are trained in turbulent channel flows matched to wing boundary-layer statistics and deployed directly onto a NACA4412 wing at $Re_c=2\times10^5$ without further training, being the so-called zero-shot control. This achieves a 28.7% reduction in skin-friction drag and a 10.7% reduction in total drag, outperforming the state-of-the-art opposition control by 40% in friction drag reduction and 5% in total drag. Training cost is reduced by four orders of magnitude relative to on-wing training, enabling scalable flow control.

Explainable deep learning reveals the physical mechanisms behind the turbulent kinetic energy equation

In this work, we investigate the physical mechanisms governing turbulent kinetic energy transport using explainable deep learning (XDL). An XDL model based on SHapley Additive exPlanations (SHAP) is used to identify and percolate high-importance structures for the evolution of the turbulent kinetic energy budget terms of a turbulent channel flow at a friction Reynolds number of $Re_τ= 125$. The results show that the important structures are predominantly located in the near-wall region and are more frequently associated with sweep-type events. In the viscous layer, the SHAP structures relevant for production and viscous diffusion are almost entirely contained within those relevant for dissipation, revealing a clear hierarchical organization of near-wall turbulence. In the outer layer, this hierarchical organization breaks down and only velocity-pressure-gradient correlation and turbulent transport SHAP structures remain, with a moderate spatial coincidence of approximately $60\%$. Finally, we show that none of the coherent structures classically studied in turbulence are capable of representing the mechanisms behind the various terms of the turbulent kinetic energy budget throughout the channel. These results reveal dissipation as the dominant organizing mechanism of near-wall turbulence, constraining production and viscous diffusion within a single structural hierarchy that breaks down in the outer layer.

GenDA: Generative Data Assimilation on Complex Urban Areas via Classifier-Free Diffusion Guidance

Urban wind flow reconstruction is essential for assessing air quality, heat dispersion, and pedestrian comfort, yet remains challenging when only sparse sensor data are available. We propose GenDA, a generative data assimilation framework that reconstructs high-resolution wind fields on unstructured meshes from limited observations. The model employs a multiscale graph-based diffusion architecture trained on computational fluid dynamics (CFD) simulations and interprets classifier-free guidance as a learned posterior reconstruction mechanism: the unconditional branch learns a geometry-aware flow prior, while the sensor-conditioned branch injects observational constraints during sampling. This formulation enables obstacle-aware reconstruction and generalization across unseen geometries, wind directions, and mesh resolutions without retraining. We consider both sparse fixed sensors and trajectory-based observations using the same reconstruction procedure. When evaluated against supervised graph neural network (GNN) baselines and classical reduced-order data assimilation methods, GenDA reduces the relative root-mean-square error (RRMSE) by 25-57% and increases the structural similarity index (SSIM) by 23-33% across the tested meshes. Experiments are conducted on Reynolds-averaged Navier-Stokes (RANS) simulations of a real urban neighbourhood in Bristol, United Kingdom, at a characteristic Reynolds number of $\mathrm{Re}\approx2\times10^{7}$, featuring complex building geometry and irregular terrain. The proposed framework provides a scalable path toward generative, geometry-aware data assimilation for environmental monitoring in complex domains.

Mode-Seeking for Inverse Problems with Diffusion Models

A pre-trained unconditional diffusion model, combined with posterior sampling or maximum a posteriori (MAP) estimation techniques, can solve arbitrary inverse problems without task-specific training or fine-tuning. However, existing posterior sampling and MAP estimation methods often rely on modeling approximations and can be computationally demanding. In this work, we propose the variational mode-seeking loss (VML), which, when minimized during each reverse diffusion step, guides the generated sample towards the MAP estimate. VML arises from a novel perspective of minimizing the Kullback-Leibler (KL) divergence between the diffusion posterior $p(\mathbf{x}_0|\mathbf{x}_t)$ and the measurement posterior $p(\mathbf{x}_0|\mathbf{y})$, where $\mathbf{y}$ denotes the measurement. Importantly, for linear inverse problems, VML can be analytically derived and need not be approximated. Based on further theoretical insights, we propose VML-MAP, an empirically effective algorithm for solving inverse problems, and validate its efficacy over existing methods in both performance and computational time, through extensive experiments on diverse image-restoration tasks across multiple datasets.