Pub Date : 2022-07-04DOI: 10.1186/s40323-022-00227-7
Stachiw, Terrin, Crain, Alexander, Ricciardi, Joseph
The authors have developed a novel physics-based nonlinear autoregressive exogeneous neural network model architecture for flight modelling across the entire flight envelope, called FlyNet. When using traditional parameter estimation and output-error methods, aircraft models are captured about a single point in the flight envelope using a first-order Taylor series to approximate forces and moments. To enable analysis throughout the entire operational envelope, the traditional models can be extended by interpolating or stitching between a number of these single-condition models. This paper completes the evolutionary next step in aircraft modelling to consider all second-order Taylor series terms instead of a subset of those and by exploiting the ability of neural networks to capture more complex and nonlinear behaviour for the efficient development of a continuous flight simulation model valid across the entire envelope. This method is valid for fixed- and rotary-wing aircraft. The behaviour of a conventional model is compared to FlyNet using flight test data collected from the National Research Council of Canada’s Bell 412HP in forward flight.
{"title":"A physics-based neural network for flight dynamics modelling and simulation","authors":"Stachiw, Terrin, Crain, Alexander, Ricciardi, Joseph","doi":"10.1186/s40323-022-00227-7","DOIUrl":"https://doi.org/10.1186/s40323-022-00227-7","url":null,"abstract":"The authors have developed a novel physics-based nonlinear autoregressive exogeneous neural network model architecture for flight modelling across the entire flight envelope, called FlyNet. When using traditional parameter estimation and output-error methods, aircraft models are captured about a single point in the flight envelope using a first-order Taylor series to approximate forces and moments. To enable analysis throughout the entire operational envelope, the traditional models can be extended by interpolating or stitching between a number of these single-condition models. This paper completes the evolutionary next step in aircraft modelling to consider all second-order Taylor series terms instead of a subset of those and by exploiting the ability of neural networks to capture more complex and nonlinear behaviour for the efficient development of a continuous flight simulation model valid across the entire envelope. This method is valid for fixed- and rotary-wing aircraft. The behaviour of a conventional model is compared to FlyNet using flight test data collected from the National Research Council of Canada’s Bell 412HP in forward flight.","PeriodicalId":37424,"journal":{"name":"Advanced Modeling and Simulation in Engineering Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138510041","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-07-02DOI: 10.1186/s40323-022-00223-x
V. Martin, Reuben H. Kraft, Thomas H. Hannah, Stephen Ellis
{"title":"An energy-based study of the embedded element method for explicit dynamics","authors":"V. Martin, Reuben H. Kraft, Thomas H. Hannah, Stephen Ellis","doi":"10.1186/s40323-022-00223-x","DOIUrl":"https://doi.org/10.1186/s40323-022-00223-x","url":null,"abstract":"","PeriodicalId":37424,"journal":{"name":"Advanced Modeling and Simulation in Engineering Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"65853809","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-07-02DOI: 10.1186/s40323-022-00224-w
E. Rajasekhar Nicodemus
{"title":"A methodology to assess and improve the physics consistency of an artificial neural network regression model for engineering applications","authors":"E. Rajasekhar Nicodemus","doi":"10.1186/s40323-022-00224-w","DOIUrl":"https://doi.org/10.1186/s40323-022-00224-w","url":null,"abstract":"","PeriodicalId":37424,"journal":{"name":"Advanced Modeling and Simulation in Engineering Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88603207","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-30DOI: 10.1186/s40323-022-00226-8
S. Cedillo, Ana-Gabriela Núñez, E. Sánchez-Cordero, L. Timbe, E. Samaniego, A. Alvarado
{"title":"Physics-Informed Neural Network water surface predictability for 1D steady-state open channel cases with different flow types and complex bed profile shapes","authors":"S. Cedillo, Ana-Gabriela Núñez, E. Sánchez-Cordero, L. Timbe, E. Samaniego, A. Alvarado","doi":"10.1186/s40323-022-00226-8","DOIUrl":"https://doi.org/10.1186/s40323-022-00226-8","url":null,"abstract":"","PeriodicalId":37424,"journal":{"name":"Advanced Modeling and Simulation in Engineering Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"65853919","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-21DOI: 10.1186/s40323-022-00221-z
Oldenburg, Jan, Borowski, Finja, Öner, Alper, Schmitz, Klaus-Peter, Stiehm, Michael
Many real world problems involve fluid flow phenomena, typically be described by the Navier–Stokes equations. The Navier–Stokes equations are partial differential equations (PDEs) with highly nonlinear properties. Currently mostly used methods solve this differential equation by discretizing geometries. In the field of fluid mechanics the finite volume method (FVM) is widely used for numerical flow simulation, so-called computational fluid dynamics (CFD). Due to high computational costs and cumbersome generation of the discretization they are not widely used in real time applications. Our presented work focuses on advancing PDE-constrained deep learning frameworks for more real-world applications with irregular geometries without parameterization. We present a Deep Neural Network framework that generate surrogates for non-geometric boundaries by data free solely physics driven training, by minimizing the residuals of the governing PDEs (i.e., conservation laws) so that no computationally expensive CFD simulation data is needed. We named this method geometry aware physics informed neural network—GAPINN. The framework involves three network types. The first network reduces the dimensions of the irregular geometries to a latent representation. In this work we used a Variational-Auto-Encoder (VAE) for this task. We proposed the concept of using this latent representation in combination with spatial coordinates as input for PINNs. Using PINNs we showed that it is possible to train a surrogate model purely driven on the reduction of the residuals of the underlying PDE for irregular non-parametric geometries. Furthermore, we showed the way of designing a boundary constraining network (BCN) to hardly enforce boundary conditions during training of the PINN. We evaluated this concept on test cases in the fields of biofluidmechanics. The experiments comprise laminar flow (Re = 500) in irregular shaped vessels. The main highlight of the presented GAPINN is the use of PINNs on irregular non-parameterized geometries. Despite that we showed the usage of this framework for Navier Stokes equations, it should be feasible to adapt this framework for other problems described by PDEs.
{"title":"Geometry aware physics informed neural network surrogate for solving Navier–Stokes equation (GAPINN)","authors":"Oldenburg, Jan, Borowski, Finja, Öner, Alper, Schmitz, Klaus-Peter, Stiehm, Michael","doi":"10.1186/s40323-022-00221-z","DOIUrl":"https://doi.org/10.1186/s40323-022-00221-z","url":null,"abstract":"Many real world problems involve fluid flow phenomena, typically be described by the Navier–Stokes equations. The Navier–Stokes equations are partial differential equations (PDEs) with highly nonlinear properties. Currently mostly used methods solve this differential equation by discretizing geometries. In the field of fluid mechanics the finite volume method (FVM) is widely used for numerical flow simulation, so-called computational fluid dynamics (CFD). Due to high computational costs and cumbersome generation of the discretization they are not widely used in real time applications. Our presented work focuses on advancing PDE-constrained deep learning frameworks for more real-world applications with irregular geometries without parameterization. We present a Deep Neural Network framework that generate surrogates for non-geometric boundaries by data free solely physics driven training, by minimizing the residuals of the governing PDEs (i.e., conservation laws) so that no computationally expensive CFD simulation data is needed. We named this method geometry aware physics informed neural network—GAPINN. The framework involves three network types. The first network reduces the dimensions of the irregular geometries to a latent representation. In this work we used a Variational-Auto-Encoder (VAE) for this task. We proposed the concept of using this latent representation in combination with spatial coordinates as input for PINNs. Using PINNs we showed that it is possible to train a surrogate model purely driven on the reduction of the residuals of the underlying PDE for irregular non-parametric geometries. Furthermore, we showed the way of designing a boundary constraining network (BCN) to hardly enforce boundary conditions during training of the PINN. We evaluated this concept on test cases in the fields of biofluidmechanics. The experiments comprise laminar flow (Re = 500) in irregular shaped vessels. The main highlight of the presented GAPINN is the use of PINNs on irregular non-parameterized geometries. Despite that we showed the usage of this framework for Navier Stokes equations, it should be feasible to adapt this framework for other problems described by PDEs.","PeriodicalId":37424,"journal":{"name":"Advanced Modeling and Simulation in Engineering Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138543693","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-21DOI: 10.1186/s40323-022-00222-y
N. Hagmeyer, M. Mayr, I. Steinbrecher, A. Popp
{"title":"One-way coupled fluid–beam interaction: capturing the effect of embedded slender bodies on global fluid flow and vice versa","authors":"N. Hagmeyer, M. Mayr, I. Steinbrecher, A. Popp","doi":"10.1186/s40323-022-00222-y","DOIUrl":"https://doi.org/10.1186/s40323-022-00222-y","url":null,"abstract":"","PeriodicalId":37424,"journal":{"name":"Advanced Modeling and Simulation in Engineering Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"65853737","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-15DOI: 10.1186/s40323-022-00220-0
Willmann, Harald, Wall, Wolfgang A.
In this article we propose an inverse analysis algorithm to find the best fit of multiple material parameters in different coupled multi-physics biofilm models. We use a nonlinear continuum mechanical approach to model biofilm deformation that occurs in flow cell experiments. The objective function is based on a simple geometrical measurement of the distance of the fluid biofilm interface between model and experiments. A Levenberg-Marquardt algorithm based on finite difference approximation is used as an optimizer. The proposed method uses a moderate to low amount of model evaluations. For a first presentation and evaluation the algorithm is applied and tested on different numerical examples based on generated numerical results and the addition of Gaussian noise. Achieved numerical results show that the proposed method serves well for different physical effects investigated and numerical approaches chosen for the model. Presented examples show the inverse analysis for multiple parameters in biofilm models including fluid-solid interaction effects, poroelasticity, heterogeneous material properties and growth.
{"title":"Inverse analysis of material parameters in coupled multi-physics biofilm models","authors":"Willmann, Harald, Wall, Wolfgang A.","doi":"10.1186/s40323-022-00220-0","DOIUrl":"https://doi.org/10.1186/s40323-022-00220-0","url":null,"abstract":"In this article we propose an inverse analysis algorithm to find the best fit of multiple material parameters in different coupled multi-physics biofilm models. We use a nonlinear continuum mechanical approach to model biofilm deformation that occurs in flow cell experiments. The objective function is based on a simple geometrical measurement of the distance of the fluid biofilm interface between model and experiments. A Levenberg-Marquardt algorithm based on finite difference approximation is used as an optimizer. The proposed method uses a moderate to low amount of model evaluations. For a first presentation and evaluation the algorithm is applied and tested on different numerical examples based on generated numerical results and the addition of Gaussian noise. Achieved numerical results show that the proposed method serves well for different physical effects investigated and numerical approaches chosen for the model. Presented examples show the inverse analysis for multiple parameters in biofilm models including fluid-solid interaction effects, poroelasticity, heterogeneous material properties and growth.","PeriodicalId":37424,"journal":{"name":"Advanced Modeling and Simulation in Engineering Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138510056","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-10DOI: 10.1186/s40323-022-00237-5
Harald Willmann, J. Nitzler, S. Brandstaeter, W. Wall
{"title":"Bayesian calibration of coupled computational mechanics models under uncertainty based on interface deformation","authors":"Harald Willmann, J. Nitzler, S. Brandstaeter, W. Wall","doi":"10.1186/s40323-022-00237-5","DOIUrl":"https://doi.org/10.1186/s40323-022-00237-5","url":null,"abstract":"","PeriodicalId":37424,"journal":{"name":"Advanced Modeling and Simulation in Engineering Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47585951","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Most real optimization problems are defined over a mixed search space where the variables are both discrete and continuous. In engineering applications, the objective function is typically calculated with a numerically costly black-box simulation. General mixed and costly optimization problems are therefore of a great practical interest, yet their resolution remains in a large part an open scientific question. In this article, costly mixed problems are approached through Gaussian processes where the discrete variables are relaxed into continuous latent variables. The continuous space is more easily harvested by classical Bayesian optimization techniques than a mixed space would. Discrete variables are recovered either subsequently to the continuous optimization, or simultaneously with an additional continuous-discrete compatibility constraint that is handled with augmented Lagrangians. Several possible implementations of such Bayesian mixed optimizers are compared. In particular, the reformulation of the problem with continuous latent variables is put in competition with searches working directly in the mixed space. Among the algorithms involving latent variables and an augmented Lagrangian, a particular attention is devoted to the Lagrange multipliers for which a local and a global estimation techniques are studied. The comparisons are based on the repeated optimization of three analytical functions and a beam design problem.
{"title":"A comparison of mixed-variables Bayesian optimization approaches","authors":"Cuesta Ramirez, Jhouben, Le Riche, Rodolphe, Roustant, Olivier, Perrin, Guillaume, Durantin, Cédric, Glière, Alain","doi":"10.1186/s40323-022-00218-8","DOIUrl":"https://doi.org/10.1186/s40323-022-00218-8","url":null,"abstract":"Most real optimization problems are defined over a mixed search space where the variables are both discrete and continuous. In engineering applications, the objective function is typically calculated with a numerically costly black-box simulation. General mixed and costly optimization problems are therefore of a great practical interest, yet their resolution remains in a large part an open scientific question. In this article, costly mixed problems are approached through Gaussian processes where the discrete variables are relaxed into continuous latent variables. The continuous space is more easily harvested by classical Bayesian optimization techniques than a mixed space would. Discrete variables are recovered either subsequently to the continuous optimization, or simultaneously with an additional continuous-discrete compatibility constraint that is handled with augmented Lagrangians. Several possible implementations of such Bayesian mixed optimizers are compared. In particular, the reformulation of the problem with continuous latent variables is put in competition with searches working directly in the mixed space. Among the algorithms involving latent variables and an augmented Lagrangian, a particular attention is devoted to the Lagrange multipliers for which a local and a global estimation techniques are studied. The comparisons are based on the repeated optimization of three analytical functions and a beam design problem.","PeriodicalId":37424,"journal":{"name":"Advanced Modeling and Simulation in Engineering Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138510043","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Nowadays, in the Scientific Machine Learning (SML) research field, the traditional machine learning (ML) tools and scientific computing approaches are fruitfully intersected for solving problems modelled by Partial Differential Equations (PDEs) in science and engineering applications. Challenging SML methodologies are the new computational paradigms named Physics-Informed Neural Networks (PINNs). PINN has revolutionized the classical adoption of ML in scientific computing, representing a novel class of promising algorithms where the learning process is constrained to satisfy known physical laws described by differential equations. In this paper, we propose a PINN-based computational study to deal with a non-linear partial differential equations system. In particular, using this approach, we solve the Gray-Scott model, a reaction–diffusion system that involves an irreversible chemical reaction between two reactants. In the unstable region of the model, we consider some a priori information related to dynamical behaviors, i. e. a supervised approach that relies on a finite difference method (FDM). Finally, simulation results show that PINNs can successfully provide an approximated Grey-Scott system solution, reproducing the characteristic Turing patterns for different parameter configurations.
{"title":"Physics-informed neural networks approach for 1D and 2D Gray-Scott systems","authors":"Giampaolo, Fabio, De Rosa, Mariapia, Qi, Pian, Izzo, Stefano, Cuomo, Salvatore","doi":"10.1186/s40323-022-00219-7","DOIUrl":"https://doi.org/10.1186/s40323-022-00219-7","url":null,"abstract":"Nowadays, in the Scientific Machine Learning (SML) research field, the traditional machine learning (ML) tools and scientific computing approaches are fruitfully intersected for solving problems modelled by Partial Differential Equations (PDEs) in science and engineering applications. Challenging SML methodologies are the new computational paradigms named Physics-Informed Neural Networks (PINNs). PINN has revolutionized the classical adoption of ML in scientific computing, representing a novel class of promising algorithms where the learning process is constrained to satisfy known physical laws described by differential equations. In this paper, we propose a PINN-based computational study to deal with a non-linear partial differential equations system. In particular, using this approach, we solve the Gray-Scott model, a reaction–diffusion system that involves an irreversible chemical reaction between two reactants. In the unstable region of the model, we consider some a priori information related to dynamical behaviors, i. e. a supervised approach that relies on a finite difference method (FDM). Finally, simulation results show that PINNs can successfully provide an approximated Grey-Scott system solution, reproducing the characteristic Turing patterns for different parameter configurations.","PeriodicalId":37424,"journal":{"name":"Advanced Modeling and Simulation in Engineering Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138510035","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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