Search NASA⌕ Search

SEARCH · Search NASA

Results for “problems”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRS2003

Dynamically Reconfigurable Approach to Multidisciplinary Problems

The complexity and autonomy of the constituent disciplines and the diversity of the disciplinary data formats make the task of integrating simulations into a multidisciplinary design optimization problem extremely time-consuming and difficult. We propose a dynamically reconfigurable approach to MDO problem formulation wherein an appropriate implementation of the disciplinary information results in basic computational components that can be combined into different MDO problem formulations and solution algorithms, including hybrid strategies, with relative ease. The ability to re-use the computational components is due to the special structure of the MDO problem. We believe that this structure can and should be used to formulate and solve optimization problems in the multidisciplinary context. The present work identifies the basic computational components in several MDO problem formulations and examines the dynamically reconfigurable approach in the context of a popular class of optimization methods. We show that if the disciplinary sensitivity information is implemented in a modular fashion, the transfer of sensitivity information among the formulations under study is straightforward. This enables not only experimentation with a variety of problem formations in a research environment, but also the flexible use of formulations in a production design environment.

Alexandrov, Natalie M.↗
NASA NTRS2003

Evaluation of Genetic Algorithm Concepts Using Model Problems: Multi-Objective Optimization - Part 2

A genetic algorithm approach suitable for solving multi-objective optimization problems is described and evaluated using a series of simple model problems. Several new features including a binning selection algorithm and a gene-space transformation procedure are included. The genetic algorithm is suitable for finding pareto optimal solutions in search spaces that are defined by any number of genes and that contain any number of local extrema. Results indicate that the genetic algorithm optimization approach is flexible in application and extremely reliable, providing optimal results for all optimization problems attempted. The binning algorithm generally provides pareto front quality enhancements and moderate convergence efficiency improvements for most of the model problems. The gene-space transformation procedure provides a large convergence efficiency enhancement for problems with non-convoluted pareto fronts and a degradation in efficiency for problems with convoluted pareto fronts. The most difficult problems --multi-mode search spaces with a large number of genes and convoluted pareto fronts-- require a large number of function evaluations for GA convergence, but always converge.

Holst, Terry L.↗
NASA NTRS2004

Unifying Temporal and Structural Credit Assignment Problems

Single-agent reinforcement learners in time-extended domains and multi-agent systems share a common dilemma known as the credit assignment problem. Multi-agent systems have the structural credit assignment problem of determining the contributions of a particular agent to a common task. Instead, time-extended single-agent systems have the temporal credit assignment problem of determining the contribution of a particular action to the quality of the full sequence of actions. Traditionally these two problems are considered different and are handled in separate ways. In this article we show how these two forms of the credit assignment problem are equivalent. In this unified frame-work, a single-agent Markov decision process can be broken down into a single-time-step multi-agent process. Furthermore we show that Monte-Carlo estimation or Q-learning (depending on whether the values of resulting actions in the episode are known at the time of learning) are equivalent to different agent utility functions in a multi-agent system. This equivalence shows how an often neglected issue in multi-agent systems is equivalent to a well-known deficiency in multi-time-step learning and lays the basis for solving time-extended multi-agent problems, where both credit assignment problems are present.

Agogino, Adrian K.↗
NASA NTRS2017

The Root Cause of the Overheating Problem

Previously we identified the receding flow, where two fluid streams recede from each other, as an open numerical problem, because all well-known numerical fluxes give an anomalous temperature rise, thus called the overheating problem. This phenomenon, although presented in several textbooks, and many previous publications, has scarcely been satisfactorily addressed and the root cause of the overheating problem not well understood. We found that this temperature rise was solely connected to entropy rise and proposed to use the method of characteristics to eradicate the problem. However, the root cause of the entropy production was still unclear. In the present study, we identify the cause of this problem: the entropy rise is rooted in the pressure flux in a finite volume formulation and is implanted at the first time step. It is found theoretically inevitable for all existing numerical flux schemes used in the finite volume setting, as confirmed by numerical tests. This difficulty cannot be eliminated by manipulating time step, grid size, spatial accuracy, etc, although the rate of overheating depends on the flux scheme used. Finally, we incorporate the entropy transport equation, in place of the energy equation, to ensure preservation of entropy, thus correcting this temperature anomaly. Its applicability is demonstrated for some relevant 1D and 2D problems. Thus, the present study validates that the entropy generated ab initio is the genesis of the overheating problem.

Liou, Meng-Sing↗
NASA NTRS2019

Exploring Network-Related Optimization Problems Using Quantum Heuristics

Network-related connectivity optimization problems are underlying a wide range of applications and are also of high computational complexity. We consider studying network optimization problems using two types of quantum heuristics.One is quantum annealing, and the other Quantum Alternating Operator Ansatz, an extension of the Quantum Approximate Optimization Algorithms for gate-model quantum computation, in which a cost-function based unitary and a non-commuting mixing unitary are applied alternately. We present problem mappings for problems of finding the spanning-tree or spanning-graph of a graph that optimizes certain costs, and a variant that further requires the spanning-tree be degree-bounded. With quantum annealing, all constraints are cast into penalty terms in the cost Hamiltonian, and the solution is encoded as the ground state of the Hamiltonian. We provide three mappings to the quadratic unconstrained binary optimization (QUBO) form, compare the resource requirements, and analyze the tradeoffs. For QAOA, we give special focus on the design of mixers based on the constraints presented in the problem, such that the system evolution remains in a subspace of the full Hilbert space where all constraints are satisfied. In the spanning-tree problem, one such hard constraint is that a mixer applied to a spanning-tree needs also be a spanning tree. This involves checking the connectivity of a subgraph, which is a global condition common for most network-related problems. We show how this feature can be efficiently represented in the mixer in a quantum coherent way, based on manipulation of a descendant-matrix and an adjacent matrix. We further develop a mixer for the spanning-graphs based on the spanning-tree mixer.

Wang, Zhihui↗
NASA NTRS2019

Study network-related optimization problems using quantum alternating optimization ansatz

Network-related connectivity optimization problems are underlying a wide range of applications and are also of high computational complexity. We consider studying network optimization problems using two types of quantum heuristics. One is quantum annealing, and the other Quantum Alternating Operator Ansatz, an extension of the Quantum Approximate Optimization Algorithms for gate-model quantum computation, in which a cost-function based unitary and a non-commuting mixing unitary are applied alternately. We present problem mappings for problems of finding the spanning-tree or spanning-graph of a graph that optimizes certain costs, and a variant that further requires the spanning-tree be degree-bounded. With quantum annealing, all constraints are cast into penalty terms in the cost Hamiltonian, and the solution is encoded as the ground state of the Hamiltonian. We provide three mappings to the quadratic unconstrained binary optimization (QUBO) form, compare the resource requirements, and analyze the tradeoffs. For QAOA, we give special focus on the design of mixers based on the constraints presented in the problem, such that the system evolution remains in a subspace of the full Hilbert space where all constraints are satisfied. In the spanning-tree problem, one such hard constraint is that a mixer applied to a spanning-tree needs also be a spanning tree. This involves checking the connectivity of a subgraph, which is a global condition common for most network-related problems. We show how this feature can be efficiently represented in the mixer in a quantum coherent way, based on manipulation of a descendant-matrix and an adjacent matrix. We further develop a mixer for the spanning-graphs based on the spanning-tree mixer.

Zhihui Wang↗
NASA NTRSDate not supplied

Content and Representation of Information Needed to Support Time-Constrained Problem Solving

NASA’s current mission-operations paradigm originated with Project Mercury and endured with minimum evolution through the Apollo Program, Space Shuttle Program, and ISS missions. At its foundation is a near-complete real-time dependence on a ground team to manage the combined state of the mission, vehicle, and crew. Utilizing many engineers and operators with broad and deep expertise; large, distributed datasets including extensive telemetry; and expansive analytical and computing power, this ground team has served as the safety net for crewed spaceflight missions over the past 60 years. This approach must change to address challenges associated with missions beyond low Earth orbit (BLEO), including infrequent resupply, reduced ability to evacuate, and delayed communications that prohibit real-time operational support. We anticipate that a necessary part of this change will be increased independence for the crew, as roles and responsibilities traditionally performed by ground teams move on board the vehicle. While many risks are associated with Earth-independent operations, one particular concern is ensuring that the crew will have adequate onboard support to perform urgent problem solving when communication with the ground is delayed or intermittent. A key resource that enables the ground team to respond to anomalies quickly and effectively is the extraordinary expertise and experience it possesses. It is comprised of 80+ experts on at any given time, with a combined 600+ years of system-specific experience across 22 unique console disciplines. A small crew will face the unprecedented challenge of independently responding to anomalies that have historically been handled by a team 20 times their size. Another important resource upon which the ground heavily relies to support procedure execution and anomaly response is data. The amount of telemetry data that each flight controller monitors is extensive. In addition, as the ground team works to further assess impacts, trouble shoot, identify workarounds, and oversee procedure execution, it accesses and synthesizes engineering and procedure information, as well as system build, test, and configuration documentation. It is not feasible nor useful to put all these data onboard as crews become more Earth independent. Each member of a small Mars mission small crew will have multiple roles beyond monitoring telemetry and data gathering, and multiple roles within anomaly resolution processes, thereby limiting their capacity for copious amounts of information. Moreover, while access is necessary, it alone is insufficient. Information will need to be compiled, refined, and represented appropriately to support the crew’s reduced attention and expertise. This work seeks to understand the content and representation of information needed to support time-constrained problem solving and decision making by the crew without real-time ground support. To build this understanding, we first surveyed the literature, focusing on how expert problem solvers construct and manipulate their mental models. Next, we interviewed expert problem solvers in spaceflight and analogous domains and surveyed industry solutions for data presentation. Finally, we analyzed current spaceflight operations by investigating flight controller anomaly resolution processes during ISS training simulations and real operational events. These methods led to creating a problem-solving framework that details common themes and features of attending to, assessing, analyzing, and acting on problems in complex, time-constrained domains. Using this framework and the results of our analysis, we identified conceptual data representations needed for crew-led problem-solving. Preliminary onboard user interface concepts to meet identified needs will be presented.

anomaly response↗
DOE OSTI2023

Designing interagency responses to wicked problems: A viable system model board game

Government agencies struggle to address wicked problems because they are open-ended, highly interdependent issues that cross agency, stakeholder, jurisdictional, and geopolitical boundaries. While both quantitative modelling and qualitative problem structuring methodologies have been used to support interagency decision making in the past, co-designing an effective interagency organization to collaboratively tackle wicked problems is more challenging. Few approaches have been developed to enable such efforts. This paper explains how the viable system model (VSM) was implemented through a board game, which was employed to co-design an interagency meta-organization that would be capable of more effectively collaborating to jointly address a wicked problem: international organized drug crime and its interface with local gangs in Chicago, USA. The board game was developed to make the VSM easier for the participants to learn, given that the cybernetic language and engineering-influenced diagrams in the original literature can be off-putting to leaders and managers. The board game was used as the final stage of a multi-method, systemic approach, which involved boundary critique and problem structuring as well as deployment of the VSM. The research findings indicate that the VSM board game, used as part of a larger mixed-methods systemic intervention, contributes to building trust in the value of systems thinking amongst the participants, and sets up a rich context for collaboration on multi-agency co-design. The game therefore offers significant promise as part of the co-design of interagency responses to wicked problems because it creates an embodied process for stakeholders to learn about the VSM. It also reduces the work involved in this learning. Thus, the game enables an effective appropriation of the VSM language and criteria.

Business & Economics↗
DOE OSTI2025

Adaptive Interface-PINNs (AdaI-PINNs) for transient diffusion: Applications to forward and inverse problems in heterogeneous media

We model transient diffusion in heterogeneous materials using a novel physics-informed neural networks framework (PINNs) termed Adaptive interface physics-informed neural networks or AdaI-PINNs (Roy et al. arXiv preprint arXiv:2406.04626, 2024). AdaI-PINNs utilize different activation functions with trainable slopes tailored to each material region within the computational domain, allowing for a fully automated and adaptive PINNs approach to model interface problems with strongly and weakly discontinuous solutions. To enhance its performance in highly heterogeneous transient diffusion systems, we prescribe a suite of robust practices, including appropriate non-dimensionalization of equations, a biased sampling method, Glorot initialization, and the hard enforcement of boundary and initial conditions. Here we evaluate the efficacy of the proposed method on several benchmark forward and inverse problems. Comparative studies on one-dimensional and two-dimensional benchmark problems reveal that the modified AdaI-PINNs outperform its unmodified counterpart, achieving root-mean-square errors that are at least two orders of magnitude better in forward problems. For inverse problems, the maximum errors in the approximated diffusion coefficients by modified AdaI-PINNs are four orders of magnitude better than those of the unmodified version. Additionally, modified AdaI-PINNs demonstrate improved stability in problems with large material mismatches.

42 ENGINEERING↗
DOE OSTI2020

Space–time reduced order model for large-scale linear dynamical systems with application to Boltzmann transport problems

A classical reduced order model for dynamical problems involves spatial reduction of the problem size. However, temporal reduction accompanied by the spatial reduction can further reduce the problem size without losing much accuracy, which results in a considerably more speed-up than the spatial reduction only. Recently, a novel space–time reduced order model for dynamical problems has been developed [17], where the space–time reduced order model shows an order of a hundred speed-up with a relative error of 10 –4 for small academic problems. However, in order for the method to be applicable to a large-scale problem, an efficient space–time reduced basis construction algorithm needs to be developed. Here we present the incremental space–time reduced basis construction algorithm. The incremental algorithm is fully parallel and scalable. Additionally, the block structure in the space–time reduced basis is exploited, which enables the avoidance of constructing the reduced space–time basis. These novel techniques are applied to a large-scale particle transport simulation with million and billion degrees of freedom. The numerical example shows that the algorithm is scalable and practical. Also, it achieves a tremendous speed-up, maintaining a good accuracy. Finally, error bounds for space-only and space–time reduced order models are derived.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Multi-variance replica exchange SGMCMC for inverse and forward problems via Bayesian PINN

Physics-informed neural network (PINN) has been successfully applied in solving a variety of nonlinear non-convex forward and inverse problems. However, the training is challenging because of the non-convex loss functions and the multiple optima in the Bayesian inverse problem. In this work, we propose a multi-variance replica exchange stochastic gradient Langevin dynamics method to tackle the challenge of the multiple local optima in the optimization and the challenge of the multiple modal posterior distribution in the inverse problem. Replica exchange methods are capable of escaping from the local traps and accelerating the convergence; two chains with different temperatures are designed where the low temperature chain aims for the local convergence, and the target of the high temperature chain is to travel globally and explore the whole loss function entropy landscape. However, it may not be efficient to solve mathematical inversion problems by using the vanilla replica method directly since the method doubles the computational cost in evaluating the forward solvers (likelihood functions) in the two chains. To address this issue, we propose to make different assumptions on the energy function estimation and this facilities one to use solvers of different fidelities in the likelihood function evaluation. More precisely, one can use a solver with low fidelity in the high temperature chain while using a solver with high fidelity in the low temperature chain. Our proposed method significantly lowers the computational cost in the high temperature chain, meanwhile preserving the accuracy and converging very fast. Here we give an unbiased estimate of the swapping rate and give an estimation of the discretization error of the scheme. To verify our idea, we design and solve four inverse problems which have multiple modes. The proposed method is also employed to train the Bayesian PINN to solve the forward and inverse problems; faster and more accurate convergence has been observed when compared to the stochastic gradient Langevin dynamics (SGLD) method and vanilla replica exchange methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Taylor approximation variance reduction for approximation errors in PDE-constrained Bayesian inverse problems

In numerous applications, surrogate models are used as a replacement for accurate parameter-to-observable mappings when solving large-scale inverse problems governed by partial differential equations (PDEs). The surrogate model may be a computationally cheaper alternative to the accurate parameter-to-observable mappings and/or may ignore additional unknowns or sources of uncertainty. The Bayesian approximation error (BAE) approach provides a means to account for the induced uncertainties and approximation errors, i.e. the errors between the accurate parameter-to-observable mapping and the surrogate. The statistics of these errors are, however, in general unknown a priori, and are thus calculated using Monte Carlo sampling. Although the sampling is typically carried out offline, i.e. before considering the data, the process can still represent a computational bottleneck. In this work, we develop a scalable computational approach for reducing the costs associated with the sampling stage of the BAE approach. Specifically, we consider the Taylor expansion of the accurate and surrogate forward models with respect to the uncertain parameter fields either as a control variate for variance reduction or as a means to directly and efficiently approximate the mean and covariance of the approximation errors. We propose efficient methods for evaluating the expressions for the mean and covariance of the Taylor approximations based on linear(-ized) PDE solves. Furthermore, the proposed approach is independent of the dimension of the uncertain parameter, depending instead on the intrinsic dimension of the data, ensuring scalability to high-dimensional problems. The potential benefits of the proposed approach are demonstrated for two high-dimensional inverse problems governed by PDE examples, namely for the estimation of a distributed Robin boundary coefficient in a linear diffusion problem, and for a coefficient estimation problem governed by a nonlinear diffusion problem.

Bayesian approximation error↗
DOE OSTI2023

Enabling Hyper-Differential Sensitivity Analysis for Ill-Posed Inverse Problems

Inverse problems constrained by partial differential equations (PDEs) play a critical role in model development and calibration. In many applications, there are multiple uncertain parameters in a model that must be estimated. However, high dimensionality of the parameters and computational complexity of the PDE solves make such problems challenging. A common approach is to reduce the dimension by fixing some parameters (which we will call auxiliary parameters) to a best estimate and use techniques from PDE-constrained optimization to estimate the other parameters. In this article, hyper-differential sensitivity analysis (HDSA) is used to assess the sensitivity of the solution of the PDE-constrained optimization problem to changes in the auxiliary parameters. Foundational assumptions for HDSA require satisfaction of the optimality conditions which are not always practically feasible as a result of ill-posedness in the inverse problem. Here we introduce novel theoretical and computational approaches to justify and enable HDSA for ill-posed inverse problems by projecting the sensitivities on likelihood informed subspaces and defining a posteriori updates. Our proposed framework is demonstrated on a nonlinear multiphysics inverse problem motivated by estimation of spatially heterogeneous material properties in the presence of spatially distributed parametric modeling uncertainties.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Fast and Scalable FFT-Based GPU-Accelerated Algorithms for Block-Triangular Toeplitz Matrices with Application to Linear Inverse Problems Governed by Autonomous Dynamical Systems

In this work, we present an efficient and scalable algorithm for performing matrix-vector multiplications (matvecs) for block Toeplitz matrices. Such matrices, which are shift-invariant with respect to their blocks, arise in the context of solving inverse problems governed by autonomous systems, and time-invariant systems in particular. In this article, we consider inverse problems that infer unknown parameters from observational data of a linear time-invariant dynamical system given in the form of partial differential equations (PDEs). Matrix-free Newton-conjugate-gradient methods are often the gold standard for solving these inverse problems, but they require numerous actions of the Hessian on a vector. Matrix-free adjoint-based Hessian matvecs require solution of a pair of linearized forward/adjoint PDE solves per Hessian action, which may be prohibitive for large-scale inverse problems. Time invariance of the forward PDE problem leads to a block Toeplitz structure of the discretized parameter-to-observable (p2o) map defining the mapping from inputs (parameters) to outputs (observables) of the PDEs. This block Toeplitz structure enables us to exploit two key properties: (1) compact storage of the p2o map and its adjoint, and (2) efficient fast Fourier transform–based Hessian matvecs. The proposed algorithm is mapped onto large multi-GPU clusters and achieves more than 80% of peak bandwidth on NVIDIA A100 GPUs. Excellent weak scaling is shown for up to 48 A100 GPUs. For the targeted problems, the implementation executes Hessian matvecs within fractions of a second, which is orders of magnitude faster than can be achieved by conventional matrix-free Hessian matvecs via forward/adjoint PDE solves.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A Quantum-Inspired Tensor Network Algorithm for Constrained Combinatorial Optimization Problems

Combinatorial optimization is of general interest for both theoretical study and real-world applications. Fast-developing quantum algorithms provide a different perspective on solving combinatorial optimization problems. In this paper, we propose a quantum-inspired tensor-network-based algorithm for general locally constrained combinatorial optimization problems. Our algorithm constructs a Hamiltonian for the problem of interest, effectively mapping it to a quantum problem, then encodes the constraints directly into a tensor network state and solves the optimal solution by evolving the system to the ground state of the Hamiltonian. We demonstrate our algorithm with the open-pit mining problem, which results in a quadratic asymptotic time complexity. Our numerical results show the effectiveness of this construction and potential applications in further studies for general combinatorial optimization problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2016

Use of the NLP10x10 Sequential Quadratic Programming Algorithm To Solve Rotorcraft Hub Loads Minimisation Problems

Previous research and experimentation on the use of a non-linear programming constrained optimisation technique to define an optimal control vector for rotorcraft applications indicated that use of this methodology was feasible and desirable in many cases. In particular, use of non-linear programming methods that solve a sequence of related quadratic-programming sub-problems were used successfully to solve these problems. Accordingly, a licence for one of the latest versions of Professor Klaus Schittkowskis very successful Sequential Quadratic Programming NLPQLP software was obtained and used to experiment with and analyse typical optimisation problems of the type encountered in various rotorcraft wind tunnel and flight tests. This research resulted in the development of the general NLPQLP Computation System that could be used to solve problems of the type encountered in various rotorcraft applications where there is a linear dependence of the measurement vector on the control vector, and where equality andor inequality constraints might be imposed. This development was accomplished on a mainframe computer not part of actual wind tunnel andor flight-test experiment, but in a format which was transferable to wind tunnel lap-top computers. Emphasis was directed toward obtaining efficiency, robustness and speed in computation.The System was developed in support of the five-bladed SMART Rotor Active Flap Rotor Hub Loads analytical minimisation research. The design and development of the Computation System was tailored to address the particular requirements of the problem to minimise a performance metric function of measured hub load harmonic angular couple components by optimising the control vector harmonic flap angular couple components subject to constraints on the amplitudes of these control vector harmonic flap angular couple components. In addition, to facilitate real time wind tunnel experimentation, the ability to rapidly selectchange the particular hub load harmonic angular couple components andor the particular control vector harmonic angular couple components to be considered in the optimisation procedure was provided in the System. This capability allows the singling out of particular hub load frequencies andor particular flap angle frequencies to be analysed during testing operations. The System was used very successfully for the SMART Active Flap Rotor Hub minimisation problems considered in the study, the results of which were presented at the American Helicopter Society Fifth Decennial Aeromechanics Specialist Conference in January 2014. Excellent agreement between cases initiated with best guess starting estimates for the control vector elements and cases initiated with zero control vector starting element estimates resulted, indicating the robustness of the NLP10x10 algorithm.

Rotorcraft Hub Loads↗
NASA NTRSDate not supplied

Spacecraft Observatory Benchmark Problem for Optical Disturbance Rejection

Since mid-1980s NASA has launched several first-generation interplanetary observatory missions. A salient feature of these missions has been the mounting of the optical payload on top of a large flexible space structure. This imposes challenging control-structure interaction problems (CSI) that have been studied over several decades. The Dec. 2021 launch of the James Webb Telescope marks the latest example of such a mission. One way to encourage development of novel control methods is to provide a benchmark problem for researchers. By the mid-2000s, there were a few well-known benchmark problems developed by the control community with a focus on CSI applications. However, in the past 15 years, the control challenges in optical observation missions have shifted from CSI to line-of-sight (LOS) precision pointing. This is because popular designs of the second-generation (Gen II) space earth missions have eliminated the large structure interface by mounting the optical payload directly on top of a rigid bus platform. The focus now is to achieve accurate pointing with maximum rejection of the surrounding disturbances. The NASA Safety and Engineering Center (NESC) has tasked T he Aerospace Corporation to develop a Benchmark Problem to study the challenging control issues that Gen II observatory missions encounter. This software tool is to be released as a public domain platform aimed at government, academic, and industry researchers. The focus of this benchmark problem is for researchers to design a set of innovative payload control laws with the maximum Optical Disturbance Rejection (ODR) capability to meet a set of pre-defined μrad-level of LOS jitter requirements. This paper describes the development of the benchmark problem. Aerospace/NASA will provide an integrated LOS plant model and disturbance/command profiles for users to run their design and simulation with as well as a user’s guide describing the required interfaces. The Aerospace Corp is also working to develop a hardware fast steering mirror testbed for users to demonstrate their innovative design in real hardware, if so desired.

Spacecraft Observatory Benchmark Problem↗
DOE OSTI2020

Convex Programs for Minimal-Area Problems

The minimal-area problem that defines string diagrams in closed string field theory asks for the metric of least area on a Riemann surface with the condition that all non-contractible closed curves have length at least 2π. This is an extremal length problem in conformal geometry as well as a problem in systolic geometry. Here, we consider the analogous minimal-area problem for homology classes of curves and, with the aid of calibrations and the max flow-min cut theorem, formulate it as a local convex program. We derive an equivalent dual program involving maximization of a concave functional. These two programs give new insights into the form of the minimal-area metric and are amenable to numerical solution. We explain how the homology problem can be modified to provide the solution to the original homotopy problem.

97 MATHEMATICS AND COMPUTING↗