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.CE
Model order reduction has the potential to enable real-time patient-specific assessment of cardiovascular flows. However, it still faces significant challenges stemming from the geometric variability of vascular anatomies. Building upon the SynthAorta dataset (Bosnjak et al., IEEE Trans. Med. Imag. 45(1), 2026) of physiological aortic geometries, we generate an extensive dataset of physiologically consistent computational fluid dynamics solutions through an automatic boundary-condition adjustment procedure. A common reference geometry allows all patient-specific anatomies to be represented by displacement fields, providing point-to-point correspondence without the need for geometric registration. Based on this dataset, we develop Graph U-Net and Transformer U-Net surrogate models to predict velocity and pressure fields at peak systole. We further investigate two strategies to enhance data efficiency and prediction accuracy: active learning and differentiable physical consistency constraints based on the finite element residual. The results show that active learning is strongly regime-dependent: while it offers little benefit over random sampling during early training, it improves performance during fine-tuning through gradient- and subspace-based acquisition strategies. Similarly, physical consistency constraints prove to be substantially more effective as a fine-tuning objective than as a regularizer applied throughout training. Finally, out-of-distribution studies demonstrate that the primary limitation of surrogate models lies in the geometric support of the underlying parametrization rather than in the neural network architectures themselves. The proposed framework combines synthetic dataset generation, geometry-aware surrogate modeling, physics-informed optimization, and active learning into a scalable workflow for inter-patient hemodynamic prediction.
physics.flu-dyn
This work presents the development and assessment of a hybrid framework coupling numerical simulation, experimental samples, data assimilation (DA) and machine learning (ML) to investigate the flow within an axial compressor stage. The methodology first implements a Multi-Fidelity Ensemble Kalman Filter (MFEnKF) which integrates experimental PIV data with a two-fidelity numerical simulation setup, combining steady-state RANS on a fixed grid with unsteady hybrid RANS/LES simulations on a moving grid. This data assimilation step successfully reduces discrepancies between experiments and CFD realizations. Besides, it provides additional high fidelity samples when compared with the available PIV data. This enriched database is used to train machine learning (ML) tools, with the objective to obtain black-box forcing terms to be included in the discretized form of the Navier-Stokes equations. These models are expected to preserve the accuracy of the DA results while not longer requiring the input of experimental data. The neural network architecture used here maps local physical features such as the velocity, the velocity gradients and the turbulent viscosity, to obtain the volume forcing terms. The analysis of the performance of such ML models shows that global accuracy is preserved but localized increased errors in specific regions of the compressor, such as close to the blade tips, can exceed those observed from the baseline RANS simulations. To resolve this issue, a Mixture of Experts (MoE) method is employed, which classifies and combines the trained ML tools for different flow regions. The discrepancy with experimental data of this method is systematically lower than the one observed for the baseline RANS solution and very similar to the one obtained with the MFEnKF.
physics.flu-dyn
Scientific machine learning provides a promising framework for solving complex problems in science and engineering. Notably, physics informed neural networks (PINNs) have shown considerable potential for solving differential equations and modelling engineering systems. Solving time fractional Navier Stokes equations (TFNSEs) on complex domains is challenging due to temporal nonlocality, nonlinear flow dynamics, geometric complexity, and incompressibility constraints. To address these challenges, we propose a geometry gated, divergence-free Gaussian radial basis function Kolmogorov Arnold network (GeoDiv KAN). The proposed architecture uses geometry dependent feature gating and a streamfunction formulation to preserve incompressibility by construction. GeoDiv KAN is evaluated for the time fractional incompressible Navier-Stokes equations on square, circular, and star-shaped domains. Numerical experiments show that GeoDiv KAN achieves higher predictive accuracy than PINN, PIKAN, RBF KAN, and DF RBFKAN across the considered benchmark problems. To establish practical relevance, GeoDiv KAN is applied to two data driven CFD cases: unsteady flow past a circular cylinder using the \href{https://doi.org/10.5281/zenodo.5039610}{Zenodo dataset} and turbulent RANS flow through a complex U bend using the \href{https://huggingface.co/datasets/JDecke/ubend-cfd}{U-bend dataset}.
cs.AI
Fine particulate matter (PM2.5) refers to particulate matter with an aerodynamic diameter of 2.5 micrometre or less. It comes from human activities, such as traffic and industry, and from wildfires, desert dust and gases emitted by vegetation. Short-term exposure to it accounts for about a million deaths a year. Operational forecasts run on grids tens of kilometres wide, which hide the pollution breathed by nearly two hundred million people a day. Machine learning has transformed weather forecasting, but data-driven forecasts of air pollution still blur extremes and lose skill as the air travels. Here we introduce Foehn, a generative model that learns from global kilometre-scale estimates of PM2.5 and computes where the air comes from. Over a year of retrospective forecasts, it outperforms the operational forecast at three stations in four and forecasts at the scale of this hidden exposure. Its ensembles are calibrated, and their mean detects local pollution extremes four days ahead as well as the operational forecast does one day ahead. Such forecasts could warn the millions whom coarse maps miss, once kilometre-scale data are available in real time.
cs.AI
Poisson equations frequently appear in various fields, such as mathematics, physics and informatics. Solving Poisson equation, however, is challenging. Traditional methods are not data-specific, although have high certainty. They require a large number of iterations due to the CFL numerical stability. In contrast, deep learning methods are data-driven and more efficient, but require accurate training data and suffer from heavy computation. To tackle these issues, we propose a wavelet-inspired Poisson solver with 24 trainable scalars. The proposed network has several advantages. First, it is compact. It has four independent kernels, each represented by six parameters, leading to 24 scalars in total. Such compact format can be deployed on most devices. Second, thanks to the loop design, it achieves higher accuracy than previous methods. A residual loop reuses the wavelet block without increasing its parameters. Numerical experiments confirm that such loop indeed improves the solving accuracy. On 10000 images, one, two, and three loops of the wavelet block lead to PSNRs of , , and dB, respectively. Third, the proposed method is computationally fast. Thanks to the wavelet transform, the proposed method has linear computation complexity, leading to high computation performance. In short, we propose a novel looped wavelet neural network with compactness, accuracy and efficiency for solving Poisson equations. Our method can be applied in various fields, such as computational fluid dynamics, image reconstruction, biomedical engineering, electromagnetic field simulation.
cs.AI
Computational fluid dynamics (CFD) is computationally expensive for iterative building design. Deep learning surrogates offer faster predictions, but generalization across varying room dimensions remains challenging. This study compares two geometry-conditioned neural network surrogate models for rapid indoor airflow and temperature field prediction under varying room sizes. During the architectural design stage, this method is relevant for real-time assessment of whether conditioned supply air will effectively provide fresh and cool air throughout rooms with varying heights and lengths. The canvas-based neural network (CaNN) explicitly encodes room size by preserving different occupied regions within a fixed canvas, whereas the coordinate-based neural network (CoNN) uses normalized coordinate channels. Both employ U-Net autoencoders to separately predict airflow and temperature fields. Evaluation uses simplified rooms with varying heights and lengths as a controlled benchmark. The results show that CaNN achieves higher agreement with CFD results than CoNN, demonstrating its potential to support performance-driven building design.
math.AP
Practical ship design requires localized refinement and performance evaluation. This paper presents a reward-directed diffusion framework for localized hull optimization. Parametric masking during dataset generation restricts geometric changes to selected variables, including the bulbous bow and forebody, while preserving full-hull continuity. Surrogate-assisted sequential Monte Carlo sampling targets reduced predicted calm-water resistance, with stability retained through training data and displacement matched during screening. An automated viscous free-surface CFD pipeline, validated against measurements for two benchmark container ships, evaluates a generated variant and GenHull E, a hull refined by a naval architect within the same representation. At matched KRISO Container Ship (KCS) displacement, the generated variant has comparable total resistance at but 45-50% higher resistance at and , missed by empirical screening. GenHull E achieves 6-8% lower total resistance up to but higher resistance above as opposing friction and pressure trends reverse the gains. Aggregating resistance across this crossover can conceal tradeoffs that emerge when friction and pressure components are evaluated separately. The assessment reveals an inability to represent a faired bulbous bow and a reward lacking viscous pressure and stability terms. These findings show how high-fidelity assessment informs improved representations and objectives for physically realizable generative designs.
cs.SD
This paper presents a maneuver-aware acoustic fault detection framework for autonomous drones that integrates Noise2Noise-inspired deep learning denoising with maneuver-conditioned reconstruction. A key practical constraint motivating this work is that labeled faulty-flight data are difficult and potentially unsafe to collect; the proposed framework therefore follows an unsupervised learning paradigm in which only nominal flight recordings are required for training. In flight environments, acoustic signals acquired from unmanned aerial vehicles are subject to variability arising both from environmental noise and from structured, maneuver-dependent aerodynamic effects. To address these challenges simultaneously, a two-stage learning architecture is developed. In the first stage, a Noise2Noise-inspired denoising model attenuates stochastic acoustic noise while preserving fault-relevant spectral-temporal structures, without requiring clean reference signals. In the second stage, a maneuver-Conditioned Convolutional AutoEncoder (maneuver-CCAE) is trained using maneuver-related labels including drone type and flight direction to model nominal acoustic behavior under varying operating conditions. Fault detection is subsequently performed using reconstruction error as an anomaly score. Experimental results demonstrate that the proposed maneuver-aware conditioning raises the area under the ROC curve (AUC) from $\AUCaeOnly$ (unconditioned baseline) to $\AUCfull$ (full model), validating the critical role of maneuver-dependent modeling. The complete framework is deployed on an NVIDIA Jetson Orin Nano Super embedded platform within a ROS2 pipeline, achieving an end-to-end fault detection latency of approximately per audio segment with a TensorRT half-precision (FP16) backend, confirming real-time viability for onboard UAV health monitoring.
cs.LG
Neural surrogates for computational fluid dynamics (CFD) have the potential to greatly enhance engineering innovation through accelerating simulation. However, the primary limitation for neural surrogates is the lack of generalization to geometries and applications beyond the training set, which is significant given the diversity of engineering scenarios. Currently, this is addressed by generating a new dataset for a specific application; however, this requires running costly numerical solvers. In this work, we take a step toward addressing this by studying neural surrogates trained across different geometries, boundary conditions, and fidelities. We find that cross-domain pretraining improves zero- and few-shot performance on held-out datasets relative to both training from scratch and transferring from domain-specific experts. In particular, finetuning a pretrained, cross-domain model can achieve 2-3x lower errors at the same sample size and use 8x fewer samples to achieve the same error, compared to training from scratch. This benefit is architecture agnostic and improves with model size and pretraining dataset diversity. Furthermore, we study how and why cross-domain pretraining works in CFD surrogates, and find that simply pooling steady-state datasets is both sufficient and effective. Given the high cost of generating CFD data, leveraging existing datasets through cross-domain pretraining will likely be a valuable strategy as future surrogates expand to tackle new problems and use cases.
physics.flu-dyn
This study considers rapidly modifying the wake shedding frequency of the flow around an airfoil using sparse sensor information, subject to constraints on the lift coefficient fluctuations. This is achieved by combining phase-amplitude reduction with nonlinear machine-learning-based sparse sensor reconstruction. We derive time-varying phase and amplitude sensitivity fields that identify the optimal spatial locations and timing for actuation from merely three sensors. Through the sensitivity fields, we analytically obtain the optimal waveform for fast synchronization of wake shedding frequency while minimizing amplitude deviation of aerodynamic responses. The proposed approach is evaluated using flows over various NACA airfoils at several post-stall angles of attack, all of which exhibit unsteady periodic vortex shedding. With the identified optimal forcing, the wake frequency is altered much faster than with a standard sinusoidal actuation. Furthermore, the amplitude-penalized forcing achieves suppression of the lift coefficient fluctuation compared to the optimal forcing without amplitude penalty. The current amplitude-penalized technique may offer an efficient path for fast flow modification without causing detrimental fluctuations in periodic aerodynamic and aeroelastic systems with fluid-structure interactions.
cs.CV
We introduce StyleFields, a DeepSDF-based architecture for high-fidelity 3D reconstruction that enables controllable geometric style mixing: the coarse structure of one object can be combined with the fine-scale details of another. The core idea is depth-aware modulation: instead of a single global code, we inject latents via multi-level Adaptive Instance Normalization at several decoder depths, and supervise matching auxiliary heads with a coarse-to-fine schedule while gradually growing network depth. This aligns early layers with global shape and later layers with high-frequency detail, achieving content-style decoupling without part labels or adversarial training. StyleFields delivers faithful reconstructions, convincing cross-instance hybrids, and consistent gains in ablations over injection depth and supervision granularity. We further demonstrate a practical application in automotive aerodynamics: a learned surrogate drag predictor serves as a differentiable objective to optimize reconstructed cars, allowing targeted edits of global form or surface details by freezing the complementary latent stream. StyleFields offers a simple, effective recipe for controllable implicit reconstruction and downstream performance-driven design.
physics.comp-ph
Natural supercavitation behind conical cavitators generates a vapor-filled envelope that, when sustained over the full body of a high-speed underwater vehicles, reduces hydrodynamic skin-friction drag and enables performance levels unattainable in fully wetted flow. Accurate prediction of maximum cavity length and maximum cavity radius and local cavity profile as functions of cavitation number and cone half-angle is essential for both the static design and the real-time shape management of super-cavitating torpedo cavitators. Classical analytical models provide computationally inexpensive predictions but exhibit systematic disagreements in the practically important regime of moderate cavitation number and large angle, where slender-body assumptions begin to break down. Existing data-driven machine learning approaches offer higher accuracy but are constrained by the prohibitive cost of multiphase computational fluid dynamics (CFD) sweeps over the full design space. This study proposes a physics-guided multi-fidelity surrogate framework based on Extended Hierarchical Kriging (PG-EHK) that addresses this challenge by fusing the multiple competing analytical cavity formulas as non-level low-fidelity (LF) trend functions corrected by a sparse set of high-fidelity (HF) CFD data. It simultaneously incorporates the analytical models regardless of their local fidelity ordering, using Bayesian-estimated scaling factors to construct the trend function as physical baseline. The resulting surrogate maps operational condition inputs to cavity geometry responses using fewer than 20 high-fidelity CFD evaluations. Cross-validation on five independent hold-out CFD cases demonstrates that the proposed PG-EHK surrogate achieves 61% reduction in prediction error compared to the best-performing individual analytical approach.
physics.flu-dyn
Body-body interactions have long been investigated to leverage the performance of various fluid-based machines. This study analyzes the flow interaction between a cylinder and a NACA0012 airfoil using direct numerical simulation and machine learning. We consider a two-dimensional incompressible flow at Reynolds number 100, where the airfoil is positioned in the wake of a cylinder. By sweeping the parameter space, composed of the distance between the cylinder and the airfoil , the relative height , and the angle of attack of the airfoil , four characteristic vortex-shedding regimes are observed. This study particularly focuses on suppressed vortex shedding at a certain arrangement as oscillation death in coupled oscillators, with the theoretical prediction of flow stability on a machine-learned low-order coordinate. Independent flows around each body are regarded as a system that exhibits isolated periodic vortex shedding at infinite distance, and interactions appear at smaller distances. We employ a synchronization-theoretic autoencoder to derive models for two coupled oscillators from an aerodynamic coefficient. The proposed approach, which enables the assessment of system stability and the prediction of vortical interaction behavior, may pave the way for the analysis of unsteady body-body interactions from the data-driven and synchronization perspectives.
cs.LG
Physics-informed neural network (PINN) training minimizes a weighted combination of partial differential equation (PDE), boundary-condition, and initial-condition losses. Because adaptive methods modify these weights during training, their weighted total losses are not always directly comparable. We compare fixed-weight PINN, gradient-normalized PINN (GNPINN), and a rule-based adaptive controller (AgenticPINN) under matched settings on a heat-equation benchmark and a simplified Czochralski-oriented thermal-fluid problem. In the crystal-growth MLP experiment, adaptive control reduced the PDE residual from the order of to , while the boundary-condition loss increased from the order of to . On the heat-equation benchmark, GNPINN achieved the lowest relative field error (0.054), whereas AgenticPINN obtained the smallest PDE residual but a relative error of 1.368. Gaussian-process surrogates were additionally evaluated using case-wise holdout tests on corrected Czochralski CFD parameter sweeps. The temperature-field error for the temperature sweep was approximately 6%, whereas the axial-velocity error for the crystal-rotation sweep was approximately 42%. These findings show that adaptive control can improve equation satisfaction while weakening other physical constraints. PINN training should therefore be evaluated using separate PDE, boundary-condition, and solution-error metrics rather than weighted total loss alone.
cs.LG
Numerical Linear Algebra (NLA) has consistently played a vital role in advancing science by providing tools to solve fundamental problems encountered in scientific and engineering applications. Over the decades, it has continually evolved to meet the demands driven by successive waves of scientific discovery. For instance, during the 1950s and 1960s, substantial efforts were devoted to developing methods for solving eigenvalue problems that emerged from the rapidly growing field of aerodynamics. This led to the discovery of the LR and QR algorithms. Later the attention turned to the solution of sparse linear systems that were common in applications like computational aerodynamics. Today we are experiencing yet another wave of major scientific advancement and NLA is once more at the heart of its development. This Machine Learning (ML) wave is proving to be utterly disruptive in science and engineering. Many tools in ML particularly Large Language Models (LLMs) are grounded in matrix and tensor methods. As we are approaching Artificial General Intelligence (AGI), it is clear that matrix methods will be called to play an even more significant role. For the numerical linear practitioner the speed of the current change makes it particularly challenging to adapt. This is a survey article that centers on machine learning techniques, with a particular focus on large language models. It has two main objectives. The first is to clarify the core concepts behind Large Language Models in a manner accessible to specialists in numerical methods. The second is to examine the key Numerical Linear Algebra concepts employed by LLM techniques, while also highlighting several significant recent contributions of NLA to the field.
quant-ph
We present a comprehensive review of quantum approaches for solving partial differential equations (PDEs) arising in computational fluid dynamics (CFD). We examine fully quantum approaches, including quantum linear system algorithms (QLSAs), ranging from the Harrow–Hassidim–Lloyd (HHL) algorithm to quantum singular value transformation (QSVT), Hamiltonian simulation, and quantum lattice Boltzmann methods (QLBMs), while emphasizing hybrid quantum–classical approaches, including quantum physics-informed neural networks (QPINNs) and amplitude-encoded variational PDE solvers. We focus on hardware-agnostic algorithms compatible with present noisy processors and emerging fault-tolerant architectures. For each framework, we analyze the mathematical formulation, algorithmic structure, and principal limitations. We also examine tensor-network (TN) representations, since CFD fields, differential operators, and geometrical information can often be encoded efficiently in low-rank form. The TN formalism bridges CFD discretizations and quantum states, operators, and circuits, enabling compact representations to be translated into tensor-programmable variational quantum algorithms (TP-VQAs). We further review benchmark problems, including Poisson, reaction, diffusion, and nonlinear model equations, and assess how well quantum algorithms capture key features of fluid dynamics. Our analysis highlights that potential quantum advantage is highly problem dependent and governed by condition number, representational complexity, state preparation, and measurement constraints. We outline capabilities, limitations, and challenges toward scalable quantum algorithms for CFD.
cs.LG
Machine-learning surrogates accelerate physical simulation, but lower prediction error need not coincide with lower error in physically relevant flow statistics. We examine this question for flow around a NACA4418 airfoil using paired computational-fluid-dynamics simulations and experimental particle-image-velocimetry measurements. A mean-preserving input intervention removes velocity fluctuations from selected regions of observed flow histories. Across four neural operators, removing fluctuations from the most energetic 10% of valid observed cells changes forecasts more than equal-area random removal. Because the masks are not matched for removed fluctuation energy, this contrast measures sensitivity, not independent evidence of physical importance. Separately, a CNO has lower velocity-field error but substantially higher two-component fluctuation-energy error than the reference on both analysis subsets. An output attenuation stress test also demonstrates disagreement between benchmark errors and domain-summed fluctuation energy. These single-benchmark results motivate reporting complementary physical diagnostics alongside aggregate prediction scores; they do not establish counterfactual physical correctness.
cs.RO
Flapping-wing vehicles regulate aerodynamic forces and moments through coordinated variations in stroke, deviation, and pitch motion. Because the resulting loads depend on both the instantaneous wing configuration and its preceding motion history, recovering suitable wing kinematics from a desired aerodynamic trajectory is a challenging inverse problem. Existing sequence models capture temporal dependencies, while spectral methods can exploit the periodic structure of flapping motion. However, unrestricted frequency-domain augmentation may interfere with temporal representations and produce inconsistent corrections across kinematic variables and prediction horizons. We propose the Bounded Channel-Adaptive Spectral Residual Gated Recurrent Unit (BCS-GRU), which retains recurrent temporal prediction as its primary representation and restricts spectral information to a controlled output-specific correction. We further introduce a causally aligned forward-consistency objective that evaluates predicted kinematics through a separately trained and frozen aerodynamic surrogate. Experiments under a unified episode-level protocol show that BCS-GRU improves inverse prediction over recurrent and adaptive-spectral baselines, with greater benefits at longer prediction horizons. Forward-consistent fine-tuning further improves surrogate-based aerodynamic consistency while maintaining mean kinematic accuracy. These results demonstrate that controlled spectral correction and forward-consistent learning provide an effective framework for history-aware inverse modelling of flapping-wing aerodynamics.
cs.CE
Pickup trucks account for 14% of new light-duty vehicles produced in the United States, yet are among the least aerodynamic. Their open cargo bed adds a flow absent from existing automotive aerodynamics datasets such as DrivAerML and SHIFT-SUV: the shear layer leaving the cab roof passes over a recirculating bed flow before separating again at the tailgate. The resulting drag lowers fuel efficiency, raises emissions and limits the range of electric trucks. Scale-resolved Computational Fluid Dynamics (CFD) is too costly for broad design exploration; neural surrogates can predict flow features at a fraction of that cost, provided they are trained on large-scale, high-fidelity, domain-specific data. We introduce SHIFT-Truck, the first such dataset for pickup trucks. It comprises 1,000 Spalart-Allmaras delayed detached-eddy simulations (SA-DDES) of a reference pickup geometry morphed across 17 shape parameters. Each case is run on a mesh of about 100 million cells at a Reynolds number of and released with time-averaged surface pressure, wall shear stress, volumetric pressure and velocity. The setup is verified by grid refinement and repeated runs, and checked against wind-tunnel measurements. We define geometry-grouped splits and benchmark four neural surrogates, DoMINO, GeoTransolver, AB-UPT and SMART, on surface and volume tracks. SHIFT-Truck also introduces controlled distribution shifts in the operating point, the input surface discretization and the vehicle archetype. Models with strong in-distribution performance can degrade substantially under these shifts: operating-condition changes expose failures to infer speed dependence, while tessellation and cross-vehicle shifts reveal markedly different robustness across architectures. SHIFT-Truck is thus a benchmark not only for surrogate accuracy but also for generalization across physical and numerical distributions.
physics.flu-dyn
The Rheological Universal Differential Equation (RUDE) framework embeds neural networks within a frame-indifferent tensorial constitutive backbone and so enables data-driven discovery of complex material rheological behavior. However, the flexibility that makes the RUDE framework attractive also makes it difficult to deploy: the learned neural network correction can make the constitutive equation numerically stiff during training, distribute corrections across non-unique combinations of tensor-basis terms, and extrapolate poorly with increasing nonlinearity, especially for industrially relevant materials with broad relaxation spectra. We develop a stability- and reliability-focused multi-mode RUDE framework that addresses three key challenges: thermodynamic admissibility, out-of-distribution prediction, and interpretability. Logarithmic compression of the input invariants and a split-network architecture improve numerical conditioning during training, while a differentiable projection layer enforces the Clausius–Duhem inequality at every time step. We illustrate the framework with both synthetic (a multi-mode Giesekus model) and experimental data on an entangled silicone polymer melt. Both models were trained on LAOS; they remain stable and accurate under unseen flow conditions, including steady shear, transient stress growth, and extensional flows, for which the unconstrained models may diverge numerically. To aid in interpretation of the contributions of each learned correction to the rheological behavior, we introduce the rheome, a compact way of representing the dominant weighted tensor-basis contributions to the overall rheological behavior. These improvements to the RUDE framework lead to stable and interpretable trained models, paving the way for implementation in computational fluid dynamics simulations and for guiding the rational design of soft material processing operations.