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With a widely attended virtual kickoff event on January 29, 2021, the National Cancer Institute (NCI) and the Department of Energy (DOE) launched a series of 4 interactive, interdisciplinary workshops-and a final concluding "World Café" on March 29, 2021-focused on advancing computational approaches for predictive oncology in the clinical and research domains of radiation oncology. These events reflect 3,870 human hours of virtual engagement with representation from 8 DOE national laboratories and the Frederick National Laboratory for Cancer Research (FNL), 4 research institutes, 5 cancer centers, 17 medical schools and teaching hospitals, 5 companies, 5 federal agencies, 3 research centers, and 27 universities. Here we summarize the workshops by first describing the background for the workshops. Participants identified twelve key questions-and collaborative parallel ideas-as the focus of work going forward to advance the field. These were then used to define short-term and longer-term "Blue Sky" goals. In addition, the group determined key success factors for predictive oncology in the context of radiation oncology, if not the future of all of medicine. These are: cross-discipline collaboration, targeted talent development, development of mechanistic mathematical and computational models and tools, and access to high-quality multiscale data that bridges mechanisms to phenotype. The workshop participants reported feeling energized and highly motivated to pursue next steps together to address the unmet needs in radiation oncology specifically and in cancer research generally and that NCI and DOE project goals align at the convergence of radiation therapy and advanced computing.

This review discusses Operator Inference, a nonintrusive reduced modeling approach that incorporates physical governing equations by defining a structured polynomial form for the reduced model, and then learns the corresponding reduced operators from simulated training data. The polynomial model form of Operator Inference is sufficiently expressive to cover a wide range of nonlinear dynamics found in fluid mechanics and other fields of science and engineering, while still providing efficient reduced model computations. The learning steps of Operator Inference are rooted in classical projection-based model reduction; thus, some of the rich theory of model reduction can be applied to models learned with Operator Inference. This connection to projection-based model reduction theory offers a pathway toward deriving error estimates and gaining insights to improve predictions. Furthermore, through formulations of Operator Inference that preserve Hamiltonian and other structures, important physical properties such as energy conservation can be guaranteed in the predictions of the reduced model beyond the training horizon. This review illustrates key computational steps of Operator Inference through a large-scale combustion example. [ABSTRACT FROM AUTHOR]

This work formulates a new approach to reduced modeling of parameterized, timedependent partial differential equations (PDEs). The method employs Operator Inference, a scientific machine learning framework combining data-driven learning and physics-based modeling. The parametric structure of the governing equations is embedded directly into the reduced-order model, and parameterized reduced-order operators are learned via a data-driven linear regression problem. The result is a reduced-order model that can be solved rapidly to map parameter values to approximate PDE solutions. Such parameterized reduced-order models may be used as physics-based surrogates for uncertainty quantification and inverse problems that require many forward solves of parametric PDEs. Numerical issues such as well-posedness and the need for appropriate regularization in the learning problem are considered, and an algorithm for hyperparameter selection is presented. The method is illustrated for a parametric heat equation and demonstrated for the FitzHugh-Nagumo neuron model. [ABSTRACT FROM AUTHOR]

This work develops a methodology for sensor placement and dynamic sensor scheduling decisions for digital twins. The digital twin data assimilation is posed as a classification problem, and predictive models are used to train optimal classification trees that represent the map from observed data to estimated digital twin states. In addition to providing a rapid digital twin updating capability, the resulting classification trees yield an interpretable mathematical representation that can be queried to inform sensor placement and sensor scheduling decisions. The proposed approach is demonstrated for a structural digital twin of a 12 ft wingspan unmanned aerial vehicle. Offline, training data are generated by simulating scenarios using predictive reduced-order models of the vehicle in a range of structural states. These training data can be further augmented using experimental or other historical data. In operation, the trained classifier is applied to observational data from the physical vehicle, enabling rapid adaptation of the digital twin in response to changes in structural health. Within this context, we study the performance of the optimal tree classifiers and demonstrate how they enable explainable structural assessments from sparse sensor measurements and also inform optimal sensor placement. [ABSTRACT FROM AUTHOR]

Digital thread is a data-driven architecture that links together information from all stages of the product lifecycle. Despite increasing application in manufacturing, maintenance/operations, and design related tasks, a principled formulation of analyzing the decision-making problem under uncertainty for the digital thread remains absent. The contribution of this article is to present a formulation using Bayesian statistics and decision theory. First, we address how uncertainty propagates in the product lifecycle and how the digital thread evolves based on the decisions we make and the data we collect. By using these mechanics, we explore designing over multiple product generations or iterations and provide an algorithm to solve the underlying multistage decision problem. We illustrate our method on an example structural design problem where our method can quantify and optimize different types and sequences of decisions, ranging from experimentation, manufacturing, and sensor placement/selection, to minimize total accrued costs. [ABSTRACT FROM AUTHOR]

This paper derives predictive reduced-order models for rocket engine combustion dynamics via Operator Inference, a scientific machine learning approach that blends data-driven learning with physics-based modelling. The non-intrusive nature of the approach enables variable transformations that expose system structure. The specific contribution of this paper is to advance the formulation robustness and algorithmic scalability of the Operator Inference approach. Regularisation is introduced to the formulation to avoid over-fitting. The task of determining an optimal regularisation is posed as an optimisation problem that balances training error and stability of long-time integration dynamics. A scalable algorithm and open-source implementation are presented, then demonstrated for a single-injector rocket combustion example. This example exhibits rich dynamics that are difficult to capture with state-of-the-art reduced models. With appropriate regularisation and an informed selection of learning variables, the reduced-order models exhibit high accuracy in re-predicting the training regime and acceptable accuracy in predicting future dynamics, while achieving close to a million times speedup in computational cost. When compared to a state-of-the-art model reduction method, the Operator Inference models provide the same or better accuracy at approximately one thousandth of the computational cost. [ABSTRACT FROM AUTHOR]

A network modelling approach to educational mapping leads to a scalable computational model that supports adaptive learning, intelligent tutors, intelligent teaching assistants, and data-driven continuous improvement. Current educationalmapping processes are generally applied at a level of resolution that is too coarse to support adaptive learning and learning analytics systems at scale. This paper proposes a network modelling approach to structure extremely fine-grained statements of learning ability called Micro-outcomes, and a method to design sensors for inferring a learner's knowledge state. These sensors take the form of high-resolution assessments and trackers that collect digital analytics. The sensors are linked to Micro-outcomes as part of the network model, enabling inference and pathway analysis. One example demonstrates the modelling approach applied to two community college subjects in College Algebra and Introductory Accounting. Application examples showcase how this modelling approach provides the design foundation for an intelligent tutoring system and intelligent teaching assistant system deployed at Arapahoe Community College and Quinsigamond Community College. A second example demonstrates the modelling approach deployed in an undergraduate aerospace engineering subject at theMassachusetts Institute of Technology to support course planning and teaching improvement. [ABSTRACT FROM AUTHOR]

Summary: A challenge in engineering design is to choose suitable objectives and constraints from many quantities of interest, while ensuring an optimization is both meaningful and computationally tractable. We propose an optimization formulation that can take account of more quantities of interest than existing formulations, without reducing the tractability of the problem. This formulation searches for designs that are optimal with respect to a binary relation within the set of designs that are optimal with respect to another binary relation. We then propose a method of finding such designs in a single optimization by defining an overall ranking function to use in optimizers, reducing the cost required to solve this formulation. In a design under uncertainty problem, our method obtains the most robust design that is not stochastically dominated faster than a multiobjective optimization. In a car suspension design problem, our method obtains superior designs according to a k‐optimality condition than previously suggested multiobjective approaches to this problem. In an airfoil design problem, our method obtains designs closer to the true lift/drag Pareto front using the same computational budget as a multiobjective optimization. [ABSTRACT FROM AUTHOR]

We propose a multifidelity dimension reduction method to identify a low-dimensional structure present in many engineering models. The structure of interest arises when functions vary primarily on a low-dimensional subspace of the high-dimensional input space, while varying little along the complementary directions. Our approach builds on the gradient-based methodology of active subspaces, and exploits models of different fidelities to reduce the cost of performing dimension reduction through the computation of the active subspace matrix. We provide a nonasymptotic analysis of the number of gradient evaluations sufficient to achieve a prescribed error in the active subspace matrix, both in expectation and with high probability. We show that the sample complexity depends on a notion of intrinsic dimension of the problem, which can be much smaller than the dimension of the input space. We illustrate the benefits of such a multifidelity dimension reduction approach using numerical experiments with input spaces of up to two thousand dimensions. [ABSTRACT FROM AUTHOR]

Summary: This paper addresses the challenge of design optimization under uncertainty when the designer only has limited data to characterize uncertain variables. We demonstrate that the error incurred when estimating a probability distribution from limited data affects the out‐of‐sample performance (ie, performance under the true distribution) of optimized designs. We demonstrate how this can be mitigated by reformulating the engineering design problem as a distributionally robust optimization (DRO) problem. We present computationally efficient algorithms for solving the resulting DRO problem. The performance of the DRO approach is explored in a practical setting by applying it to an acoustic horn design problem. The DRO approach is compared against traditional approaches to optimization under uncertainty, namely, sample‐average approximation and multiobjective optimization incorporating a risk reduction objective. In contrast with the multiobjective approach, the proposed DRO approach does not use an explicit risk reduction objective but rather specifies a so‐called ambiguity set of possible distributions and optimizes against the worst‐case distribution in this set. Our results show that the DRO designs, in some cases, significantly outperform those designs found using the sample‐average or the multiobjective approach. [ABSTRACT FROM AUTHOR]

Additively manufactured wings can be aeroelastically tailored, which offers the potential for increased air vehicle efficiency via lighter structures. This paper develops a methodology to design aeroelastically tailored wings using additively manufactured lattice structures. Adaptive meshing techniques are used to design the topology of the lattice to align with the load direction, and the lattice is optimized to minimize the structural weight and to improve the flutter margin. To alleviate the computational effort of aeroelastically tailoring a structure, a low-order model for the dynamics of the lattice structure is developed. This structural low-order model is coupled to a previously developed physics-based transonic flutter model to compute the aeroelastic behavior of wings with internal lattice structures. The structural low-order model is validated by comparing against the full-order structural dynamics model. Finally, the design methodology is applied to the design of an internal structure of an aircraft wing to increase that wing's flutter speed. [ABSTRACT FROM AUTHOR]

The immense design freedom offered by additive manufacturing yields tremendous benefits, but it also raises the question of how to best go about designing components to exploit this design freedom. In early design phases, design tools need to utilize this freedom, but do so with low computational cost and with a good estimate of the final weight to correctly assess the part's influence on the overall product design. This is especially important for aerospace designs. In this paper, a design methodology is devised for cellular structures to be manufactured using additive manufacturing techniques, specifically for such early design phases. This design methodology uses adaptive meshing techniques to design the topology of the cellular structure, after which the struts of that cellular structure are optimized separately to reduce the dimensionality of the problem. The method is demonstrated for a small generic bracket and an aircraft bracket design from the literature. For these problems, our method is fast enough to evaluate many thousands of design options. This results in identifying promising candidate designs for further detailed design work. [ABSTRACT FROM AUTHOR]

This paper presents a structure-exploiting nonlinear model reduction method for systems with general nonlinearities. First, the nonlinear model is lifted to a model with more structure via variable transformations and the introduction of auxiliary variables. The lifted model is equivalent to the original model; it uses a change of variables but introduces no approximations. When discretized, the lifted model yields a polynomial system of either ordinary differential equations or differential-algebraic equations, depending on the problem and lifting transformation. Proper orthogonal decomposition (POD) is applied to the lifted models, yielding a reduced-order model for which all reduced-order operators can be precomputed. Thus, a key benefit of the approach is that there is no need for additional approximations of nonlinear terms, which is in contrast with existing nonlinear model reduction methods requiring sparse sampling or hyper-reduction. Application of the lifting and POD model reduction to the FitzHugh-Nagumo benchmark problem and to a tubular reactor model with Arrhenius reaction terms shows that the approach is competitive in terms of reduced model accuracy with state-of-the-art model reduction via POD and discrete empirical interpolation while having the added benefits of opening new pathways for rigorous analysis and input-independent model reduction via the introduction of the lifted problem structure. [ABSTRACT FROM AUTHOR]

Summary: In optimization under uncertainty for engineering design, the behavior of the system outputs due to uncertain inputs needs to be quantified at each optimization iteration, but this can be computationally expensive. Multifidelity techniques can significantly reduce the computational cost of Monte Carlo sampling methods for quantifying the effect of uncertain inputs, but existing multifidelity techniques in this context apply only to Monte Carlo estimators that can be expressed as a sample average, such as estimators of statistical moments. Information reuse is a particular multifidelity method that treats previous optimization iterations as lower fidelity models. This work generalizes information reuse to be applicable to quantities whose estimators are not sample averages. The extension makes use of bootstrapping to estimate the error of estimators and the covariance between estimators at different fidelities. Specifically, the horsetail matching metric and quantile function are considered as quantities whose estimators are not sample averages. In an optimization under uncertainty for an acoustic horn design problem, generalized information reuse demonstrated computational savings of over 60% compared with regular Monte Carlo sampling. [ABSTRACT FROM AUTHOR]

Abstract: For many engineering systems, current design methodologies do not adequately quantify and manage uncertainty as it arises during the design process, which can lead to unacceptable risks, increases in programmatic cost, and schedule overruns. This paper develops new sensitivity analysis methods that can be used to better understand and mitigate the effects of uncertainty in system design. In particular, a new entropy‐based sensitivity analysis methodology is introduced, which apportions output uncertainty into contributions due to not only the variance of input factors and their interactions, but also to features of the underlying probability distributions that are related to distribution shape and extent. Local sensitivity analysis techniques are also presented, which provide computationally inexpensive estimates of the change in output uncertainty resulting from design modifications. The proposed methods are demonstrated on an engineering example to show how they can be used in the design context to systematically manage uncertainty budgets—which specify the allowable level of uncertainty for a system—by helping to identify design alternatives, evaluate trade‐offs between available options, and guide decisions regarding the allocation of resources. [ABSTRACT FROM AUTHOR]

Educational mapping is the process of analyzing an educational system to identify entities, relationships and attributes. This paper proposes a network modeling approach to educational mapping. Current mapping processes in education typically represent data in forms that do not support scalable learning analytics. For example, a curriculum map is usually a table, where relationships among curricular elements are represented implicitly in the rows of the table. The proposed network modeling approach overcomes this limitation through explicit modeling of these relationships in a graph structure, which in turn unlocks the ability to perform scalable analyses on the dataset. The paper presents network models for educational use cases, with concrete examples in curriculum mapping, accreditation mapping and concept mapping. Illustrative examples demonstrate how the formal modeling approach enables visualization and learning analytics. The analysis provides insight into learning pathways, supporting design of adaptive learning systems. It also permits gap analysis of curriculum coverage, supporting student advising, student degree planning and curricular design at scales ranging from an entire institution to an individual course. [ABSTRACT FROM AUTHOR]

This paper presents methodology to enable path planning for an unmanned aerial vehicle that uses dynamic data-driven flight capability estimation. The main contribution of the work is a general mathematical approach that leverages offline high-fidelity physics-based modeling together with onboard sensor measurements to achieve dynamic path planning. The mathematical framework, expressed as a constrained partially observable Markov decision process, accounts for vehicle capability constraints and is robust to modeling error and disturbances in both the vehicle process and measurement models. Vehicle capability constraints are incorporated using probabilistic support vector machine surrogates of high-fidelity physics-based models that adequately capture the richness of the vehicle dynamics. Sensor measurements are treated in a general manner and can include combinations of multiple modalities such as that through global positioning system signals, inertial mass unit outputs, and structural strain data of the airframe. Results are presented for a simulated three-dimensional environment and point-mass airplane model. The vehicle can dynamically adjust its trajectory according to the observations it receives about its current state of health, thereby retaining a high probability of survival and mission success. [ABSTRACT FROM AUTHOR]

As a measure to manage the climate impact of aviation, significant enhancements to aviation technologies and operations are necessary. When assessing these enhancements and their respective impacts on the climate, it is important that we also quantify the associated uncertainties. This is important to support an effective decision and policymaking process. However, such quantification of uncertainty is challenging, especially in a complex system that comprises multiple interacting components. The uncertainty quantification task can quickly become computationally intractable and cumbersome for one individual or group to manage. Recognizing the challenge of quantifying uncertainty in multicomponent systems, we utilize a divide-and-conquer approach, inspired by the decomposition-based approaches used in multidisciplinary analysis and optimization. Specifically, we perform uncertainty analysis and global sensitivity analysis of our multicomponent aviation system in a decomposition-based manner. In this work, we demonstrate how to handle a high-dimensional multicomponent interface using sensitivity-based dimension reduction and a novel importance sampling method. Our results demonstrate that the decomposition-based uncertainty quantification approach can effectively quantify the uncertainty of a feed-forward multicomponent system for which the component models are housed in different locations and owned by different groups. [ABSTRACT FROM PUBLISHER]

Quantification and management of uncertainty are critical in the design of engineering systems, especially in the early stages of conceptual design. This paper presents an approach to defining budgets on the acceptable levels of uncertainty in design quantities of interest, such as the allowable risk in not meeting a critical design constraint and the allowable deviation in a system performance metric. A sensitivity-based method analyzes the effects of design decisions on satisfying those budgets, and a multi-objective optimization formulation permits the designer to explore the tradespace of uncertainty reduction activities while also accounting for a cost budget. For models that are computationally costly to evaluate, a surrogate modeling approach based on high-dimensional model representation achieves efficient computation of the sensitivities. An example problem in aircraft conceptual design illustrates the approach. [ABSTRACT FROM AUTHOR]

This paper develops a multi-information source formulation for aerospace design under uncertainty problems. As a specific demonstration of the approach, it presents the optimization under uncertainty of an advanced subsonic transport aircraft developed to meet the NASA N + 3 goals and shows how the multi-information source approach enables practical turnaround time for this conceptual aircraft optimization under uncertainty problem. In the conceptual design phase, there are often uncertainties about future developments of the underlying technologies. An aircraft design that is robust to uncertainty is more likely to meet performance requirements as the technologies mature in the intermediate and detailed design phases, reducing the need for expensive redesigns. In the particular example selected here to present the new approach, the multi-information source approach uses an information-reuse estimator that takes advantage of the correlation of the aircraft model in the design space to reduce the number of model evaluations needed to achieve a given standard error in the Monte Carlo estimates of the relevant design statistics (mean and variance). Another contribution of the paper is to extend the approach to reuse information during trade studies that involve solving multiple optimization under uncertainty problems, enabling the analysis of the risk-performance tradeoff in optimal aircraft designs. [ABSTRACT FROM AUTHOR]

One of the major challenges in the Bayesian solution of inverse problems governed by partial differential equations (PDEs) is the computational cost of repeatedly evaluating numerical PDE models, as required by Markov chain Monte Carlo (MCMC) methods for posterior sampling. This paper proposes a data-driven projection-based model reduction technique to reduce this computational cost. The proposed technique has two distinctive features. First, the model reduction strategy is tailored to inverse problems: the snapshots used to construct the reduced-order model are computed adaptively from the posterior distribution. Posterior exploration and model reduction are thus pursued simultaneously. Second, to avoid repeated evaluations of the full-scale numerical model as in a standard MCMC method, we couple the full-scale model and the reduced-order model together in the MCMC algorithm. This maintains accurate inference while reducing its overall computational cost. In numerical experiments considering steady-state flow in a porous medium, the data-driven reduced-order model achieves better accuracy than a reduced-order model constructed using the classical approach. It also improves posterior sampling efficiency by several orders of magnitude compared with a standard MCMC method. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY It is important to design robust and reliable systems by accounting for uncertainty and variability in the design process. However, performing optimization in this setting can be computationally expensive, requiring many evaluations of the numerical model to compute statistics of the system performance at every optimization iteration. This paper proposes a multifidelity approach to optimization under uncertainty that makes use of inexpensive, low-fidelity models to provide approximate information about the expensive, high-fidelity model. The multifidelity estimator is developed based on the control variate method to reduce the computational cost of achieving a specified mean square error in the statistic estimate. The method optimally allocates the computational load between the two models based on their relative evaluation cost and the strength of the correlation between them. This paper also develops an information reuse estimator that exploits the autocorrelation structure of the high-fidelity model in the design space to reduce the cost of repeatedly estimating statistics during the course of optimization. Finally, a combined estimator incorporates the features of both the multifidelity estimator and the information reuse estimator. The methods demonstrate 90% computational savings in an acoustic horn robust optimization example and practical design turnaround time in a robust wing optimization problem. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we present a framework for achieving constrained optimal real-time control for large-scale systems with fast dynamics. The methodology uses the explicit solution of the model predictive control problem combined with model reduction, in an output-feedback implementation. The explicit solution of the model predictive control problem leads to online model predictive control functionality without having to solve an optimization problem at each time step. Reduced-order models are derived using a goal-oriented, model-constrained optimization formulation that yields efficient models tailored to the control application at hand. The approach is illustrated on a challenging large-scale flow problem that aims to control the shock position in a supersonic diffuser. [ABSTRACT FROM AUTHOR]

This work develops an efficient real-time inverse formulation for inferring the aerodynamic surface pressures on a hypersonic vehicle from sparse measurements of the structural strain. The approach aims to provide real-time estimates of the aerodynamic loads acting on the vehicle for ground and flight testing, as well as guidance, navigation, and control applications. Specifically, the approach targets hypersonic flight conditions where direct measurement of the surface pressures is challenging due to the harsh aerothermal environment. For problems employing a linear elastic structural model, the inference problem can be posed as a least-squares problem with a linear constraint arising from a finite element discretization of the governing elasticity partial differential equation. Due to the linearity of the problem, an explicit solution is given by the normal equations. Precomputation of the resulting inverse map enables rapid evaluation of the surface pressure and corresponding integrated quantities, such as the force and moment coefficients. The inverse approach additionally allows for uncertainty quantification, providing insights for theoretical recoverability and robustness to sensor noise. Numerical studies demonstrate the estimator performance for reconstructing the surface pressure field, as well as the force and moment coefficients, for the Initial Concept 3.X (IC3X) conceptual hypersonic vehicle. [ABSTRACT FROM AUTHOR]

This paper focuses on the construction of accurate and predictive data-driven reduced models of large-scale numerical simulations with complex dynamics and sparse training datasets. In these settings, standard, single-domain approaches may be too inaccurate or may overfit and hence generalize poorly. Moreover, processing large-scale datasets typically requires significant memory and computing resources, which can render single-domain approaches computationally prohibitive. To address these challenges, we introduce a domain-decomposition formulation into the construction of a data-driven reduced model. In doing so, the basis functions used in the reduced model approximation become localized in space, which can increase the accuracy of the domain-decomposed approximation of the complex dynamics. The decomposition furthermore reduces the memory and computing requirements to process the underlying large-scale training dataset. We demonstrate the effectiveness and scalability of our approach in a large-scale three-dimensional unsteady rotating-detonation rocket engine simulation scenario with more than 75 million degrees of freedom and a sparse training dataset. Our results show that compared to the single-domain approach, the domain-decomposed version reduces both the training and prediction errors for pressure by up to 13% and up to 5% for other key quantities, such as temperature, and fuel, and oxidizer mass fractions. Lastly, our approach decreases the memory requirements for processing by almost a factor of four, which in turn reduces the computing requirements as well. [ABSTRACT FROM AUTHOR]

Transonic aeroelasticity is an important consideration in the conceptual design of next-generation aircraft configurations. This paper develops a low-order physics-based flutter model for swept high-aspect-ratio wings. The approach builds upon a previously developed flutter model that uses the flowfield's lowest moments of vorticity and volume-source density perturbations as its states. The contribution of this paper is a new formulation of the model for swept high-aspect-ratio wings. The aerodynamic model is calibrated using offline two-dimensional unsteady transonic computational-fluid-dynamics simulations. Combining that aerodynamic model with a beam model results in a low-dimensional overall aeroelastic system. The low computational cost of the model permits its incorporation in a conceptual design tool for next-generation transport aircraft. The model's capabilities are demonstrated by finding transonic flutter boundaries for different clamped-wing configurations and investigating the influence of transonic flutter on the planform design of next-generation transport aircraft. [ABSTRACT FROM AUTHOR]

This paper presents a physical low-order model for two-dimensional unsteady transonic airfoil flow, based on small unsteady disturbances about a known steady flow solution. This is in contrast to traditional small-disturbance theory, which assumes small disturbances about the freestream. The states of the low-order model are the flowfield's lowest moments of vorticity and volume-source density perturbations, and their evolution equation coefficients are calibrated using off-line unsteady computational fluid dynamics simulations through dynamic mode decomposition. The resulting low-order unsteady flow model is coupled to a typical-section structural model, thus enabling prediction of transonic flutter onset for wings with moderate to high aspect ratios. The method is fast enough to permit incorporation of transonic flutter constraints in conceptual aircraft design calculations. The accuracy of this low-order model is demonstrated for forced pitching and heaving simulations of an airfoil in compressible flow. Finally, the model is used to describe the influence of compressibility on the flutter boundary, and its accuracy is demonstrated for the Isogai Case A classical flutter test case. [ABSTRACT FROM AUTHOR]

This paper presents a new approach for optimization under uncertainty in the presence of probabilistic, interval, and mixed uncertainties, avoiding the need to specify probability distributions on uncertain parameters when such information is not readily available. Existing approaches for optimization under these types of uncertainty mostly rely on treating combinations of statistical moments as separate objectives, but this can give rise to stochastically dominated designs. Here, horsetail matching is extended for use with these types of uncertainties to overcome some of the limitations of existing approaches. The formulation delivers a single, differentiable metric as the objective function for optimization. It is demonstrated on algebraic test problems, the design of a wing using a low-fidelity coupled aerostructural code, and the aerodynamic shape optimization of a wing using computational fluid dynamics analysis. [ABSTRACT FROM AUTHOR]

This paper introduces a multifidelity method that can produce accurate estimates of the flutter boundary at a reduced cost by combining information from low- and high-fidelity aeroelastic models. Estimating the flutter boundary in the presence of nonlinear aerodynamic phenomena is challenging because high-fidelity aeroelastic models are expensive to evaluate, and flutter analysis requires many model evaluations. On the other hand, relatively inexpensive approximate aeroelastic models (low-fidelity models) exist and are routinely applied to reduce the cost of estimating flutter, albeit with lower accuracy. The multifidelity method introduced here uses an active learning algorithm to leverage information from low-fidelity models. A multifidelity statistical surrogate is used to fit damping coefficient estimates computed with different aeroelastic models. This surrogate is used to estimate the uncertainty in the prediction of the flutter boundary, which drives the selection of new evaluations. The effectiveness of the multifidelity method is demonstrated by estimating the aeroelastic flutter boundary of a typical section model at a cost 85% lower when compared with the bisection method. Four aeroelastic models are considered in this example: three models (including the high-fidelity model) use a computational fluid dynamics solver based on the Euler equations, whereas one model uses a two-dimensional doublet-lattice method. [ABSTRACT FROM AUTHOR]