Abstract

The simulation of engineering problems is quite often a complex task that can be time consuming. In this context, the use of Hyper Reduced Order Models (HROMs) is a promising alternative for real-time simulations. In this work, we study the design of HROMs for non-linear problems with a moving source. Applications to nonlinear phase change problems with temperature dependent thermophysical properties are particularly considered; however, the techniques developed can be applied in other fields as well.

A basic assumption in the design of HROMs is that the quantities that will be hyper-reduced are k-compressible in a certain basis in the sense that these quantities have at most k non-zero significant entries when expressed in terms of that basis. To reach the computational speed required for a real-time application, k must be small. This work examines different strategies for addressing hyper-reduction of the nonlinear terms with the objective of obtaining k-compressible signals with a notably small k. To improve performance and robustness, it is proposed that the different contributing terms to the residual are separately hyper-reduced. Additionally, the use of moving reference frames is proposed to simulate and hyper-reduce cases that contain moving heat sources. Two application examples are presented: the solidification of a cube in which no heat source is present and the welding of a tube in which the problem posed by a moving heat source is analysed.

Abstract

In this paper we are addressing a new paradigm in the field of simulation-based engineering sciences (SBES) to face the challenges posed by current ICT technologies. Despite the impressive progress attained by simulation capabilities and techniques, some challenging problems remain today intractable. These problems, that are common to many branches of science and engineering, are of different nature. Among them, we can cite those related to high-dimensional problems, which do not admit mesh-based approaches due to the exponential increase of degrees of freedom. We developed in recent years a novel technique, called Proper Generalized Decomposition (PGD). It is based on the assumption of a separated form of the unknown field and it has demonstrated its capabilities in dealing with high-dimensional problems overcoming the strong limitations of classical approaches. But the main opportunity given by this technique is that it allows for a completely new approach for classic problems, not necessarily high dimensional. Many challenging problems can be efficiently cast into a multidimensional framework and this opens new possibilities to solve old and new problems with strategies not envisioned until now. For instance, parameters in a model can be set as additional extra-coordinates of the model. In a PGD framework, the resulting model is solved once for life, in order to obtain a general solution that includes all the solutions for every possible value of the parameters, that is, a sort of computational vademecum. Under this rationale, optimization of complex problems, uncertainty quantification, simulation-based control and real-time simulation are now at hand, even in highly complex scenarios, by combining an off-line stage in which the general PGD solution, the vademecum, is computed, and an on-line phase in which, even on deployed, handheld, platforms such as smartphones or tablets, real-time response is obtained as a result of our queries.

Abstract

Abstract

Cost-effective parameteric surrogate models of unsteady aerodynamic loads acting on a flapping wing are highly desirable. They would enable real time aerodynamic load prediction, multiobjective optimisation and optimal control of intelligent flapping wing flight devices. In the present work, a parametric surrogate modeling framework for unsteady aerodynamic loads based on a non-intrusive reduced order modeling approach is presented. The unsteady flow past a plunging 2D flat plate is considered where the aerodynamic load time histories are obtained for different plunging frequencies and amplitudes using a potential flow solver. The parametric non-intrusive reduced order model (p-NIROM) for the obtained loads is constructed using a combination of snapshot proper orthogonal decomposition (POD) for dimensionality reduction and a fully connected feed forward neural network (FCNN) for modeling the input parametric dependency. Both, linear and non-linear FCNN based p-NIROM are explored and compared on the basis of load time history reconstruction accuracy. The non-linear FCNN regression for the p-NIROM is observed to generalise well for unseen parametric instances as compared to the linear approach when a systematic data sampling strategy is adopted.

Abstract

During each aircraft program a vast amount of aerodynamics data has to be generated to judge performance, structural loads as well as handling qualities. Within the past years the usage of computational fluid dynamics has significantly increased providing accurate insights into aircraft behaviour at early design stages and therefore at least partially enabled the mitigation of costly design changes. However, fully relying on high fidelity aerodynamic data is still computational prohibitive. Hence, data-driven models have gained an increasing attention in recent years. These methods not only provide continuous models but also enable the inclusion of highly accurate aerodynamic results in time-critical environments. This paper aims at applying deep learning techniques to derive such models and compare them to state of the art reduced order modeling techniques. In particular, three deep learning methods, a Multilayer perceptron for distribution predictions, a Multi-layer perceptron for pointwise predictions and an Autoencoder coupled with an interpolation technique are compared to Proper Orthogonal Decomposition and Isomap with latent space interpolation. For all methods an efficient methodology to determine hyperparameters is outlined and applied. Results are presented for an Airbus provided XRF1 dataset which includes surface pressure distributions at various Mach numbers and angles of attack.

Abstract

In this work the Reduced-Order Subscales for Proper Orthogonal Decomposition models are presented. The basic idea consists in splitting the full-order solution into the part which can be captured by the reduced-order model and the part which cannot, the subscales, for which a model is required. The proposed model for the subscales is defined as a linear function of the solution of the reduced-order model. The coefficients of this linear function are obtained by comparing the solution of the full-order model with the solution of the reduced-order model for the same initial conditions, which, for convenience, are evaluated in the snapshots used to train the original reduced-order-model. The difference between both solutions are the subscales, for which a model can be built using a least-squares procedure. The subscales are then introduced as a correction in the reduced-order model, resulting in an important improvement in accuracy. The enhanced reduced-order model is tested in several numerical examples. These practical cases show that the use of the subscales leads to more accurate solutions, successfully corrects errors introduced by hyper-reduction, and allows to solve complex flow problems using a reduced number of degrees of freedom.

Abstract

Model reduction for fluid flow simulation continues to be of great interest across a number of scientific and engineering fields. In a previous work [1], we explored the use of Neural Ordinary Differential Equations (NODE) as a non-intrusive method for propagating the latent-space dynamics in reduced order models. Here, we investigate employing deep autoencoders for discovering the reduced basis representation, the dynamics of which are then approximated by NODE. The ability of deep autoencoders to represent the latent-space is compared to the traditional proper orthogonal decomposition (POD) approach, again in conjunction with NODE for capturing the dynamics. Additionally, we compare their behavior with two classical non-intrusive methods based on POD and radial basis function interpolation as well as dynamic mode decomposition. The test problems we consider include incompressible flow around a cylinder as well as a real-world application of shallow water hydrodynamics in an estuarine system. Our findings indicate that deep autoencoders can leverage nonlinear manifold learning to achieve a highly efficient compression of spatial information and define a latentspace that appears to be more suitable for capturing the temporal dynamics through the NODE framework.

Abstract

Various modal decomposition techniques have been developed in the last decade [1­11]. We focus on data-driven approches, and since data flow volume is increasing day by day, it is important to study the performance of order reduction and feature detection algorithms. In this work we compare the performance and feature detection behaviour of energy and frequency based algorithms (Proper Orthogonal Decomposition [1­3] and Dynamic Mode Decomposition [4­6, 8­11]) on two data set testcases taken from fluid dynamics.