arXiv subjects

Philipp Bekemeyer

Publications and source records attributed to Philipp Bekemeyer.

9 recordsLinked to original sources

arXiv2026

Spatio-Temporal Prediction of Unsteady Airfoil Aerodynamics Using Augmented Graph Neural Ordinary Differential Equations with Exogenous Controls

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.

cs.LG↗

arXiv2026

Evaluation of State-of-the-Art Deep Learning Architectures for Aerodynamical Predictions

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↗

arXiv2026

Solving Nonlinear Partial Differential Equations via a Hybrid Newton Method Using Quantum Linear System Solver

To approximate solutions of complex nonlinear partial differential equations remains a computational challenge, especially for sets of equations relevant in industry, such as Euler or Navier-Stokes equations. Even the most sophisticated computational fluid dynamic algorithms coupled with powerful supercomputers can not find approximate solutions for several design challenges in both adequate time and scale-resolving accuracy. One difficulty arises from solving high dimensional, strongly nonlinear partial differential equations, such as the Navier-Stokes equations, which capture the underlying physics. For nearly all classical algorithms, methods closely related to Newton's method are used to approximate a solution to the problem. Approximately solving the large-scale linear systems of equations occurring in this iterative scheme is generally a main contributor to the total computational complexity. In this paper a new quantum linear system solver supporting Newton's classical method to solve nonlinear partial differential equations is introduced. We present a new variant of the HHL algorithm, requiring less apriori information regarding the eigenvalues of the corresponding matrix. We apply this quantum linear system solver in a hybrid quantum-classical fashion to solve nonlinear partial differential equations. Moreover, a resource estimation for advanced use-cases of practical relevance is provided. Our results demonstrate how quantum computation may improve existing classical methodologies for solving nonlinear partial differential equations. This approach provides another promising application of quantum computers and presents a possible way forward for handling nonlinearities on inherently linear quantum systems.

quant-ph↗

arXiv2026

Goal-Driven Adaptive Sampling Strategies for Machine Learning Models Predicting Fields

Machine learning models are widely regarded as a way forward to tackle multi-query challenges that arise once expensive black-box simulations such as computational fluid dynamics are investigated. However, ensuring the desired level of accuracy for a certain task at minimal computational cost, e.g. as few black-box samples as possible, remains a challenges. Active learning strategies are used for scalar quantities to overcome this challenges and different so-called infill criteria exists and are commonly employed in several scenarios. Even though needed in various field an extension of active learning strategies towards field predictions is still lacking or limited to very specific scenarios and/or model types. In this paper we propose an active learning strategy for machine learning models that are capable if predicting field which is agnostic to the model architecture itself. For doing so, we combine a well-established Gaussian process model for a scalar reference value and simultaneously aim at reducing the epistemic model error and the difference between scalar and field predictions. Different specific forms of the above-mentioned approach are introduced and compared to each other as well as only scalar-valued based infill. Results are presented for the NASA common research model for an uncertainty propagation task showcasing high level of accuracy at significantly smaller cost compared to an approach without active learning.

cs.LG↗

arXiv2025

Fusing CFD and measurement data using transfer learning

Aerodynamic analysis during aircraft design usually involves methods of varying accuracy and spatial resolution, which all have their advantages and disadvantages. It is therefore desirable to create data-driven models which effectively combine these advantages. Such data fusion methods for distributed quantities mainly rely on proper orthogonal decomposition as of now, which is a linear method. In this paper, we introduce a non-linear method based on neural networks combining simulation and measurement data via transfer learning. The network training accounts for the heterogeneity of the data, as simulation data usually features a high spatial resolution, while measurement data is sparse but more accurate. In a first step, the neural network is trained on simulation data to learn spatial features of the distributed quantities. The second step involves transfer learning on the measurement data to correct for systematic errors between simulation and measurement by only re-training a small subset of the entire neural network model. This approach is applied to a multilayer perceptron architecture and shows significant improvements over the established method based on proper orthogonal decomposition by producing more physical solutions near nonlinearities. In addition, the neural network provides solutions at arbitrary flow conditions, thus making the model useful for flight mechanical design, structural sizing, and certification. As the proposed training strategy is very general, it can also be applied to more complex neural network architectures in the future.

cs.LG↗

arXiv2025

Predicting Onflow Parameters Using Transfer Learning for Domain and Task Adaptation

Determining onflow parameters is crucial from the perspectives of wind tunnel testing and regular flight and wind turbine operations. These parameters have traditionally been predicted via direct measurements which might lead to challenges in case of sensor faults. Alternatively, a data-driven prediction model based on surface pressure data can be used to determine these parameters. It is essential that such predictors achieve close to real-time learning as dictated by practical applications such as monitoring wind tunnel operations or learning the variations in aerodynamic performance of aerospace and wind energy systems. To overcome the challenges caused by changes in the data distribution as well as in adapting to a new prediction task, we propose a transfer learning methodology to predict the onflow parameters, specifically angle of attack and onflow speed. It requires first training a convolutional neural network (ConvNet) model offline for the core prediction task, then freezing the weights of this model except the selected layers preceding the output node, and finally executing transfer learning by retraining these layers. A demonstration of this approach is provided using steady CFD analysis data for an airfoil for i) domain adaptation where transfer learning is performed with data from a target domain having different data distribution than the source domain and ii) task adaptation where the prediction task is changed. Further exploration on the influence of noisy data, performance on an extended domain, and trade studies varying sampling sizes and architectures are provided. Results successfully demonstrate the potential of the approach for adaptation to changing data distribution, domain extension, and task update while the application for noisy data is concluded to be not as effective.

cs.LG↗

arXiv2024

Physics-Informed Neural Networks for Transonic Flows around an Airfoil

Physics-informed neural networks have gained popularity as a deep-learning based parametric partial differential equation solver. Especially for engineering applications, this approach is promising because a single neural network could substitute many classical simulations in multi-query scenarios. Only recently, researchers have successfully solved subsonic flows around airfoils with physics-informed neural networks by utilizing mesh transformations to precondition the training. However, compressible flows in the transonic regime could not be accurately approximated due to shock waves resulting in local discontinuities. In this article, we propose techniques to successfully approximate solutions of the compressible Euler equations for sub- and transonic flows with physics-informed neural networks. Inspired by classical numerical algorithms for solving conservation laws, the presented method locally introduces artificial dissipation to stabilize shock waves. We compare different viscosity variants such as scalar- and matrix-valued artificial viscosity, and validate the method at transonic flow conditions for an airfoil, obtaining good agreement with finite-volume simulations. Finally, the suitability for parametric problems is showcased by approximating transonic solutions at varying angles of attack with a single network. The presented work enables the application of parametric neural network based solvers to a new class of industrially relevant flow conditions in aerodynamics and beyond.

physics.flu-dyn↗

arXiv2024

Partitioned Surrogates and Thompson Sampling for Multidisciplinary Bayesian Optimization

The long runtime associated with simulating multidisciplinary systems challenges the use of Bayesian optimization for multidisciplinary design optimization (MDO). This is particularly the case if the coupled system is modeled in a partitioned manner and feedback loops, known as strong coupling, are present. This work introduces a method for Bayesian optimization in MDO called "Multidisciplinary Design Optimization using Thompson Sampling", abbreviated as MDO-TS. Instead of replacing the whole system with a surrogate, we substitute each discipline with such a Gaussian process. Since an entire multidisciplinary analysis is no longer required for enrichment, evaluations can potentially be saved. However, the objective and associated uncertainty are no longer analytically estimated. Since most adaptive sampling strategies assume the availability of these estimates, they cannot be applied without modification. Thompson sampling does not require this explicit availability. Instead, Thompson sampling balances exploration and exploitation by selecting actions based on optimizing random samples from the objective. We combine Thompson sampling with an approximate sampling strategy that uses random Fourier features. This approach produces continuous functions that can be evaluated iteratively. We study the application of this infill criterion to both an analytical problem and the shape optimization of a simple fluid-structure interaction example.

cs.CE↗

arXiv2023

Physics-Informed Neural Networks for Parametric Compressible Euler Equations

The numerical approximation of solutions to the compressible Euler and Navier-Stokes equations is a crucial but challenging task with relevance in various fields of science and engineering. Recently, methods from deep learning have been successfully employed for solving partial differential equations by incorporating the equations into a loss function that is minimized during the training of a neural network. This approach yields a so-called physics-informed neural network. It is not based upon classical discretizations, such as finite-volume or finite-element schemes, and can even address parametric problems in a straightforward manner. This has raised the question, whether physics-informed neural networks may be a viable alternative to conventional methods for computational fluid dynamics. In this article we introduce an adaptive artificial viscosity reduction procedure for physics-informed neural networks enabling approximate parametric solutions for forward problems governed by the stationary two-dimensional Euler equations in sub- and supersonic conditions. To the best of our knowledge, this is the first time that the concept of artificial viscosity in physics-informed neural networks is successfully applied to a complex system of conservation laws in more than one dimension. Moreover, we highlight the unique ability of this method to solve forward problems in a continuous parameter space. The presented methodology takes the next step of bringing physics-informed neural networks closer towards realistic compressible flow applications.

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