Reconstructing directed and weighted topologies of phase-locked oscillator networks

The formalism of complex networks is extensively employed to describe the dynamics of interacting agents in several applications. The features of the connections among the nodes in a network are not always provided beforehand, hence the problem of appropriately inferring them often arises. Here, we present a method to reconstruct directed and weighted topologies (REDRAW) of networks of heterogeneous phase-locked nonlinear oscillators. We ultimately plan on using REDRAW to infer the interaction structure in human ensembles engaged in coordination tasks, and give insights into the overall behavior

On complex power nonnegative matrices

Power nonnegative matrices are defined as complex matrices having at least one nonnegative integer power. We exploit the possibility of deriving a Perron Frobenius-like theory for these matrices, obtaining three main results and drawing several consequences. We study, in particular, the relationships with the set of matrices having eventually nonnegative powers, the inverse of M-type matrices and the set of matrices whose columns (rows) sum up to one

A preconditioning approach to the pagerank computation problem

AbstractSome spectral properties of the transition matrix of an oriented graph indicate the preconditioning of Euler–Richardson (ER) iterative scheme as a good way to compute efficiently the vertexrank vector associated with such graph. We choose the preconditioner from an algebra U of matrices, thereby obtaining an ERU method, and we observe that ERU can outperform ER in terms of rate of convergence. The proposed preconditioner can be updated at a very low cost whenever the graph changes, as is the case when it represents a generic set of information. The particular U utilized requires a surplus of operations per step and memory allocations, which make ERU superior to ER for not too wide graphs. However, the observed high improvement in convergence rate obtained by preconditioning and the general theory developed, are a reason for investigating different choices of U, more efficient for huge graphs

DOMAIN-AWARE MULTIFIDELITY LEARNING FOR DESIGN OPTIMIZATION

Accurate physics-based models are essential to the design and optimization of engineering systems, to compute key performance indicators associated with alternative design solutions. The implementation of high-fidelity models in simulation-based design optimization poses significant challenges due to the relevant computational cost frequently associated with their execution. However, real world engineering systems can rely on the availability of multiple models or approximations of their physics, representations characterized by different computational complexity and accuracy. Those alternative models can be cheaper to evaluate and can thus be exploited to enhance the efficiency of the optimization task. Multifidelity methods allow to combine multiple sources of information at different levels of fidelity, potentially exploiting the affordability of low fidelity evaluations to massively explore the design space, then enriching the accuracy through a reduced number of high-fidelity queries [1]. Many multifidelity optimization methods combine data from multiple models into a probabilistic surrogate, frequently delaying the identification of promising design alternatives that could rather be more efficiently captured if domain specific expertise were also used to inform the search [2]. To address this challenge, we present original domain-aware multifidelity frameworks to accelerate design optimization and improve the quality of the solution. In particular, our strategy is based on an active learning scheme that combines data-driven and physics-informed utility functions, to include the expert knowledge about the specific physical phenomena during the search for the optimal design. This allows to tailor the selection of the physical model to evaluate and increase the efficiency of the learning process, using at best a limited amount of high-fidelity data to sensitively improve the design solution. We discuss several applications of the proposed framework for aerospace design optimization problems, considering atmospheric flight at low and high altitudes for both aeronautics and space applications. [1] Peherstorfer, B., Willcox, K., Gunzburger, M. Survey of multifidelity methods in uncertainty propagation, inference, and optimization. Siam Review (2018) 60(3): 550–591. [2] Di Fiore, F., Maggiore, P. Mainini L. Multifidelity domain-aware learning for the design of re-entry vehicles. Structural and Multidisciplinary Optimization (2021) 64: 3017–303

Non-Myopic Multifidelity Bayesian Optimization

Bayesian optimization is a popular framework for the optimization of black box functions. Multifidelity methods allows to accelerate Bayesian optimization by exploiting low-fidelity representations of expensive objective functions. Popular multifidelity Bayesian strategies rely on sampling policies that account for the immediate reward obtained evaluating the objective function at a specific input, precluding greater informative gains that might be obtained looking ahead more steps. This paper proposes a non-myopic multifidelity Bayesian framework to grasp the long-term reward from future steps of the optimization. Our computational strategy comes with a two-step lookahead multifidelity acquisition function that maximizes the cumulative reward obtained measuring the improvement in the solution over two steps ahead. We demonstrate that the proposed algorithm outperforms a standard multifidelity Bayesian framework on popular benchmark optimization problems

NM-MF: Non-Myopic Multifidelity Framework for Constrained Multi-Regime Aerodynamic Optimization

The exploration and trade-off analysis of different aerodynamic design configurations requires solving optimization problems. The major bottleneck to assess the optimal design is the large number of time-consuming evaluations of high-fidelity computational fluid dynamics (CFD) models, necessary to capture the non-linear phenomena and discontinuities that occur at higher Mach number regimes. To address this limitation, we introduce an original non-myopic multifidelity Bayesian framework aimed at including expensive high-fidelity CFD simulations for the optimization of the aerodynamic design. Our scheme proposes a novel two-step lookahead policy to maximize the improvement of the solution quality considering the rewards of future steps, and combines it with utility functions informed by the fluid dynamic regime and the information extracted from data, to wisely select the aerodynamic model to interrogate. We validate the proposed framework for the case of a constrained drag coefficient optimization problem of a NACA 0012 airfoil, and compare the results to other popular multifidelity and single-fidelity optimization frameworks. The results suggest that our strategy outperforms the other approaches, allowing to significantly reduce the drag coefficient through a principled selection of limited evaluations of the high-fidelity CFD model

Domain-Aware Active Learning for Multifidelity Optimization

Bayesian optimization is a popular strategy for the optimization of black-box objective functions [1]. In many engineering applications, the objective can be evaluated with multiple representations at different levels of fidelity, to enhance a trade-off between cost and accuracy. Accordingly, multifidelity methods have been proposed in a Bayesian framework to efficiently combine information sources, using low-fidelity models to enable the exploration of design alternatives, and improve the accuracy of the solution through limited high-fidelity evaluations [2]. Most multifidelity methods based on active learning search the optimal design considering only the information extracted from the surrogate model. This can preclude the evaluation of promising design configurations that can be captured only including the knowledge of the particular physical phenomena involved [3]. To address this issue, this presentation discusses original domain-aware multifidelity Bayesian frameworks to accelerate design analysis and optimization performances. In particular, our strategy comes with an active learning scheme to adaptively sample the design space, combining statistical data from the surrogate model with physical information from the specific domain. Our formulation introduces physics-informed utility functions as additional contributions to the acquisition functions. This permits to enhance the active learning with a physicsbased insight and to realize a form of domain awareness which is beneficial to the efficiency and accuracy of the optimization task. The presentation will discuss several applications and implementations of the proposed approach for single discipline and multidisciplinary aerospace design optimization problems. [1] Snoek, J., Larochelle, H.. Adams, R.P. Practical bayesian optimization of machine learning algorithms. Advances in neural information processing systems. (2012) 25. [2] Peherstorfer, B., Willcox, K., Gunzburger, M. Survey of multifidelity methods in uncertainty propagation, inference, and optimization. Siam Review (2018) 60(3): 550–591. [3] Di Fiore, F., Maggiore, P. Mainini L. Multifidelity domain-aware learning for the design of re-entry vehicles. Structural and Multidisciplinary Optimization (2021

Euler-Richardson method preconditioned by weakly stochastic matrix algebras : a potential contribution to Pagerank computation

Let S be a column stochastic matrix with at least one full row. Then S describes a Pagerank-like random walk since the computation of the Perron vector x of S can be tackled by solving a suitable M-matrix linear system Mx = y, where M = I − τ A, A is a column stochastic matrix and τ is a positive coefficient smaller than one. The Pagerank centrality index on graphs is a relevant example where these two formulations appear. Previous investigations have shown that the Euler- Richardson (ER) method can be considered in order to approach the Pagerank computation problem by means of preconditioning strategies. In this work, it is observed indeed that the classical power method can be embedded into the ER scheme, through a suitable simple preconditioner. Therefore, a new preconditioner is proposed based on fast Householder transformations and the concept of low complexity weakly stochastic algebras, which gives rise to an effective alternative to the power method for large-scale sparse problems. Detailed mathematical reasonings for this choice are given and the convergence properties discussed. Numerical tests performed on real-world datasets are presented, showing the advantages given by the use of the proposed Householder-Richardson method

Multifidelity modeling for the design of re-entry capsules

The design and optimization of space systems presents many challenges associated with the variety of physical domains involved and their coupling. A practical example is the case of satellites and space vehicles designed to re-enter the atmosphere upon completion of their mission [1]. For these systems, aerodynamics and thermodynamics phenomena are strongly coupled and relate to structural dynamics and vibrations, chemical non equilibrium phenomena that characterize the atmosphere, specific re-entry trajectory, and geometrical shape of the body. Blunt bodies are common geometric configurations used in planetary re-entry (e.g. Apollo Command Module, Mars Viking probe, etc.). These geometries permit to obtain high aerodynamic resistance to decelerate the vehicle from orbital speeds along with contained aerodynamic lift for trajectory control. The large radius-of-curvature of the bodies’ nose allows to reduce the heat flux determined by the high temperature effects behind the shock wave. The design and optimization of these bodies would largely benefit from accurate analyses of the re-entry flow field through high-fidelity representations of the aerodynamic and aerothermodynamic phenomena. However, those high-fidelity representations are usually in the form of computer models for the numerical solutions of PDEs (e.g. Navier-Stokes equations, heat equations, etc.) which require significant computational effort and are commonly excluded from preliminary multidisciplinary design and trade-off analysis. This work addresses the integration of high-fidelity computer-based simulations for the multidisciplinary design of space systems conceived for controlled re-entry in the atmosphere. In particular, we discuss the use of multifidelity methods to obtain efficient aerothermodynamic models of the re-entering vehicles. Multifidelity approaches allow to accelerate the exploration and evaluation of design alternatives through the use of different representations of a physical system/process, each characterized by a different level of fidelity and associated computational expense [2, 3]. By efficiently combining less-expensive information from low-fidelity models with a principled selection of few expensive simulations, multifidelity methods allow to incorporate high-fidelity costly information for multidisciplinary design analysis and optimization [4–7]. This presentation proposes a multifidelity Bayesian optimization framework leveraging surrogate models in the form of gaussian processes, which are progressively updated through acquisition functions based on expected improvement. We introduce a novel formulation of the multifideltiy expected improvement including both data-driven and physics-informed utility functions, specifically implemented for the case of the design optimization of an Orion-like atmospheric re-entry vehicle. The results show that the proposed formulation gives better optimization results (lower minimum) than single fidelity Bayesian optimization based on low-fidelity simulations only. The outcome suggests that the multifidelity expected improvement algorithm effectively enriches the information content with the high-fidelity data. Moreover, the computational cost associated with 100 iterations of our multifidelity strategy is sensitively lower than the computational burden of 6 iterations of a single fidelity framework invoking the high-fidelity model. References [1] Gallais, P., Atmospheric re-entry vehicle mechanics, Springer Science and Business Media, 2007. [2] Peherstorfer, B., Willcox, K., and Gunzburger, M., “Survey of Multifidelity Methods in Uncertainty Propagation, Inference, and Optimization,” SIAM Review, Vol. 60, 2018, pp. 550–591. [3] Fernandez-Godino, G., Park, C., Kim, N., and Haftka, R., “Issues in Deciding Whether to Use Multifidelity Surrogates,” AIAA Journal, 2019, p. 16. [4] Mainini, L., and Maggiore, P., “A Multifidelity Approach to Aerodynamic Analysis in an Integrated Design Environment,” AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, AIAA, 2012. [5] Goertz, S., Zimmermann, R., and Han, Z. H., “Variable-fidelity and reduced-order models for aero data for loads predictions,” Computational Flight Testing, 2013, pp. 99–112. [6] Meliani, M., Bartoli, N., Lefebvre, T., Bouhlel, M.A., J., Martins, and Morlier, J., “Multi-fidelity efficient global optimization: Methodology and application to airfoil shape design,” AIAA Aviation 2019 Forum, AIAA, 2019. [7] Beran, P., Bryson, D., Thelen, A., Diez, M., and Serani, A., “Comparison of Multi-Fidelity Approaches for Military Vehicle Design,” AIAA Aviation 2020 Forum, AIAA, 2020

Multifidelity Learning for the Design of Re-Entry Capsules

The design and optimization of re-entry capsules presents many challenges associated with the variety of physical domains involved and their couplings. Examples are capsules for the transfer of astronauts to the international space station and for future Lunar and Martian exploration missions. For these vehicles, aerodynamics and thermodynamics phenomena are strongly coupled and relate to structural dynamics and vibrations, chemical non equilibrium phenomena that characterize the atmosphere, specifi c re-entry trajectory, and geometrical shape of the body. The design and optimization of these capsules would largely benefi t from accurate analyses of the re-entry flow field through high- fidelity representations of the aerothermodynamic phenomena. However, those high- fidelity representations are usually in the form of computer models for the numerical solutions of PDEs (e.g. Navier-Stokes equations, heat equations, etc.) which require signifi cant computational effort and are commonly excluded from preliminary multidisciplinary design and trade-off analysis. This presentation discusses the use of multi fidelity methods to integrate high- fidelity simulations in order to obtain efficient aerothermodynamic models of the re-entering vehicles. Multi fidelity approaches allow to accelerate the exploration and evaluation of design alternatives through the use of different representations of a physical system/process, each characterized by a different level of fidelity and associated computational expense. By efficiently combining less-expensive information from low- fidelity models with a principled selection of few expensive simulations, multi fidelity methods allow to incorporate high-fidelity costly information for design analysis and optimization. Speci fically, we propose a multifi delity active learning strategy to accelerate the multidisciplinary design optimization (MDO) of a re-entry vehicle. The active learning scheme is formulated to be both data driven and domain-aware, and is implemented for the design of an Orion-like re-entry capsule. The MDO problem comprises trajectory analysis, propulsion system model, aerothermodynamic models, and structural model of the thermal protection systems (TPS). The design objectives are the minimization of the propellant mass burned during the entry maneuver, the structural mass of the TPS and the temperature reached by the TPS structure. The results show that our multifidelity scheme allows to efficiently improve the design solution through a limited number of high- fidelity evaluations