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All sources NASA NTRS DOE OSTI

DOE OSTI2024

The Average Spectrum Norm and Near-Optimal Tensor Completion

We propose the average spectrum norm to study the minimum number of measurements required to approximate a multidimensional array (i.e., sample complexity) via low-rank tensor recovery. Our focus is on the tensor completion problem, where the aim is to estimate a multiway array using a subset of tensor entries corrupted by noise. Our average spectrum norm-based analysis provides near-optimal sample complexities, exhibiting dependence on the ambient dimensions and rank that do not suffer from exponential scaling as the order increases.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1985

Minimal norm constrained interpolation

In computational fluid dynamics and in CAD/CAM, a physical boundary is usually known only discreetly and most often must be approximated. An acceptable approximation preserves the salient features of the data such as convexity and concavity. In this dissertation, a smooth interpolant which is locally concave where the data are concave and is locally convex where the data are convex is described. The interpolant is found by posing and solving a minimization problem whose solution is a piecewise cubic polynomial. The problem is solved indirectly by using the Peano Kernal theorem to recast it into an equivalent minimization problem having the second derivative of the interpolant as the solution. This approach leads to the solution of a nonlinear system of equations. It is shown that Newton's method is an exceptionally attractive and efficient method for solving the nonlinear system of equations. Examples of shape-preserving interpolants, as well as convergence results obtained by using Newton's method are also shown. A FORTRAN program to compute these interpolants is listed. The problem of computing the interpolant of minimal norm from a convex cone in a normal dual space is also discussed. An extension of de Boor's work on minimal norm unconstrained interpolation is presented.

Irvine, L. D.↗

NASA NTRS1988

Numerical results on the transcendence of constants involving pi, e, and Euler's constant

The existence of simple polynomial equations (integer relations) for the constants e/pi, e + pi, log pi, gamma (Euler's constant), e exp gamma, gamma/e, gamma/pi, and log gamma is investigated by means of numerical computations. The recursive form of the Ferguson-Fourcade algorithm (Ferguson and Fourcade, 1979; Ferguson, 1986 and 1987) is implemented on the Cray-2 supercomputer at NASA Ames, applying multiprecision techniques similar to those described by Bailey (1988) except that FFTs are used instead of dual-prime-modulus transforms for multiplication. It is shown that none of the constants has an integer relation of degree eight or less with coefficients of Euclidean norm 10 to the 9th or less.

Bailey, David H.↗

NASA NTRS1990

Intelligent control and adaptive systems; Proceedings of the Meeting, Philadelphia, PA, Nov. 7, 8, 1989

Various papers on intelligent control and adaptive systems are presented. Individual topics addressed include: control architecture for a Mars walking vehicle, representation for error detection and recovery in robot task plans, real-time operating system for robots, execution monitoring of a mobile robot system, statistical mechanics models for motion and force planning, global kinematics for manipulator planning and control, exploration of unknown mechanical assemblies through manipulation, low-level representations for robot vision, harmonic functions for robot path construction, simulation of dual behavior of an autonomous system. Also discussed are: control framework for hand-arm coordination, neural network approach to multivehicle navigation, electronic neural networks for global optimization, neural network for L1 norm linear regression, planning for assembly with robot hands, neural networks in dynamical systems, control design with iterative learning, improved fuzzy process control of spacecraft autonomous rendezvous using a genetic algorithm.

Rodriguez, Guillermo↗

DOE OSTI2026

Dual Representations and H ∞ -Optimal Control of Partial Differential Equations

We consider H ∞ -optimal state-feedback control of the class of linear Partial Differential Equations (PDEs) which admit a Partial Integral Equation (PIE) representation. While linear matrix inequalities are commonly used for optimal control of Ordinary Differential Equations (ODEs), the absence of a universal state-space representation and suitable dual form prevents such methods from being applied to optimal control of PDEs. Specifically, for ODEs, the controller synthesis problem is defined in state-space, and duality is used to resolve the bilinearity of that synthesis problem. Recently, the PIE representation was proposed as a universal state-space representation for linear PDE systems. In this paper, we show that any PDE system represented by a PIE admits a dual PIE with identical stability and I/O properties. This result allows us to reformulate the stabilizing and optimal state-feedback control problems as convex optimization over the cone of positive Partial Integral (PI) operators. Operator inversion formulae then allow us to construct feedback gains for the original PDE system. The results are verified through application to several canonical problems in optimal control of PDEs and indicate the resulting bounds on H ∞ norm are not conservative.

42 ENGINEERING↗

NASA NTRS2001

RIACS Workshop on the Verification and Validation of Autonomous and Adaptive Systems

The long-term future of space exploration at NASA is dependent on the full exploitation of autonomous and adaptive systems: careful monitoring of missions from earth, as is the norm now, will be infeasible due to the sheer number of proposed missions and the communication lag for deep-space missions. Mission managers are however worried about the reliability of these more intelligent systems. The main focus of the workshop was to address these worries and hence we invited NASA engineers working on autonomous and adaptive systems and researchers interested in the verification and validation (V&V) of software systems. The dual purpose of the meeting was to: (1) make NASA engineers aware of the V&V techniques they could be using; and (2) make the V&V community aware of the complexity of the systems NASA is developing.

Pecheur, Charles↗

DOE OSTI2024

Methods of Securing Chemical and Pharmaceutical Knowledge and Recommendations for International Institutions to Enhance Research Integrity

Here, this paper examines strategies for securing chemical and pharmaceutical expertise in a globalized research environment, focusing on safeguarding intellectual property and preventing the misuse of sensitive and potentially dual-use information. The product of collective efforts between Pacific Northwest National Laboratory, Carol Davila University of Medicine and Pharmacy, and New Bulgarian University, highlights the challenges and opportunities posed by cross-border research collaborations, particularly in the context of differing regulatory frameworks and research cultures. It explores current mechanisms to prevent data loss and unauthorized access to sensitive information while assessing the effectiveness of existing security measures, frameworks, and international export control regimes. The approach examines the differing methodologies for promoting transparency, trust-building, and mutual accountability in joint research projects to cultivate secure data-sharing practices and intellectual property. It provides recommendations for international institutions to implement security guidelines in framing research priorities, encourages continual training and education programs, and the integration of processes for monitoring research compliance. This partnership aims to advance scientific innovation while maintaining global stability, ensuring compliance with international norms, and safeguarding valuable intellectual property as measures in chemical and pharmaceutical research security practices continue to expand due to international collaboration and knowledge exchange.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS2017

Reconciling CloudSat and GPM Estimates of Falling Snow

Satellite-based estimates of falling snow have been provided by CloudSat (launched in 2006) and the Global Precipitation Measurement (GPM) core satellite (launched in 2014). The CloudSat estimates are derived from W-band radar measurements whereas the GPM estimates are derived from its scanning Ku- and Ka-band Dual-Frequency Precipitation Radar (DPR) and 13-channel microwave imager (GMI). Each platform has advantages and disadvantages: CloudSat has higher resolution (approximately 1.5 km) and much better sensitivity (-28 dBZ), but poorer sampling (nadir-only and daytime-only since 2011) and the reflectivity-snowfall (Z-S) relationship is poorly constrained with single-frequency measurements. Meanwhile, DPR suffers from relatively poor resolution (5 km) and sensitivity (approximately 13 dBZ), but has cross-track scanning capability to cover a 245-km swath. Additionally, where Ku and Ka measurements are available, the conversion of reflectivity to snowfall rate is better-constrained than with a single frequency.

S Joseph Munchak↗