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QuantifyML: How good is my machine learning model?

This paper presents an approach, QuantifyML, which employs model counting to assess the learnability and robustness of machine learning models. Typically the efficacy of machine learning models is determined by computing their accuracy statistically on test data sets. However, this may be misleading, if the test data is not representative of the problem that is being studied. Further, two different models may have the same accuracy on a given data set, measured statistically, but may be very different in their behavior on unseen data. Also, models with high accuracy could have poor adversarial robustness. In QuantifyML, our goal is to precisely quantify the extent to which machine learning models have learned and generalized from the given data. In QuantifyML, a trained model is translated into a C program, which is fed to the CBMC model checking tool to produce a formula in Conjunctive Normal Form (CNF), which in turn is analyzed with state-of-the-art model counters to efficiently obtain precise counts w.r.t different outputs. QuantifyML enables i) evaluating the learnability of models by comparing the counts for the outputs to ground truth, expressed as logical predicates (if available), ii) comparing the performance of different models that may be built with different machine learning algorithms (e.g., decision-trees vs. neural networks), and iii) quantifying the robustness of trained models around given inputs. Our evaluation demonstrates these applications of QuantifyML on decision trees and neural networks trained to learn relational properties of graphs, for which we know the ground truth, and to perform image classification, for which we do not have the ground truth, but we can quantify local robustness.

Deep Neural Networks↗

Improved thermodynamic modeling of the no-vent fill process and correlation with experimental data

The United States' plans to establish a permanent manned presence in space and to explore the Solar System created the need to efficiently handle large quantities of subcritical cryogenic fluids, particularly propellants such as liquid hydrogen and liquid oxygen, in low- to zero-gravity environments. One of the key technologies to be developed for fluid handling is the ability to transfer the cryogens between storage and spacecraft tanks. The no-vent fill method was identified as one way to perform this transfer. In order to understand how to apply this method, a model of the no-vent fill process is being developed and correlated with experimental data. The verified models then can be used to design and analyze configurations for tankage and subcritical fluid depots. The development of an improved macroscopic thermodynamic model is discussed of the no-vent fill process and the analytical results from the computer program implementation of the model are correlated with experimental results for two different test tanks.

Taylor, William J.↗

Exact and Approximate Probabilistic Symbolic Execution

Probabilistic software analysis seeks to quantify the likelihood of reaching a target event under uncertain environments. Recent approaches compute probabilities of execution paths using symbolic execution, but do not support nondeterminism. Nondeterminism arises naturally when no suitable probabilistic model can capture a program behavior, e.g., for multithreading or distributed systems. In this work, we propose a technique, based on symbolic execution, to synthesize schedulers that resolve nondeterminism to maximize the probability of reaching a target event. To scale to large systems, we also introduce approximate algorithms to search for good schedulers, speeding up established random sampling and reinforcement learning results through the quantification of path probabilities based on symbolic execution. We implemented the techniques in Symbolic PathFinder and evaluated them on nondeterministic Java programs. We show that our algorithms significantly improve upon a state-of- the-art statistical model checking algorithm, originally developed for Markov Decision Processes.

Symbolic Execution↗

A Case for High-Fidelity Material Response Modeling

Material response modeling of heatshields for planetary entry vehicles has remained largely unchanged since Aerotherm Corp. introduced the CMA program in 1967. Modern models, like FIAT, have tread the same path, introducing efficiencies and better material property data along the way, but otherwise following the same underlying model paradigm. The CMA approach has worked well for heatshield design up to this point. However, there are three motivations for the material response community to pursue higher fidelity beyond simplified, CMA-derived models. The first motivation is that missions are becoming increasingly demanding and complex and, as they do, confidence in simplified models naturally decreases. Second, reliability of materials is now as much or more of a driving concern for mission designers than thermal response. Third, NASA and other agencies are increasingly interested in flight instrumentation for engineering science. This latter motivation places far stricter requirements on model accuracy in order to meet requirements for flight environment reconstruction.

Barnhardt, Michael D.↗

Comparing Theoretically Scaled Biomechanical Models

BACKGROUND An investigation into incorporating space suit aspects required a 50th-percentile male model which was not part of the existing dataset of models. Previously, theoretical models for 5th-percentile female and 95th-percentile male were created utilizing a scaled test subject as close as possible to the target height and weight. Scaling factors were created by taking the height ratio and applying it uniformly to the model body segments, then fine tuning to ensure the theoretical model’s height is as expected. This study was initiated to examine the existing method of isometrically scaling in OpenSim [1,2] and to create alternative methods which do not rely on an existing subject being close in height and weight to the theoretical model of interest. Generating a theoretical biomechanical model provides additional abilities without the reliance on available OpenSim models or real subjects. Gained abilities include creating different percentile models and attaining representative anthropometry for any target height/weight, such as targeting specific crew populations or gaps within the current dataset. METHODS AND RESULTS This study includes 3 methods for generating the theoretical model; utilizing the modified unscaled OpenSim Full Body Rajagopal Model (FBRM) [3,4], a dataset of scaled OpenSim models, and existing scaling factors from Dumas et al. [5]. All methods use the Anthropometric Survey of US Army Personnel (ANSUR II) [6] as an input of necessary anthropometric measurements. The following measurements are retrieved from the ANSUR II collection: mass, stature, cervicale height, acromial height, axilla height, waist height, trochanterion height, lateral femoral epicondyle height, lateral malleolus height, acromion-radiale length, radiale-stylion length, palm length, ball of foot length, bicristal breadth, bimalleolar breadth. Some of the measurements are direct segment lengths and others are utilized to derive segment lengths. Height, weight, and age ranges are the required inputs to parse the collection for a mean value of the measurements. A simple iterative process may be necessary for the output of mean mass and stature consistent with the theoretical model of interest. In some cases, one may specify exact values instead of a range but that is dependent upon whether those exact values pertain to a single subject from the ANSUR II collection. Equations from Dumas et al. were used to calculate scaling factors for the two methods that utilize OpenSim scaled and unscaled models. In the third method, Dumas’ scaling factors were used directly instead of generating our own. After scaling factors are achieved, they are applied along with the mass and segment lengths retrieved from ANSUR II in order to calculate the segment mass, Center of Mass (CoM), mass Moment of Inertia (MoI), and the joint location in the parent frame. The theoretical models from the different methods were compared to the previous existing method of isometrically scaling in OpenSim, as well as the standards found in NASA STD-3000 [7] and the NASA Human Integration Design Handbook [8]. The whole-body center of mass is the main comparison performed between the models and the standards. The body segment mass properties were also compared when possible. In some cases, the standards do not provide complete data, or the center of mass location is not provided with respect to the appropriate joint coordinate system. For a 50th-percentile male subject, results from isometric scaling in OpenSim and the method utilizing the unscaled FBRM were compared to the standards in NASA STD-3000. According to the standard, the whole-body vertical CoM location was taken from the head vertex to the CoM. The standards provide 80.2 cm for the CoM vertical component whereas isometric scaling in OpenSim and utilizing the unscaled FBRM provide 82.2 and 82.3 cm, respectively. Through definition, the whole-body CoM in the medial/lateral direction agreed across the models. Investigation is on-going to clearly identify the reference point pertaining to dorsal/ventral whole-body CoM position in standards and relate that to the theoretical models. REFERENCES [1] Delp, S.L., et al., “OpenSim: Open-source Software to Create and Analyze Dynamic Simulations of Movement”, IEEE Transactions on Biomedical Engineering, (2007). [2] Seth, A., Hicks J.L., Uchida, T.K., Habib, A., Dembia, C.L., Dunne, J.J., Ong, C.F., DeMers, M.S., Rajagopal, A., Millard, M., Hamner, S.R., Arnold, E.M., Yong, J.R., Lakshmikanth, S.K., Sherman,n M.A., Delp, S.L. OpenSim: Simulating musculoskeletal dynamics and neuromuscular control to study human and animal movement. Plos Computational Biology, 14(7). (2018) [3] R. K. Huffman, W. K. Thompson, C. A. Gallo, L. J. Quiocho, “Improvement of Scaling and Inverse Kinematic Results with Additional Upper Body Joints Added to Opensim Rajagopal Model”, NASA Human Research Program Investigator’s Workshop, (2019). [4] Huffman R.K., Thompson W., Gallo C., “Modified OpenSim Rajagopal Full Body Model”, New Technology Report, MSC-26872-1. (August 2020). [5] Dumas R., Cheze L. and Verriest J., 2007. “Adjustments to McConville et al. and Young et al. body segment inertial parameters”. Journal of Biomechanics 40, pp. 543-553 [6] Gordon C.C., 2012 “Anthropometric Survey of U.S. Army Personnel: Methods and Summary Statistics”, US Army Natick Soldier RD&E Center. [7] NASA STD-3000/REV-B, 1995. “The Man-System Integration Standards” [8] NASA/SP-2010-3407/REV-1, 2014. “The Human Integration Design Handbook (HIDH)”

F N Matari↗

Overview on Basis and Use of Performance Prediction Methods

The lecture outlines the basic methods of component matching which are central to the prediction of gas turbine performance. Steady state prediction of off-design performance must be done at the beginning of an engine development program, to ensure that the engine can satisfy all the mission requirements. The matching techniques can be extended to predict transient performance, which is essential for controls development and to ensure good engine handling. The large amount of computation required demands the use of computer modelling and the role of modelling in the development program and the basic requirements for performance modelling are described.

H I H Saravanamuttoo↗

Software Tools for Analysis of Bonded Joints

Linear and nonlinear springs have been used to model adhesives in bonded joints. This presentation describes two programs which obtain stresses and strains in bonded joints. For a given bonded joint model, these programs read the corresponding NASTRAN input and output files, use the spring forces or deformations to obtain the adhesive stresses or strain fields, sort the stresses and strains in descending order, and generate Mathematica plot files for three dimensional visualization of the stress and strain fields.

Tahmasebi, Farhad↗

Probabilistic/Fracture-Mechanics Model For Service Life

Computer program makes probabilistic estimates of lifetime of engine and components thereof. Developed to fill need for more accurate life-assessment technique that avoids errors in estimated lives and provides for statistical assessment of levels of risk created by engineering decisions in designing system. Implements mathematical model combining techniques of statistics, fatigue, fracture mechanics, nondestructive analysis, life-cycle cost analysis, and management of engine parts. Used to investigate effects of such engine-component life-controlling parameters as return-to-service intervals, stresses, capabilities for nondestructive evaluation, and qualities of materials.

Watkins, T., Jr.↗

Grid2: A Program for Rapid Estimation of the Jovian Radiation Environment: A Numeric Implementation of the GIRE2 Jovian Radiation Model for Estimating Trapped Radiation for Mission Concept Studies

Grid2 is a program that utilizes the Galileo Interim Radiation Electron model 2 (GIRE2) Jovian radiation model to compute fluences and doses for Jupiter missions. (Note: The iterations of these two softwares have been GIRE and GIRE2; likewise Grid and Grid2.) While GIRE2 is an important improvement over the original GIRE radiation model, the GIRE2 model can take as long as a day or more to compute these quantities for a complete mission. Grid2 fits the results of the detailed GIRE2 code with a set of grids in local time and position thereby greatly speeding up the execution of the model--minutes as opposed to days. The Grid2 model covers the time period from 1971 to 2050and distances of 1.03 to 30 Jovian diameters (Rj). It is available as a direct-access database through a FORTRAN interface program. The new database is only slightly larger than the original grid version: 1.5 gigabytes (GB) versus 1.2 GB.

Europa↗

The 60 GHz radiometric local vertical sensor experiment

The experiment concept involves the use of millimeter wave radiation the atmospheric oxygen to provide vertical sensing information to a satellite-borne radiometer. The radiance profile studies require the calculation of ray brightness temperature as a function of tangential altitude and atmosphere model, and the computer program developed for this purpose is discussed. Detailed calculations have been made for a total of 12 atmosphere models, including some showing severe warning conditions. The experiment system analysis investigates the effect of various design choices on system behavior. Calculated temperature profiles are presented for a wide variety of frequencies, bandwidths, and atmosphere models. System performance is determined by the convolution of the brightness temperature and an assumed antenna pattern. A compensation scheme to account for different plateau temperatures is developed and demonstrated. The millimeter wave components developed for the local vertical sensor are discussed, with emphasis on the antenna, low noise mixer, and solid state local oscillator. It was concluded that a viable sensing technique exists, useful over a wide range of altitude with an accuracy generally on the order of 0.01 degree or better.

Grauling, C. H., Jr.↗

Analysis of rocket engine injection combustion processes

Mixing methodology improvement for the JANNAF DER and CICM injection/combustion analysis computer programs was accomplished. ZOM plane prediction model development was improved for installation into the new standardized DER computer program. An intra-element mixing model developing approach was recommended for gas/liquid coaxial injection elements for possible future incorporation into the CICM computer program.

Salmon, J. W.↗

Deep anistropic shell program for tire analysis

A finite element program was constructed to model the mechanical response of a tire, treated as a deep anisotropic shell, to specified static loads. The program is based on a Sanders Budiansky type shell theory with the effects of transverse shear deformation and bending-extensional coupling included. A displacement formulation is used together with a total Lagrangian description of the deformation. Sixteen-node quadrilateral elements with bicubic shape functions are employed. The Noor basis reduction technique and various type of symmetry considerations serve to improve the computational efficiency.

Andersen, C. M.↗

Advances in Entry Systems Modeling: Modeling Summer Visit 2025 Technical Reports

This NASA Technical Memorandum presents the collective work carried out during the Modeling Summer Visit (MSV) 2025, a collaborative research program between NASA Ames Research Center and three leading European research institutions: the University of Bordeaux, the von Karman Institute (VKI), and Ecole Polytechnique. Held from July 7th to August 1st, 2025, the NASA ARC MSV program brought together 42 researchers from Europe to work alongside NASA staff on 22 projects in entry systems modeling. The program was organized by Bruno Dias, Sergio Fraile-Izquierdo, and Jeremie Meurisse from Analytical Mechanics Associates, Inc., in collaboration with Marc Massot (Ecole Polytechnique), Jean Lachaud (University of Bordeaux), and Thierry Magin (VKI). The MSV program traces its origins to an initiative started by Nagi N. Mansour in 2018, with this 2025 edition representing a consolidation and expansion of that original vision. The projects were organized into six thematic groups: Porous Media, Numerical Methods, Plasma/Rarefied Methods, Experimental Reconstruction, Flow and Material Coupling Methods, and Transition and High-Speed Flows. Throughout the four-week program, participants presented their work in three public presentations (July 7th, July 21st, and August 1st), allowing for continuous feedback and discussion of their evolving research.

Plasmas↗

A mathematical model of a tilt-wing aircraft for piloted simulation

A mathematical model of a tilt-wing aircraft that was used in a piloted, six-degree-of-freedom flight simulation application is described. Two types of control systems developed for the math model are discussed: a conventional, programmed-flap wing-tilt control system and a geared-flap wing-tilt control system. The primary objective was to develop the capability to study tilt-wing aircraft. Experienced Tilt-wing pilots subjectively evaluated the model using programmed-flap control to assess the quality of the simulation. The math model was then applied to study geared-flap control to investigate the possibility of eliminating the need for auxilary pitch-control devices (such as the horizontal tail rotor or tail jet used in earlier tilt-wing designs). This investigation was performed in the moving-base simulation environment, and the vehicle responses with programmed-flap and geared-flap control were compared. The results of the evaluation of the math model are discussed.

Totah, Joseph J.↗

The New NASA Orbital Debris Engineering Model ORDEM 3.0

The NASA Orbital Debris Program Office (ODPO) has released its latest Orbital Debris Engineering Model, ORDEM 3.0. It supersedes ORDEM 2.0. This newer model encompasses the Earth satellite and debris flux environment from altitudes of low Earth orbit (LEO) through geosynchronous orbit (GEO). Debris sizes of 10 microns through 1 m in non-GEO and 10 cm through 1 m in GEO are modeled. The inclusive years are 2010 through 2035. The ORDEM model series has always been data driven. ORDEM 3.0 has the benefit of many more hours from existing data sources and from new sources that weren't available to past versions. Returned surfaces, ground tests, and remote sensors all contribute data. The returned surface and ground test data reveal material characteristics of small particles. Densities of fragmentation debris particles smaller than 10 cm are grouped in ORDEM 3.0 in terms of high-, medium-, and lowdensities, along with RORSAT sodium-potassium droplets. Supporting models have advanced significantly. The LEO-to-GEO ENvironment Debris model (LEGEND) includes an historical and a future projection component with yearly populations that include launched and maneuvered intacts, mission related debris (MRD), and explosion and collision fragments. LEGEND propagates objects with ephemerides and physical characteristics down to 1 mm in size. The full LEGEND yearly population acts as an a priori condition for a Bayesian statistical model. Specific, well defined populations are added like the Radar Ocean Reconnaissance Satellite (RORSAT) sodium-potassium (NaK) droplets, recent major accidental and deliberate collision fragments, and known anomalous debris event fragments. For microdebris of sizes 10 microns to 1 mm the ODPO uses an in-house Degradation/Ejecta model in which a MLE technique is used with returned surface data to estimate populations. This paper elaborates on the upgrades of this model over previous versions highlighting the material density splits and consequences of that to the penetration risk to spacecraft.

Krisko, P. H.↗

The New NASA Orbital Debris Engineering Model ORDEM 3.0

The NASA Orbital Debris Program Office (ODPO) has released its latest Orbital Debris Engineering Model, ORDEM 3.0. It supersedes ORDEM 2000, now referred to as ORDEM 2.0. This newer model encompasses the Earth satellite and debris flux environment from altitudes of low Earth orbit (LEO) through geosynchronous orbit (GEO). Debris sizes of 10 micron through larger than 1 m in non-GEO and 10 cm through larger than 1 m in GEO are available. The inclusive years are 2010 through 2035. The ORDEM model series has always been data driven. ORDEM 3.0 has the benefit of many more hours of data from existing sources and from new sources than past ORDEM versions. The object data range in size from 10 μm to larger than 1 m, and include in situ and remote measurements. The in situ data reveals material characteristics of small particles. Mass densities are grouped in ORDEM 3.0 in terms of 'high-density', represented by 7.9 g/cc, 'medium-density' represented by 2.8 g/cc and 'low-density' represented by 1.4 g/cc. Supporting models have also advanced significantly. The LEO-to-GEO ENvironment Debris model (LEGEND) includes an historical and a future projection component with yearly populations that include launched and maneuvered intact spacecraft and rocket bodies, mission related debris, and explosion and collision event fragments. LEGEND propagates objects with ephemerides and physical characteristics down to 1 mm in size. The full LEGEND yearly population acts as an a priori condition for a Bayesian statistical model. Specific populations are added from sodium potassium droplet releases, recent major accidental and deliberate collisions, and known anomalous debris events. This paper elaborates on the upgrades of this model over previous versions. Sample validation results with remote and in situ measurements are shown, and the consequences of including material density are discussed as it relates to heightened risks to crewed and robotic spacecraft

Krisko, P. H.↗

Constitutive modeling for isotropic materials

The objective of the program is to evaluate and develop existing constitutive models for use in finite-element structural analysis of turbine engine hot section components. The class of constitutive equation studied is considered unified in that all inelastic deformation including plasticity, creep, and stress relaxation are treated in a single term rather than a classical separation of plasticity (time independent) and creep (time dependent) behavior. The unified theories employed also do not utilize the classical yield surface or plastic potential concept. The models are constructed from an appropriate flow law, a scalar kinetic relation between strain rate, temperature and stress, and evolutionary equations for internal variables describing strain or work hardening, both isotropic and directional (kinematic). This and other studies have shown that the unified approach is particularly suited for determining the cyclic behavior of superalloy type blade and vane materials and is entirely compatible with three-dimensional inelastic finite-element formulations. The behavior was examined of a second nickel-base alloy, MAR-M247, and compared it with the Bodner-Partom model, further examined procedures for determining the material-specific constants in the models, and exercised the MARC code for a turbine blade under simulated flight spectrum loading. Results are summarized.

Lindholm, Ulric S.↗

Component-specific modeling

Accomplishments are described for a 3 year program to develop methodology for component-specific modeling of aircraft hot section components (turbine blades, turbine vanes, and burner liners). These accomplishments include: (1) engine thermodynamic and mission models, (2) geometry model generators, (3) remeshing, (4) specialty three-dimensional inelastic structural analysis, (5) computationally efficient solvers, (6) adaptive solution strategies, (7) engine performance parameters/component response variables decomposition and synthesis, (8) integrated software architecture and development, and (9) validation cases for software developed.

Mcknight, R. L.↗