Gonzalo Rubio

Juan Manzanero, Gonzalo Rubio, Esteban Ferrer et al.

We analyse instabilities due to aliasing errors when solving one dimensional non-constant advection speed equations and discuss means to alleviate these types of errors when using high order discontinuous Galerkin (DG) schemes. First, we compare analytical bounds for the continuous and discrete version of the PDEs. Whilst traditional $L^2$ norm energy bounds applied to the discrete PDE do not always predict the physical behaviour of the continuous version of the equation, more strict elliptic norm bounds correctly bound the behaviour of the continuous PDE. Having derived consistent bounds, we analyse the effectiveness of two stabilising techniques: over-integration and split form variations (conservative, non-conservative and skew-symmetric). Whilst the former is shown to not alleviate aliasing in general, the latter ensures an aliasing-free solution if the splitting form of the discrete PDE is consistent with the continuous equation. The success of split form de-aliasing is restricted to DG schemes with the summation-by-parts simultaneous-approximation-term (SBP-SAT) properties (e.g. DG with Gauss-Lobatto points). Numerical experiments are included to illustrate the theoretical findings.

Juan Manzanero, Esteban Ferrer, Gonzalo Rubio et al.

We analyse numerical errors (dissipation and dispersion) introduced by the discretisation of inviscid and viscous terms in energy stable discontinuous Galerkin methods. First, we analyse these methods using a linear von Neumann analysis (for a linear advection-diffusion equation) to characterise their properties in wave-number space. Second, we validate these observations using the 3D Taylor-Green Vortex Navier-Stokes problem to assess transitional/turbulent flows. We show that the dissipation introduced by upwind Riemann solvers affects primarily high wave-numbers. This dissipation may be increased, through a penalty parameter, until a critical value. However, further augmentation of this parameter leads to a decrease of dissipation, reaching zero for very large values. Regarding the dissipation introduced by second order derivatives, we show that this dissipa- tion acts at low and medium wave-numbers (lower wave-numbers compared to upwind Riemann solvers). In addition, we analyse the Spectral Vanishing Viscosity (SVV) technique, previously used in continuous discretisations (e.g. Fourier), to find that with an appropriate kernel (which damps selected modes) it is possible to control the amount of dissipation introduced in the low and medium wave-number range. Combining these ideas, we finally propose a DG-SVV approach that uses a Smagorinsky model to compute the numerical viscosity. This DG-SVV approach is tested in an isotropic laminar/turbulent under-resolved scenario. Combining the SVV technique with a low dissipation Riemann solver, we obtain a scheme capable of maintaining low dissipation levels for laminar flows, whilst providing the correct dissipation for all wave-number ranges in turbulent regimes.

David Huergo, Gonzalo Rubio, Esteban Ferrer

Reinforcement learning (RL) has emerged as a promising approach to automating decision processes. This paper explores the application of RL techniques to optimise the polynomial order in the computational mesh when using high-order solvers. Mesh adaptation plays a crucial role in improving the efficiency of numerical simulations by improving accuracy while reducing the cost. Here, actor-critic RL models based on Proximal Policy Optimization offer a data-driven approach for agents to learn optimal mesh modifications based on evolving conditions. The paper provides a strategy for p-adaptation in high-order solvers and includes insights into the main aspects of RL-based mesh adaptation, including the formulation of appropriate reward structures and the interaction between the RL agent and the simulation environment. We discuss the impact of RL-based mesh p-adaptation on computational efficiency and accuracy. We test the RL p-adaptation strategy on a 1D inviscid Burgers' equation to demonstrate the effectiveness of the strategy. The RL strategy reduces the computational cost and improves accuracy over uniform adaptation, while minimising human intervention.

Andrés Mateo-Gabín, Kenza Tlales, Eusebio Valero et al.

We present a novel unsupervised machine-learning sock sensor based on Gaussian Mixture Models (GMMs). The proposed GMM sensor demonstrates remarkable accuracy in detecting shocks and is robust across diverse test cases with significantly less parameter tuning than other options. We compare the GMM-based sensor with state-of-the-art alternatives. All methods are integrated into a high-order compressible discontinuous Galerkin solver, where two stabilization approaches are coupled to the sensor to provide examples of possible applications. The Sedov blast and double Mach reflection cases demonstrate that our proposed sensor can enhance hybrid sub-cell flux-differencing formulations by providing accurate information of the nodes that require low-order blending. Besides, supersonic test cases including high Reynolds numbers showcase the sensor performance when used to introduce entropy-stable artificial viscosity to capture shocks, demonstrating the same effectiveness as fine-tuned state-of-the-art sensors. The adaptive nature and ability to function without extensive training datasets make this GMM-based sensor suitable for complex geometries and varied flow configurations. Our study reveals the potential of unsupervised machine-learning methods, exemplified by this GMM sensor, to improve the robustness and efficiency of advanced CFD codes.

David Huergo, Martín de Frutos, Eduardo Jané et al.

We present a novel approach to automate and optimize anisotropic p-adaptation in high-order h/p solvers using Reinforcement Learning (RL). The dynamic RL adaptation uses the evolving solution to adjust the high-order polynomials. We develop an offline training approach, decoupled from the main solver, which shows minimal overcost when performing simulations. In addition, we derive an inexpensive RL-based error estimation approach that enables the quantification of local discretization errors. The proposed methodology is agnostic to both the computational mesh and the partial differential equation to be solved. The application of RL to mesh adaptation offers several benefits. It enables automated and adaptive mesh refinement, reducing the need for manual intervention. It optimizes computational resources by dynamically allocating high-order polynomials where necessary and minimizing refinement in stable regions. This leads to computational cost savings while maintaining the accuracy of the solution. Furthermore, RL allows for the exploration of unconventional mesh adaptations, potentially enhancing the accuracy and robustness of simulations. This work extends our original research, offering a more robust, reproducible, and generalizable approach applicable to complex three-dimensional problems. We provide validation for laminar and turbulent cases: circular cylinders, Taylor Green Vortex and a 10MW wind turbine to illustrate the flexibility of the proposed approach.

David Ramos, Lucas Lacasa, Eusebio Valero et al.

The main objective of this paper is to introduce a transfer learning-enhanced deep reinforcement learning (DRL) methodology that is able to optimise the geometry of any airfoil based on concomitant aerodynamic and structural integrity criteria. To showcase the method, we aim to maximise the lift-to-drag ratio $C_L/C_D$ while preserving the structural integrity of the airfoil -- as modelled by its maximum thickness -- and train the DRL agent using a list of different transfer learning (TL) strategies. The performance of the DRL agent is compared with Particle Swarm Optimisation (PSO), a traditional gradient-free optimisation method. Results indicate that DRL agents are able to perform purely aerodynamic and hybrid aerodynamic/structural shape optimisation, that the DRL approach outperforms PSO in terms of computational efficiency and aerodynamic improvement, and that the TL-enhanced DRL agent achieves performance comparable to the DRL one, while further saving substantial computational resources.

Lucas Lacasa, Abel Pardo, Pablo Arbelo et al.

Methods of Machine and Deep Learning are gradually being integrated into industrial operations, albeit at different speeds for different types of industries. The aerospace and aeronautical industries have recently developed a roadmap for concepts of design assurance and integration of neural network-related technologies in the aeronautical sector. This paper aims to contribute to this paradigm of AI-based certification in the context of supervised learning, by outlining a complete validation pipeline that integrates deep learning, optimization and statistical methods. This pipeline is composed by a directed graphical model of ten steps. Each of these steps is addressed by a merging key concepts from different contributing disciplines (from machine learning or optimization to statistics) and adapting them to an industrial scenario, as well as by developing computationally efficient algorithmic solutions. We illustrate the application of this pipeline in a realistic supervised problem arising in aerostructural design: predicting the likelikood of different stress-related failure modes during different airflight maneuvers based on a (large) set of features characterising the aircraft internal loads and geometric parameters.

Ángel Ladrón, Miguel Sánchez-Domínguez, Javier Rozalén et al.

Fatigue life prediction is essential in both the design and operational phases of any aircraft, and in this sense safety in the aerospace industry requires early detection of fatigue cracks to prevent in-flight failures. Robust and precise fatigue life predictors are thus essential to ensure safety. Traditional engineering methods, while reliable, are time consuming and involve complex workflows, including steps such as conducting several Finite Element Method (FEM) simulations, deriving the expected loading spectrum, and applying cycle counting techniques like peak-valley or rainflow counting. These steps often require collaboration between multiple teams and tools, added to the computational time and effort required to achieve fatigue life predictions. Machine learning (ML) offers a promising complement to traditional fatigue life estimation methods, enabling faster iterations and generalization, providing quick estimates that guide decisions alongside conventional simulations. In this paper, we present a ML-based pipeline that aims to estimate the fatigue life of different aircraft wing locations given the flight parameters of the different missions that the aircraft will be operating throughout its operational life. We validate the pipeline in a realistic use case of fatigue life estimation, yielding accurate predictions alongside a thorough statistical validation and uncertainty quantification. Our pipeline constitutes a complement to traditional methodologies by reducing the amount of costly simulations and, thereby, lowering the required computational and human resources.