Papers
Machine learning for physics, as it is published.
New work from arXiv on CFD surrogates, neural operators and physics-informed learning, refreshed every hour. Search it, filter by topic, or start with the papers we keep coming back to.
Papers
New work from arXiv on CFD surrogates, neural operators and physics-informed learning, refreshed every hour. Search it, filter by topic, or start with the papers we keep coming back to.
1,058 papers in CFD surrogates · newest first
cs.LG
Spatial atomic layer deposition (SALD) is a leading atmospheric-pressure, high-throughput route to industrial ALD, but design and control are limited by the cost of predicting surface coverage: high-fidelity CFD is far too slow for operating-window scans, while analytic models miss transport modulation such as the gas curtain. We present a physics-chemistry-informed neural network (PCINN), a hybrid surrogate with CFD-level accuracy at real-time speed: a query returns coverage in about 7 ms, roughly 5x10^4 times faster than a CFD solve, reaching a test R^2_log = 0.998 (leave-one-out R^2_raw = 0.974) from only 30 training cases spanning four orders of magnitude in coverage. The architecture is not a black box: a small network learns only the operating-condition to near-wall concentration closure, while the known surface kinetics is a hard-coded, trainable chemistry layer integrated along the substrate trajectory. This single-scalar bottleneck keeps it accurate under sparse data, interpretable and invertible. We add a full identifiability analysis (Fisher information, profile likelihood). The adsorption energy E_ads and desorption rate k_des are robustly identifiable; k_ads is not separately identifiable at a single temperature (only k_ads*c_wall is). Across four temperatures the prefactor nu and E_ads bind along a weakly identifiable degeneracy valley of slope 0.065 eV/decade, derived analytically as k_B T_eff ln(10) and turned into a reliability diagnostic: a seven-chemistry mismatch matrix shows it is invariant under any single-Arrhenius mismatch and shifts only when a second thermally activated process appears, so a slope departure flags unmodelled site heterogeneity. Data come from simulation with known ground truth inverted by the same kinetic form, so the study verifies pipeline self-consistency and the identifiability boundary, not real parameters.
physics.flu-dyn
The aerodynamic design of turbomachinery is critical to the performance of the overall energy system, yet it is challenging due to the complex non-linear flow physics and the presence of multiple-target design compromises. Denoising diffusion model, as one of the leading approaches in generative machine learning, has shown its advantages of high design solution accuracy and diversity in many engineering applications. In this study, we bring it to the 3D inverse design problem of turbomachinery, using centrifugal compressors as a classic representative, to demonstrate the new methodology for complex geometry designs. A diffusion model-centred design framework has been developed in this study. By specifying the desired design condition (mass flow rate and rotational speed) and targeted performance (pressure ratio and efficiency), the trained diffusion model returns directly the 3D compressor geometry that satisfies the condition inputs. Compared to traditional deterministic forward design approaches, the proposed method not only generates accurate geometry solutions to inverse design problems, but also enables effective exploration of the entire design space, providing a diverse set of candidate solutions. In addition, this paper presents the first study to directly train on 3D blade geometry coordinates rather than parametrised representations, demonstrating the feasibility of coordinate-based learning while enabling a highly flexible framework applicable to a wide range of designs. The trained diffusion model achieves excellent design capability, with solution accuracy up to 99% and unfeasible designs less than 1%. Furthermore, the solution diversity of the trained diffusion model is also quantitatively verified by means of comparing the distribution of the solution sets generated from the diffusion model and from direct sampling of physical parameters.
cs.LG
Monte Carlo simulation of calorimeter showers is a principal bottleneck for the High-Luminosity LHC, and diffusion models have emerged as fast, high-fidelity surrogates. Their denoising objective is purely statistical, however: a model can minimize it while placing the physics wrong. Existing physics-informed generative methods cannot close this gap, because they assume a closed-form law, a governing PDE residual or a hard per-sample constraint, that a shower does not supply: no per-sample PDE governs a stochastic cascade, and energy conservation fixes only one scalar per shower. Standard metrics ignore the correlation structure across calorimeter layers and voxels, comparing showers only in a physics feature space. We address both gaps. We introduce the Correlation Frobenius Distance (CFD), a single normalized score for correlation fidelity at layer-wise and voxel-wise scales. We then encode the soft per-sample structure available in a shower as two physics-aware auxiliary losses: a variance-stabilized voxel residual loss grounded in counting statistics, and a graph Laplacian loss over the detector geometry. We combine both with denoising through GradBlend, which anchors the step magnitude to the denoising gradient while letting the auxiliary steer its direction, yielding Lantern, a physics-guided diffusion surrogate. On CaloChallenge Dataset 2, injecting the physics losses through task-symmetric rules such as PCGrad, GradNorm, IMTL-G, and ConFIG inflates FPD by 2-100x relative to denoising alone, whereas GradBlend admits the same signal without regression and, with the Laplacian loss, Lantern improves both FPD and CFD. Our ablation on the auxiliary loss scheduler shows that the voxel residual loss, whose gradient conflicts with denoising, requires a terminal denoising-only phase to preserve shower fidelity, whereas the non-conflicting Laplacian loss is insensitive to the schedule.
physics.flu-dyn
Self-excited aerodynamic flows arise across a broad range of systems and can drive nonlinear fluid-structure interactions and aeroelastic instabilities that are challenging and computationally expensive to predict. This paper presents a physics-guided neural differential equation (DE) reduced order model (ROM) combining a nonlinear fluid oscillator, a finite-memory multi-input Volterra series, and a compact neural network correction. The multi-input aerodynamic formulation is generalized to m structural modes, capturing direct and nonlinear cross-modal coupling. The model is identified from a single prescribed-motion CFD simulation with simultaneous excitation of all retained structural modes, and is then coupled with the structural equations of motion for efficient aeroelastic prediction. Applied to transonic buffet over the ONERA OAT15A airfoil, the time-marching ROM predicts aeroelastic stability, frequency lock-in, and limit cycle amplitudes in good agreement with full-order reference solutions. The ROM is used to provide substantial new insight into buffet-induced aeroelastic instabilities involving more than one structural mode.
physics.flu-dyn
Neural surrogates are widely used in scientific machine learning for fast prediction of three-dimensional (3D) thermo-fluid fields. However, generating training data using conventional numerical solvers often incurs substantial computational and storage costs. We propose to train an attention graph neural network by minimizing the finite-volume method (FVM) residuals of the governing equations. These residuals are evaluated directly on the mesh, requiring no labeled data. We evaluate the trained surrogates against computational fluid dynamics (CFD) references and a data-supervised baseline across four scenarios. On the two steady-state benchmarks, each solved on the same mesh as its CFD reference, the FVM-loss model reproduces the reference flow and temperature fields with mean field-averaged normalized root-mean-square errors (nRMSEs) near 3%, including the buoyancy-energy coupling. On the two parametric transient cases, the FVM-loss model attains lower rollout errors than the supervised baseline in almost every field, while avoiding the data-generation cost entirely. These results indicate that the FVM loss can provide a practical training signal for neural surrogates and reduce the model development cost.
cs.NE
Hydrogen infrastructure in enclosed environments, such as parking facilities for fuel cell vehicles, presents significant safety challenges due to hydrogen's low ignition energy and wide flammability range. Current monitoring systems are largely reactive, detecting leaks only after hazardous concentrations have formed. This study develops a computational framework for proactive sensor placement optimization by integrating computational fluid dynamics (CFD), genetic algorithm (GA) optimization, and a DeepSets neural surrogate. A CFD database of 180 scenarios was generated for a representative 50 m x 30 m x 3 m garage, covering multiple leak positions, rates (1-150 g/s), and ventilation conditions (ACH = 3-10 per hour). Sensor placement was optimized using a multi-objective GA and compared with uniform, random, and surrogate-assisted approaches. The GA achieved a detection rate of 96.1% within 60 s and reduced blind areas to 0.12%, corresponding to an approximately 5% improvement in composite fitness over a uniform baseline. The DeepSets surrogate reproduced near-optimal configurations with a fitness gap below 0.01 while reducing CFD evaluations by 89% and computational time by two orders of magnitude. Detection performance and spatial coverage remained comparable to the GA, demonstrating that surrogate-assisted optimization can retain solution quality while enabling rapid design iteration. Overall, the results show that CFD-informed optimization improves detection effectiveness and reduces sensor requirements compared to conventional layouts. The proposed framework supports scalable deployment and provides a foundation for integrating optimized sensor networks with digital twin systems for real-time monitoring and risk assessment.
physics.flu-dyn
Wall-modelled large-eddy simulation (WMLES) treats the subgrid-scale (SGS) closure, wall closure and numerical discretization as independent components, although their effects are coupled through the same resolved field. We present a differentiable hybrid neural–CFD framework in which the SGS and wall closures are learned jointly, end-to-end, within a differentiable flow solver, using only low-order statistics as training targets. Each closure is a composed neural operator: a trainable neural network followed by a fixed differentiable layer that preserves the structure of its conventional counterpart, so that the network learns only the functions left undetermined by the conventional form. Because every operation is differentiable, gradients of the training loss are back-propagated through the coupled solver, allowing both neural closures to be optimized consistently against the flow field, rather than fitted offline or in isolation. We demonstrate the framework, denoted Hybrid-Joint, on a zero-pressure-gradient turbulent boundary layer across a posteriori tests spanning Re_θ= 600–6500, computational domains and mesh resolutions. The model outperforms WMLES baselines, extrapolates to more than four times the highest training Reynolds number, and transfers to grids and domains absent from training. It recovers a logarithmic mean-velocity region, not imposed by the wall closure, and reproduces the resolved energy spectra accurately, although spectral information is excluded from the training objective. Ablation studies show that learning either closure alone is insufficient and that only joint optimization recovers the full set of statistics, confirming that SGS closure, wall closure and discretization are coupled and must be trained jointly. Once trained, the closures are reused without retraining across all cases, so that training cost is amortized over repeated deployment.
physics.flu-dyn
High-fidelity computational fluid dynamics (CFD) provides detailed aerodynamic data for vehicle design, but its cost limits design iteration. Neural-operator surrogates reduce this cost, yet their deterministic predictions do not indicate when a geometry or surface region is reliable. This study develops a conformal-prediction framework for reliability-aware automotive aerodynamic surrogate modeling on the DrivAerML dataset. GeoTransolver is the main backbone, while Transolver assesses transfer across neural-operator architectures. For drag coefficient prediction, conformalized quantile regression constructs calibrated case-level intervals. For surface pressure and wall shear stress (WSS), point prediction is combined with residual-scale estimation and residual-normalized conformal calibration to obtain spatially adaptive intervals. Global absolute, point-adaptive normalized, and case-wise normalized calibration are compared under split and cross-validation-assisted out-of-fold protocols. All experiments target 90% nominal coverage. Conformal calibration corrects the under-coverage of raw drag-coefficient quantile intervals, while out-of-fold score aggregation reduces the Monte Carlo coverage standard deviation from 10.41 to 3.10 percentage points. For surface fields, point-adaptive normalized calibration yields the narrowest near-nominal intervals, reducing mean width by 22.68% for pressure and 25.35%–27.09% for WSS under the out-of-fold protocol. Case-wise normalized calibration is more conservative but improves vehicle-level reliability. Smoothness regularization reduces the residual-scale local-variation score by 74.29% and lowers interval widths without material coverage loss. The framework converts deterministic neural-operator outputs into calibrated reliability indicators for prioritizing uncertain vehicle geometries and surface regions in follow-up CFD verification.
eess.SY
Wind farm control (WFC) plays a crucial role in mitigating the wake effect, the negative aerodynamic interactions among wind turbines. Recent advances in data-driven control and artificial intelligence offer new opportunities to design more intelligent WFC systems, motivating the need for a tool that supports interactive design and validation in simulation. To address this, we present ffconnect, a general, open-source Python-based interface for FAST.Farm, a mid-fidelity wind farm simulator. Compared to prior work, ffconnect introduces a restructured Application Programming Interface (API) with enriched state access and supports integrating FAST.Farm with modern scientific computing and machine learning ecosystems by building entirely on Python. In experiments, ffconnect shows negligible runtime overhead compared to the original FAST.Farm across a range of simulation lengths and farm sizes, and demonstrates its effectiveness through a yaw-tracking case study. Finally, we provide the source code of ffconnect to keep it accessible for general users.
cs.LG
Unsteady aerodynamic phenomena, such as gusts, turbulence, and fluid-structure interactions affect an aircraft during flight. For design, optimisation and certification, it is indispensable to quantify such unsteady aerodynamic effects. Industry-standard computational fluid dynamics methods, such as solving the unsteady Reynolds-averaged Navier-Stokes equations or the linearized frequency domain method, are either computationally expensive or restricted by assumptions like linearity. Once trained, machine learning methods are capable of computing non-linear relationships very fast, making them suitable as surrogate models. By autoregressively applying graph neural networks (GNNs), operating on a discretised spatial domain, spatio-temporal predictions can be made. However, autoregressive GNNs suffer from error accumulation leading to unstable rollouts over time. Here we show that combining GNNs with augmented Neural Ordinary Differential Equations yields temporally stable predictions of the surface forces on a pitching airfoil. We found that our approach, called GNODE, based on Graph Neural Ordinary Differential Equations, provides temporally more stable, spatially smoother, and overall more accurate results than an autoregressive GNN baseline. Tests are conducted on a dataset consisting of a simulations of a pitching airfoil, including transonic shocks, transient behaviour and dynamic non-linearities. Augmenting GNODEs with additional latent dimensions improves the expressivity and accuracy by capturing underlying history effects. The developed method demonstrates an approach that is suitable to model non-linear spatio-temporal systems with exogenous inputs.
physics.flu-dyn
Recent advances in data-driven modelling have highlighted the potential of hybrid approaches which combine Tensor Basis Neural Networks (TBNN) with Universal Differential Equations (UDE) to discover frame-invariant, non-linear viscoelastic constitutive models. These hybrid models enable the creation of digital twins for complex viscoelastic fluids, offering direct transferability to computational fluid dynamics simulations. In this work, we introduce a reduced dimensional tensor basis formulation that enhances both the physical consistency of the learned representations with respect to the training data and the numerical stability of subsequent simulations. The UDE architecture is embedded into an open-source finite volume solver in which the constitutive response is generated dynamically at runtime based on local fluid flow conditions. Training on synthetic datasets generated using a range of well established viscoelastic models in oscillatory shear flows alone, the performance of the resulting UDEs is evaluated under extrapolation to unseen conditions and flow-types. These include deploying the UDEs in viscometric extensional flows as well as 2D and 3D benchmark flows, such as the 4:1 sudden contraction and cross-slot, providing a quantitative analysis of their capabilities, limitations and failure modes. The proposed reduced-basis framework enables data-efficient discovery of frame-invariant constitutive models that generalise beyond their training regime, capturing key flow features such as the onset and growth of flow-induced elastic instabilities in strong extensional flows even though trained solely on shear data. Quantitative accuracy decreases as extrapolation increases, but incorporating first normal stress difference information further improves quantitative accuracy and extends predictive fidelity to higher Deborah numbers.
physics.flu-dyn
Surrogate models are used to substitute classical numerical solvers in engineering applications where the computational cost of the latter becomes infeasible. For instance, in aerodynamics such models offer cost-effective alternatives to computational fluid dynamics in problems such as shape optimization and load analysis, which oftentimes require high-fidelity simulations for a multitude of different parameter combinations. A specific class of deep learning-based surrogate models termed operator learning models directly approximates the solution operators to the partial differential equations underlying the physical phenomenon, thereby learning to replicate solutions to entire families of problems. However, while nowadays numerous architectures of this type get published, corresponding benchmark studies remain scarce. In this article, we advance the study of AI-based surrogate methods by thoroughly benchmarking four state-of-the-art operator learning models on their aptitude for applications in aerospace engineering. In two experiments, we assess the models' capabilities of predicting the surface pressure distribution on two-dimensional airfoil shapes of varying complexity and on an industrial-scale three-dimensional aircraft configuration. Thereby, we evaluate the models' abilities to fulfill frequent requirements in aerodynamics such as capturing discontinuities (shocks) in the solutions, scalability towards excessive amounts of mesh points and handling of data scarcity. Accompanied by a careful analysis, our findings drive forward the field of AI-based surrogate modeling by providing detailed insights into the strengths and weaknesses of the individual architectures, thus allowing to identify priorities for future developments. In particular the Bi-Stride Multi-Scale Graph Neural Network and Transolver(++) are highlighted as promising surrogate models for aerodynamical applications.
physics.flu-dyn
In this study, a conditional diffusion model – a class of generative machine learning models – is developed to generate synthetic, experimental data-based trajectories of turbulent flames. Generated experimental data corresponds to simultaneous field measurements, namely OH planar laser-induced fluorescence (OH-PLIF) fields and multi-component particle image velocimetry (PIV) fields, for attached and detached flame states in a swirl combustor configuration. This is done using an x-prediction flow matching framework combined with a pixel-based spatiotemporal transformer, which is capable of generating entire spatiotemporal slabs containing synthetic flame evolution at inference time, conditioned on the flame regime. Using this framework, synthetic flames were found to preserve key flame features and statistical consistency across space and time, particularly at the large scales – deviations at high temporal frequencies and small spatial length scales were found to depend on the time-span of the generated space-time slabs. An extrapolation task of transition synthesis is also conducted, in which the conditional diffusion model is used to synthesize spatiotemporally coherent flame transitions (flame liftoff and reattachment) unseen by the model during training. This was accomplished using a model for the denoising transition velocity that relies on time-varying linear combinations of attached and detached denoising velocities, leading to an approach that (a) allows for control of the generated transition directions and timescales, and (b) retains sample-to-sample variability in the generated transitions in the process. Overall, this study provides a promising pathway for the utilization of experimental data-based generative models as a new means of data exploration in data-sparse environments, complementing both experiments and computational fluid dynamics-based approaches.
physics.plasm-ph
Many nonlinear physical systems exhibit an initial transient phase in which perturbations grow before nonlinear interactions lead to a statistically steady state. While this saturated regime is of primary interest, direct numerical simulations must resolve the full transient dynamics before reaching it, incurring significant computational cost. In Computational Fluid Dynamics, reduced-order approaches such as Large Eddy Simulation mitigate computational cost by modeling small-scale dynamics, enabling tractable approximations of turbulent flows. In contrast, for systems such as gyrokinetics, comparably effective closures for the full dynamics are not generally available, and high-fidelity simulations remain necessary. Existing surrogate modeling approaches for these systems are autoregressive, hence they suffer from accumulating error. We instead propose to bypass explicit time evolution by directly modeling the distribution of saturated states under an ergodicity assumption, stating that ensemble averages over samples are equivalent to time averages of a single long simulation. We introduce GyroFlow, a latent generative model that directly estimates steady-state statistics of gyrokinetic turbulence in 5D phase space, without resolving the transient phase. GyroFlow generates saturated snapshots from noise, conditioned on dimensionless operating parameters and outperforms autoregressive, reduced-order, and other generative approaches, while providing substantial speedup. To evaluate generation quality we propose FGyD, a distributional metric computed in the latent space of a pretrained gyrokinetic model, and show that it correlates with downstream flux accuracy and solver convergence. Finally, GyroFlow can be used to warm-start the numerical code used to produce the data.
math.NA
Accurate, spatially resolved flow field measurements are essential for the reliable assessment of hemodynamic quantities in cardiovascular research and clinical practice. Experimental techniques, such as 4D flow MRI, PIV, or Doppler ultrasound, often yield data that are sparse, noisy, or under-resolved, particularly near vessel walls and in regions of complex flow. This limits the fidelity of distributed or derived hemodynamic indicators such as the wall shear stress and the clinical utility of such measurements. To address these challenges, we propose a physics-informed neural network (PINN) framework that integrates the incompressible Navier-Stokes equations with velocity measurements coming from experimental flow field data. By embedding physical laws into data, PINN enhances the reconstruction of velocity fields, enables the estimation of unmeasured quantities such as pressure and wall shear stress, and improves the spatial resolution of hemodynamic indicators. We show the effectiveness of our approach using both in silico and experimental data. First, we apply our method to the FDA nozzle benchmark, leveraging both control particle image velocimetry (PIV) measurements and computational fluid dynamics (CFD) simulations. Next, we apply our method to the more complex case of blood flow in an aneurysm model, exploiting in vitro 4D flow MRI data. In both cases, the synergy between data-driven learning and physics-based regularization yields results that align more closely with ground truth observations than standard CFD or pure data-driven approaches. Our findings highlight the potential of PINNs to improve the fidelity of under-resolved flow field measurements and yield spatially resolved hemodynamic indicators.
physics.flu-dyn
Machine-learning surrogates for computational fluid dynamics (CFD) predict steady flow fields far faster than classical solvers, but emit a single field with no built-in way to know whether to trust it – especially out of distribution. We make the surrogate audit itself against the governing physics: we compute the discretised steady-state Reynolds-averaged (RANS) residual of the prediction and ask what jobs it can do. Our central finding is a clean two-way dissociation: the physics residual is a reliable, backbone-robust trust signal (it tells you where the prediction is wrong) but a poor correction objective (it does not tell you how to fix it). As a trust signal, the residual's per-case rank correlation with field error is consistently positive across three architecturally distinct backbones and a second dataset of laminar bluff bodies; it flags the worst-decile cases with AUROC , and a distribution-free split-conformal layer attains its target coverage. As a correction objective, the residual fails: reducing it does not reduce field error. The monotone-residual acceptance gate built on it, by contrast, does help. Separately, a learned deep-equilibrium corrector trained toward ground truth lowers volume-field error on a state-of-the-art backbone; a controlled ablation that removes the residual input matches this gain, so the improvement comes from the learned correction, not from conditioning on the residual. The contribution is a self-auditing, calibrated trust layer, the residual's two roles (trust signal yes, correction objective no), and the learned correction it accompanies, demonstrated on a competitive surrogate and released as the open-source neuroforge-cfd package.
physics.flu-dyn
We present a physics-constrained machine learning framework for accelerating the direct numerical simulation (DNS) of turbulent reacting flows. The model replaces the direct evaluation of detailed chemical source terms with a surrogate that predicts reaction rates from a reduced thermochemical state. To improve physical consistency, the second law of thermodynamics is incorporated as a training constraint by enforcing non-negative entropy generation, which restricts the evolution of the thermochemical state to physically admissible directions and improves stability during time integration. The approach is demonstrated on DNS of a two-dimensional planar lean premixed methane-air flame interacting with a turbulent flow field. The model reproduces detailed-chemistry results with high fidelity while achieving more than an order-of-magnitude reduction in computational cost. Furthermore, a residual-based synthetic data augmentation strategy enables parametric exploration by constructing new training data from the original dataset, allowing accurate simulation at new inlet conditions without additional detailed-chemistry CFD runs. These results demonstrate that thermodynamically constrained machine learning can provide reliable and computationally efficient surrogates for detailed chemistry in high-fidelity combustion simulations.
cs.RO
Precise control and positioning of autonomous underwater vehicles (AUVs) is critical for sampling, maintenance, and survey applications. Reinforcement learning (RL) offers rapid controller development while handling a range of deployment parameters via domain randomization (DR). However, DR is limited by the underlying simulation's capacity to model real physics such as drag, which is a large contributor to sim-to-real gaps. Computational fluid dynamics (CFD) provides high-fidelity drag models but has significant computational cost. Thus, in this paper we train surrogate approximations of CFD data of a given vehicle, providing drag estimates 700,000x faster than solving for drag at each time step with CFD within the RL training pipeline. We deploy a Proximal Policy Optimization (PPO) policy zero-shot on a 6-DOF AUV in which policy training is performed on these surrogate drag models (SDMs), providing analysis on zero-shot transfer, reward shaping sensitivity, and physical parameter perturbations. On 15 identical segments in the ocean, we observe median gains of 19% in mean tracking error and 31% in control effort compared to the equivalent inertia box model. Our SDM based RL controller better predicts zero-shot transfer and reaches the most waypoints across all three reward shaping choices that we evaluate. Finally, we add 0.907 kg to the vehicle perturbing the mass, center-of-mass, and center-of-buoyancy. The policy reaches 100% of waypoints only when the SDM drag model is used; the policy fails to reach any of the 15 waypoints when the other drag models are used.
cs.CV
Engineering shape optimization faces challenges in both expert-dependent problem setup and surrogate-model reliability. In practical aerodynamic design, optimization settings such as editable regions, deformation ranges, and design-preservation constraints are typically specified manually by experienced engineers, while surrogate-based optimization may become unreliable for heterogeneous geometry databases and out-of-distribution designs. To address these challenges, we propose a knowledge-constrained shape-optimization framework that translates knowledge-based constraints and user intent into quantifiable parameters of DFFD-based deformation operators, enabling engineering-aware and controllable constrained optimization. We further develop a Mixture-of-Experts Neural Operator (MoE-NO) to improve drag prediction and trend consistency over heterogeneous aerodynamic datasets. Based on the MoE-NO encoder and Mahalanobis distance, an uncertainty-estimation strategy is introduced to detect out-of-distribution geometries and selectively trigger physics-solver feedback for local sample enrichment. Experiments on in-house MPV, SUV, and Sedan datasets show that MoE-NO achieves a test-set MAPE of and a trend-prediction accuracy of , outperforming the best baseline results of and , respectively. Vehicle shape-optimization experiments further yield CFD-validated drag coefficient reductions of approximately to .
physics.flu-dyn
Data-driven turbulence closures are commonly calibrated by embedding a CFD solver within an inverse procedure that requires a converged flow solution at every optimization iteration, which is fragile and costly. We instead formulate closure identification as a PDE-constrained, data-driven inverse problem within a physics-informed neural network (PINN), and subsequently stabilize the inferred closure for deployment in a numerical solver. This separation eliminates the training cost of repeated CFD solves and associated adjoint or ensemble evaluations, providing substantial flexibility to investigate alternative closure forms. Using this flexibility, we develop four closures: three model the Reynolds stress on a realizable tensor basis—a local map, a non-local model transporting the turbulent kinetic energy and recovering the out-of-plane normal stress, and the same with a learned length scale —and a fourth models the Reynolds force directly, free of the realizability constraint. All four are trained across six two-dimensional bluff-body wakes at and deployed frozen in a standard finite-element solver, stabilized primarily by input-gradient smoothing. Under a strict leave-one-shape-out (LOSO) protocol, all four reduce the field errors of a steady SST - baseline, most strongly on the mean velocity. The learned-length-scale closure is most accurate on the stress fields, while the force model generalizes best on the mean velocity and drag (LOSO drag error ). The closures also train efficiently on Particle Image Velocimetry data, enabling geometries intractable for DNS.