Article
Mechanics
Li-Wei Chen, Berkay A. Cakal, Xiangyu Hu, Nils Thuerey
Summary: In this study, deep learning methods were used to efficiently predict flow fields and loads for aerodynamic shape optimization. The trained U-net-based deep neural network models successfully inferred flow fields and calculated gradient flows for optimizing shapes, showing great promise for general aerodynamic design problems. The results demonstrate that the DNN models are capable of accurately predicting flow fields and generating satisfactory aerodynamic forces, even without specific training for aerodynamic forces.
JOURNAL OF FLUID MECHANICS
(2021)
Article
Computer Science, Interdisciplinary Applications
Roland Ewert, Johannes Kreuzinger
Summary: A generalized method of decomposing the compressible Navier-Stokes equations into coupled flow and acoustic equations is introduced, providing essential coupling terms to account for feedback from acoustics to flow. Subsonic simulations reveal the significant impact of feedback terms on tone characteristics in various cases, highlighting the importance of properly considering flow-acoustic interactions.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Operations Research & Management Science
Valentin Calisti, Ilaria Lucardesi, Jean-Francois Scheid
Summary: In this study, we investigate the shape differentiability of a general functional that depends on the solution of a stationary Stokes-elasticity system in two dimensions with small loads. We consider the differentiability with respect to variations in the reference elastic domain using shape perturbations with diffeomorphisms. The shape derivative is calculated using the velocity method, involving the material derivatives of the solution of the fluid-structure interaction problem. The adjoint method is then applied to obtain a simplified expression for the shape derivative.
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
(2023)
Article
Mathematics
Anass Bouchnita, Anastasia Mozokhina, Patrice Nony, Jean-Pierre Llored, Vitaly Volpert
Summary: This study proposes a methodology that uses computational modeling and machine learning to identify COVID-19 patients with a high thromboembolism risk. Through numerical simulations and mathematical modeling, it is shown that COVID-19 increases the size of thrombus formation and the peak concentration of thrombin generation. Finally, a dataset of hemostatic responses from virtual COVID-19 patients and healthy subjects is used to train machine learning algorithms for predicting the risk of thrombosis in COVID-19 patients.
Article
Computer Science, Artificial Intelligence
Fang Bai, Adrien Bartoli
Summary: This paper introduces the problem of deformable Generalized Procrustes Analysis (GPA) and resolves fundamental ambiguities using shape constraints requiring eigenvalues of shape covariance. A closed-form and optimal solution based on eigenvalue decomposition is provided, handling regularization and favoring smooth deformation fields. This method is applicable to most common transformation models, offering a fast, globally optimal and widely applicable solution.
INTERNATIONAL JOURNAL OF COMPUTER VISION
(2022)
Article
Mechanics
T. H. B. Demont, S. K. F. Stoter, E. H. van Brummelen
Summary: In this article, the behavior of the Abels-Garcke-Grun Navier-Stokes-Cahn-Hilliard diffuse-interface model for binary-fluid flows as the diffuse-interface thickness approaches zero is studied. The optimal order of the m-epsilon scaling relation and its impact on the convergence rate of the diffuse-interface solution to the sharp-interface solution are elucidated. The case of an oscillating droplet is investigated, and new analytical expressions for small-amplitude oscillations are derived. The sharp-interface limit of the Navier-Stokes-Cahn-Hilliard equations is probed using an adaptive finite-element method.
JOURNAL OF FLUID MECHANICS
(2023)
Article
Mathematics
Lingjun Liu, Danli Wang, Lingda Xu
Summary: In this paper, we consider the time-asymptotic stability of a composite wave consisting of a viscous contact wave and two rarefaction waves for the Cauchy problem of 1-D compressible Navier-Stokes equations with space-periodic perturbations. The key is to construct a suitable ansatz that carries the same oscillation as the initial data, but the construction is more subtle due to the degeneration of the contact discontinuity. We propose a novel method for constructing robust ansatzes that allows for the same weight function to be used on different variables and wave patterns while maintaining control over the errors. Furthermore, we demonstrate the unique global-in-time solution and the stability of the composite wave under space-periodic perturbations through the energy method.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2023)
Article
Computer Science, Interdisciplinary Applications
Nils Margenberg, Dirk Hartmann, Christian Lessig, Thomas Richter
Summary: We present DNN-MG, a deep neural network multigrid solver for the instationary Navier-Stokes equations. The combination of a geometric multigrid solver and a recurrent neural network with memory improves computational efficiency. DNN-MG reduces computation time by solving on coarse levels with the multi-grid method and correcting interpolated solutions on fine levels using a compact neural network.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Mathematics, Applied
Alexander G. Zimmerman, Julia Kowalski
Summary: The enthalpy method accurately solves the multi-physics problem involving natural convection and phase change by separating mesh refinement from nonlinearity regularization and providing effective numerical solutions. Sensitivity analysis on key parameters effectively reduces numerical errors.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
Article
Mechanics
Niklas Fehn, Martin Kronbichler, Peter Munch, Wolfgang A. Wall
Summary: This study contributes to the investigation of the well-known energy dissipation anomaly in inviscid limit by conducting high-resolution numerical simulations of the three-dimensional Taylor-Green vortex problem. The interesting observation is made that the kinetic energy evolution does not tend towards exact energy conservation as the spatial resolution of numerical scheme increases. This raises the question of whether the results obtained can be seen as a numerical confirmation of the famous energy dissipation anomaly and elaborates on an indirect approach for the identification of finite-time singularities based on energy arguments.
JOURNAL OF FLUID MECHANICS
(2021)
Review
Quantum Science & Technology
Frank Gaitan
Summary: This article introduces a new quantum algorithm for solving nonlinear partial differential equations that cannot be efficiently simulated by classical computers. Specifically, it focuses on the Navier-Stokes equations governing viscous fluid flow. The construction and verification of this algorithm show a significant quantum speed-up, opening up new opportunities for quantum computing applications in the economy.
ADVANCED QUANTUM TECHNOLOGIES
(2021)
Article
Computer Science, Software Engineering
Johannes Schwarz, Kristjan Axelsson, Daniel Anheuer, Martin Richter, Johanna Adam, Martin Heinrich, Ruediger Schwarze
Summary: Classical continuum methods are inadequate for gas flows with higher Knudsen numbers. Various models have been developed in the past to extend the classical Navier-Stokes equations (CNSE) and incorporate the particle nature of the medium. One such approach considers the kinetic theory of gases, leading to the derivation of the extended Navier-Stokes equations (ENSE). Numerical methods, such as the Finite-Volume-Method, are commonly used to solve the CNSE, and this study utilizes the open-source tool OpenFOAM to develop an ENSE solver, which offers significant performance advantages by implicitly discretizing certain terms and defining additional diffusion face-flux fields. The results are validated against analytical formulas using a simple microchannel test case.
Article
Computer Science, Interdisciplinary Applications
Afsoun Rahnama Falavarjani, David Salac
Summary: Many multiphase fluid systems exhibit a breakdown of the no-slip condition at the material interface, causing a difference in tangential velocity between the inner and outer fluid. A numerical model is presented to investigate these systems in both two- and three-dimensions, using a hybrid Navier-Stokes projection method and the Immersed Interface Method. The model shows excellent agreement with experimental and computational results, and is able to explore the influence of interfacial slip in various multiphase fluid systems.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Engineering, Marine
Ivana Martic, Nastia Degiuli, Kornelija Borcic, Carlo Giorgio Grlj
Summary: This paper uses CFD to study the effect of shallow water on the total resistance of a solar catamaran, and obtains relevant conclusions through numerical simulation and analysis.
JOURNAL OF MARINE SCIENCE AND ENGINEERING
(2023)
Article
Mechanics
Sasan Tavakoli, Tommi Mikkola, Spyros Hirdaris
Summary: The paper introduces a Fluid Structure Interaction (FSI) method for predicting hydroelastic water entry. The method utilizes momentum exchange between fluid and solid to calculate pressure, deformation, and stresses during impact. By using the finite volume method, a computational code is applied to solve flexible fluid-structure interactions, providing better momentum matching at the fluid-solid interface. The study demonstrates that the pressure on an elastic body can be predicted using a simple equation based on momentum exchange.
JOURNAL OF FLUID MECHANICS
(2023)
Article
Mathematics
Martin Hess, Gianluigi Rozza
Summary: This work investigates the use of sparse polynomial interpolation as a model order reduction method for the parametrized incompressible Navier-Stokes equations and compares it with established reduced basis techniques. The findings suggest that sparse polynomial interpolation is a valid instrument in the toolbox of ROM methods.
VIETNAM JOURNAL OF MATHEMATICS
(2023)
Article
Computer Science, Interdisciplinary Applications
Federico Pichi, Francesco Ballarin, Gianluigi Rozza, Jan S. Hesthaven
Summary: This study investigates bifurcating fluid phenomena using a reduced order modelling approach with the help of artificial neural networks. The authors discuss a POD-NN approach for dealing with non-smooth solutions of nonlinear parametrized PDEs. They apply this approach to study the Coanda effect in a channel and the lid-driven triangular cavity flow, considering the effects of domain configuration on bifurcation points. Additionally, they propose a reduced manifold-based bifurcation diagram for efficiently recovering critical points evolution and analyzing pattern flow behavior.
COMPUTERS & FLUIDS
(2023)
Article
Engineering, Multidisciplinary
Umberto Emil Morelli, Patricia Barral, Peregrina Quintela, Gianluigi Rozza, Giovanni Stabile
Summary: In this article, we investigate the estimation of transient mold-slab heat flux in continuous casting molds using thermocouples measurements in the mold plates. We formulate this problem as the estimation of a Neumann boundary condition given pointwise state observations. We present the mold thermal model and assumptions, and then formulate the boundary heat flux estimation problem in a deterministic inverse problem setting using a sequential approach. We develop novel direct methodologies for different formulations of the inverse problem, and test their performance in benchmark cases.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2023)
Article
Mathematics, Applied
Elena Zappon, Alfio Quarteroni, Andrea Manzoni
Summary: This paper proposes a reduced order modeling (ROM) strategy to solve parametrized one-way coupled problems. The strategy combines reduced basis method and discrete empirical interpolation method to efficiently interpolate or project Dirichlet data. The proposed technique is numerically verified for various steady and unsteady problems.
ADVANCES IN COMPUTATIONAL MATHEMATICS
(2023)
Article
Engineering, Multidisciplinary
Paolo Conti, Giorgio Gobat, Stefania Fresca, Andrea Manzoni, Attilio Frangi
Summary: To accurately simulate complex phenomena governed by partial differential equations (PDEs) with reduced computational costs, a data-driven, non-intrusive framework is proposed in this work. This framework combines reduced order model (ROM) construction with reduced dynamics identification using autoencoder neural networks and parametric sparse identification of nonlinear dynamics (SINDy). It allows for efficient computation of full-time solutions at new parameter instances and tracking the evolution of periodic steady-state responses. The proposed method shows remarkable capabilities in generalizing with respect to both time and parameters, as demonstrated in applications to structural mechanics and fluid dynamics problems.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Computer Science, Interdisciplinary Applications
Anna Ivagnes, Giovanni Stabile, Andrea Mola, Traian Iliescu, Gianluigi Rozza
Summary: In this paper, data-driven closure/correction terms are developed to improve the accuracy of pressure and velocity in reduced order models (ROMs) for fluid flows. The proposed pressure-based data-driven variational multiscale ROM uses available data to construct closure/correction terms for the momentum equation and continuity equation. Numerical investigation shows that the novel pressure data-driven variational multiscale ROM yields significantly more accurate velocity and pressure approximations compared to the standard ROM and the original data-driven variational multiscale ROM without pressure components.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Mathematics, Applied
Anna Ivagnes, Nicola Demo, Gianluigi Rozza
Summary: In this work, a model order reduction framework is proposed for dealing with inverse problems in a non-intrusive setting. The computational load of inverse problems, especially in a partial differential equation context, is huge due to the iterative optimization process. To accelerate this procedure, a numerical pipeline involving artificial neural networks is applied to parametrize the boundary conditions, compress the dimensionality of snapshots, and approximate the parametric solution manifold. This approach provides a general framework capable of ad-hoc parametrization of the inlet boundary and quickly converges to the optimal solution thanks to model order reduction. The results obtained by applying these methods to two different CFD test cases are presented in this contribution.
JOURNAL OF SCIENTIFIC COMPUTING
(2023)
Article
Mathematics, Applied
Francesco Romor, Giovanni Stabile, Gianluigi Rozza
Summary: Non-affine parametric dependencies, nonlinearities, and advection-dominated regimes can hinder the development of efficient reduced-order models based on linear subspace approximations. Data-driven methods utilizing autoencoders and their variants have shown promise, but there is a need for increased interpretability, especially in regions with limited data and outside the training range. Additionally, exploiting knowledge of the model's physics during the predictive phase is important. To address these challenges, we implement the non-linear manifold method introduced by Lee and Carlberg (J Comput Phys 404:108973, 2020) and combine it with hyper-reduction achieved through reduced over-collocation and teacher-student training of a reduced decoder. We evaluate the methodology on a 2D non-linear conservation law and a 2D shallow water model, comparing it to a purely data-driven approach using a long-short term memory network for time evolution.
JOURNAL OF SCIENTIFIC COMPUTING
(2023)
Article
Computer Science, Artificial Intelligence
Laura Meneghetti, Nicola Demo, Gianluigi Rozza
Summary: The aim of this research is to apply classical Model Order Reduction techniques to Deep Neural Networks, reducing the number of layers in a pre-trained network for embedded systems with storage constraints. By combining dimensionality reduction techniques with input-output mappings, the reduced networks achieve comparable accuracy to the original Convolutional Neural Network while saving memory allocation. The research focuses on image recognition, testing the methodology using VGG-16 and ResNet-110 architectures against CIFAR-10, CIFAR-100, and a custom dataset.
APPLIED INTELLIGENCE
(2023)
Article
Engineering, Biomedical
Ludovica Cicci, Stefania Fresca, Andrea Manzoni, Alfio Quarteroni
Summary: Reducing computational time is crucial for translating patient-specific simulations into clinical practice. By combining reduced basis method with deep learning, this approach provides accurate solutions to parametrized cardiac mechanics problems at significantly reduced computational cost.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING
(2023)
Article
Engineering, Multidisciplinary
Fabian Key, Max von Danwitz, Francesco Ballarin, Gianluigi Rozza
Summary: In this work, two challenges in simulation-based methods are discussed. The first challenge involves handling problems with complex domain deformations and changes in the domain topology. The second challenge arises in scenarios with parametric problems where computational resources and evaluation time are critical. To address these complexities, a novel projection-based model order reduction approach is presented, which takes advantage of the time-continuous space-time formulation. Two examples in engineering and biomedical applications are examined, showing the effectiveness of the approach in reducing computational expense while maintaining accuracy.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2023)
Article
Computer Science, Interdisciplinary Applications
Arash Hajisharifi, Francesco Romano, Michele Girfoglio, Andrea Beccari, Domenico Bonanni, Gianluigi Rozza
Summary: Investigating fluid-solid systems is crucial in many industrial processes, but simulating such systems is expensive. Therefore, we developed a non-intrusive data-driven reduced order model for Computational Fluid Dynamics-Discrete Element Method simulations.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Computer Science, Interdisciplinary Applications
Michele Girfoglio, Annalisa Quaini, Gianluigi Rozza
Summary: We propose a Reduced Order Model (ROM) for the Navier-Stokes equations with nonlinear filtering stabilization, which combines a three-step algorithm called Evolve-Filter-Relax (EFR) with an efficient finite volume method. The novelty lies in the use of a nonlinear indicator function within the EFR algorithm to identify regions needing regularization. The ROM combines a projection approach for velocity and pressure fields with a data-driven reduction method for the indicator function.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Mathematics, Interdisciplinary Applications
Ludovica Cicci, Stefania Fresca, Stefano Pagani, Andrea Manzoni, Alfio Quarteroni
Summary: The study demonstrates the use of reduced order models (ROMs) to overcome the computational challenges in simulating virtual scenarios in cardiac mechanics, where traditional full-order models (FOMs) are replaced. The projection-based ROMs provide accurate predictions of structural deformation and pressure-volume loop of the left ventricular tissue, at a lower cost compared to FOMs. However, the construction of ROM approximations for time-dependent cardiac mechanics is complex due to the nonlinear and multiscale nature of the problem.
MATHEMATICS IN ENGINEERING
(2023)
Proceedings Paper
Engineering, Civil
Matteo Torzoni, Andrea Manzoni, Stefano Mariani
Summary: This paper presents a methodology for reliable real-time structural health monitoring using a multi-fidelity deep neural network. The proposed approach is able to accurately locate and quantify damage, and can effectively combine datasets with different fidelities without prior assumptions. It provides numerous advantages over single-fidelity based models for structural health monitoring purposes.
EUROPEAN WORKSHOP ON STRUCTURAL HEALTH MONITORING (EWSHM 2022), VOL 2
(2023)