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NASA NTRS2017

Decoupled Method for Reconstruction of Surface Conditions From Internal Temperatures On Ablative Materials With Uncertain Recession Model

Obtaining measurements of flight environments on ablative heat shields is both critical for spacecraft development and extremely challenging due to the harsh heating environment and surface recession. Thermocouples installed several millimeters below the surface are commonly used to measure the heat shield temperature response, but an ill-posed inverse heat conduction problem must be solved to reconstruct the surface heating environment from these measurements. Ablation can contribute substantially to the measurement response making solutions to the inverse problem strongly dependent on the recession model, which is often poorly characterized. To enable efficient surface reconstruction for recession model sensitivity analysis, a method for decoupling the surface recession evaluation from the inverse heat conduction problem is presented. The decoupled method is shown to provide reconstructions of equivalent accuracy to the traditional coupled method but with substantially reduced computational effort. These methods are applied to reconstruct the environments on the Mars Science Laboratory heat shield using diffusion limit and kinetically limited recession models.

Oliver, A. Brandon↗

NASA NTRS1987

Recursive inverse kinematics for robot arms via Kalman filtering and Bryson-Frazier smoothing

This paper applies linear filtering and smoothing theory to solve recursively the inverse kinematics problem for serial multilink manipulators. This problem is to find a set of joint angles that achieve a prescribed tip position and/or orientation. A widely applicable numerical search solution is presented. The approach finds the minimum of a generalized distance between the desired and the actual manipulator tip position and/or orientation. Both a first-order steepest-descent gradient search and a second-order Newton-Raphson search are developed. The optimal relaxation factor required for the steepest descent method is computed recursively using an outward/inward procedure similar to those used typically for recursive inverse dynamics calculations. The second-order search requires evaluation of a gradient and an approximate Hessian. A Gauss-Markov approach is used to approximate the Hessian matrix in terms of products of first-order derivatives. This matrix is inverted recursively using a two-stage process of inward Kalman filtering followed by outward smoothing. This two-stage process is analogous to that recently developed by the author to solve by means of spatial filtering and smoothing the forward dynamics problem for serial manipulators.

Rodriguez, G.↗

DOE OSTI2026

Large-momentum effective theory’s asymptotic extrapolation vs the inverse problem

Large-momentum effective theory is a physics-guided systematic expansion to calculate light-cone parton distributions, including collinear (PDFs) and transverse-momentum-dependent ones, at any fixed momentum fraction 𝑥 within a range of [𝑥 min , 𝑥 max ]. It theoretically solves the ill-posed inverse problem that afflicts other theoretical approaches to collinear PDFs, such as short-distance factorizations. Recently, Dutrieux et al. raised practical concerns about whether current or even future lattice data will have sufficient precision in the subasymptotic correlation region to support an error-controlled extrapolation—and if not, whether it becomes an inverse problem where the relevant uncertainties cannot be properly quantified. While we agree that not all current lattice data have the desired precision to qualify for an asymptotic extrapolation, some calculations do, and more are expected in the future. We comment on the analysis and results in Dutrieux et al. and argue that a physics-based systematic extrapolation still provides the most reliable error estimates, even when the data quality is not ideal. In contrast, reframing the long-distance asymptotic extrapolation as a data-driven-only inverse problem with ad hoc mathematical conditioning could lead to unnecessarily conservative errors.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

ML-based Dimension Reduction Strategies

Deep learning (DL)--based surrogate models have achieved success in various applications in carbon capture and storage (CCS). However, the model training on high-dimensional spaces is computationally expensive and impractical for large-scale and complex geological models, because the models usually contain hundreds of thousands to millions of grid cells, each with a set of parameters. Furthermore, the high cost of generating training data with sufficient variation is another limitation of model training on high-dimensional spaces, which may result in overfitting and reduce the model efficiency and prediction performance. We proposed the workflow incorporating dimension reduction methods and deep learning models, which aim to extract the latent variables of input parameters and output state variables, and then build the mapping function at the latent spaces. The proposed workflow can significantly reduce the computational complexity in solving both forward and inverse problems compared to models trained on high-dimensional spaces. Dimensionality reduction models showed great potential in workflows for fast reservoir simulation, history matching, prior model generation, visualization, and more, ultimately enhancing DL model performance in related SMART Work Packages.

Hosseini, Seyyed↗

DOE OSTI2024

SQMS Quantum R&D in Machine Learning, Optimization and Sensing beyond Fundamental Physics Applications

This newly formed team at SQMS under the Ecosystem Thrust is looking to develop capabilities impacting societal advances outside the core domain of HEP and condensed matter physics. We explicitly leverage the experimental and algorithmic innovations developed across all groups as well as connect to broad-scope external projects of the diverse team of PIs. As the inaugural set of projects, we are studying numerically quantum machine learning models inspired by efficiently trainable echo-state and orthogonal neural networks and developing designs for related experiments to be performed on quantum processors based on SQMS SRF cQED technology and Rigetti s transmon arrays. Investigated models exploit ideas and lessons learned from multiple prior work by SQMS team members in a variety of internal and external activities [R1]. Target initial applications include noisy signal processing, potentially captured by quantum sensors or noisy QPUs, as well as simulation and classification of healthcare data. For instance, image reconstruction of the brain s electrical properties by solving the inverse Maxwell equation problem with uncertainty [R2] through a hybrid quantum-classical physics-informed architecture for time-dependent processes [R3]. The group is also investigating the application and development of novel quantum sensors based on magnetic levitation of a superconducting sphere coupled to a superconducting qubit. This coupling enables high-precision measurements of the position of the sphere, which can be used for sensitive detection of forces, enabling practical applications such as gravimetry for geophysics analysis, or accelerometry for GPS-denied navigation [R4] [R1] Rieffel, Eleanor G., Ata Akbari Asanjan, M. Sohaib Alam, Namit Anand, David E. Bernal Neira, Sophie Block, Lucas T. Brady et al. "Assessing and advancing the potential of quantum computing: A NASA case study." Future Generation Computer Systems (2024). [R2] Yu, X., Serrall s, J.E., Giannakopoulos, I.I., Liu, Z., Daniel, L., Lattanzi, R. and Zhang, Z., 2023. Pifon-ept: Mr-based electrical property tomography using physics-informed fourier networks. IEEE Journal on Multiscale and Multiphysics Computational Techniques. [R3] Wudarski, Filip, Daniel OConnor, Shaun Geaney, Ata Akbari Asanjan, Max Wilson, Elena Strbac, P. Aaron Lott, and Davide Venturelli. "Hybrid quantum-classical reservoir computing for simulating chaotic systems." arXiv preprint arXiv:2311.14105 (2023). [R4] Higgins, Gerard, Saarik Kalia, and Zhen Liu. "Maglev for dark matter: Dark-photon and axion dark matter sensing with levitated superconductors." Physical Review D 109.5 (2024): 055024.

Venturelli, Davide↗

NASA NTRS1974

Numerical modelling of instantaneous plate tectonics

Assuming lithospheric plates to be rigid, 68 spreading rates, 62 fracture zones trends, and 106 earthquake slip vectors are systematically inverted to obtain a self-consistent model of instantaneous relative motions for eleven major plates. The inverse problem is linearized and solved iteratively by a maximum-likelihood procedure. Because the uncertainties in the data are small, Gaussian statistics are shown to be adequate. The use of a linear theory permits (1) the calculation of the uncertainties in the various angular velocity vectors caused by uncertainties in the data, and (2) quantitative examination of the distribution of information within the data set. The existence of a self-consistent model satisfying all the data is strong justification of the rigid plate assumption. Slow movement between North and South America is shown to be resolvable.

Minster, J. B.↗

NASA NTRS1989

New results concerning the use of kinematically redundant manipulators in microgravity environments

This paper is concerned with the development of control strategies for kinematically redundant manipulators to be used in Space Station laboratories. These robots must be able to conduct experiments and manufacturing processes without disturbing the microgravity environment, and thus their dynamic base reactions/motions must be nearly eliminated. Redundant degrees of freedom permit the inverse kinematics problem to be solved in conjuction with the minimization of a cost function defined as a weighted sum of the base reactions. It is shown that the weights in the cost function should be used as an additional set of parameters in the minimization problem. The actual performance of the local optimal trajectory approach is demonstrated to be not as good as was previously reported.

Quinn, R. D.↗

NASA NTRS1992

The magnetic field of Neptune

A model is given of the planetary magnetic field of Neptune based on a spherical harmonic analysis of the observations obtained by the Voyager 2. Generalized inverse techniques are used to partially solve a severely underdetermined inverse problem, and the resulting model is nonunique since the observations are limited in spatial distribution. Dipole, quadrupole, and octupole coefficients are estimated independently of other terms, and the parameters are shown to be well constrained by the measurement data. The large-scale features of the magnetic field including dipole tilt, offset, and harmonic content are found to characterize a magnetic field that is similar to that of Uranus. The traits of Neptune's magnetic field are theorized to relate to the 'ice' interior of the planet, and the dynamo-field generation reflects this poorly conducting planet.

Connerney, J. E. P.↗

NASA NTRS1993

Numerical model for the Programmable Multirole Furnace (PMZF)

The present account of the Programmable Multizone Furnace numerical model uses various examples to illustrate the ways in which the model serves as an optimization, test, prediction, and visualization tool; a numerical PID-control algorithm obtains the desired sample temperature distributions and allows the model to solve an inverse heat transfer problem where the desired sample temperature profile is the input and the required heater power distribution is the output of numerical simulations. Parametric studies show how the total power consumption of the furnace is affected by such design variables as the conductivity.

Kassemi, M.↗

NASA NTRS1989

Machine learning in motion control

The existing methodologies for robot programming originate primarily from robotic applications to manufacturing, where uncertainties of the robots and their task environment may be minimized by repeated off-line modeling and identification. In space application of robots, however, a higher degree of automation is required for robot programming because of the desire of minimizing the human intervention. We discuss a new paradigm of robotic programming which is based on the concept of machine learning. The goal is to let robots practice tasks by themselves and the operational data are used to automatically improve their motion performance. The underlying mathematical problem is to solve the problem of dynamical inverse by iterative methods. One of the key questions is how to ensure the convergence of the iterative process. There have been a few small steps taken into this important approach to robot programming. We give a representative result on the convergence problem.

Su, Renjeng↗

NASA NTRS2011

Inversion of Magnetic Measurements of the CHAMP Satellite Over the Pannonian Basin

The Pannonian Basin is a deep intra-continental basin that formed as part of the Alpine orogeny. In order to study the nature of the crustal basement we used the long-wavelength magnetic anomalies acquired by the CHAMP satellite. The anomalies were distributed in a spherical shell, some 107,927 data recorded between January 1 and December 31 of 2008. They covered the Pannonian Basin and its vicinity. These anomaly data were interpolated into a spherical grid of 0.5 x 0.5, at the elevation of 324 km by the Gaussian weight function. The vertical gradient of these total magnetic anomalies was also computed and mapped to the surface of a sphere at 324 km elevation. The former spherical anomaly data at 425 km altitude were downward continued to 324 km. To interpret these data at the elevation of 324 km we used an inversion method. A polygonal prism forward model was used for the inversion. The minimum problem was solved numerically by the Simplex and Simulated annealing methods; a L2 norm in the case of Gaussian distribution parameters and a L1 norm was used in the case of Laplace distribution parameters. We INTERPRET THAT the magnetic anomaly WAS produced by several sources and the effect of the sable magnetization of the exsolution of hemo-ilmenite minerals in the upper crustal metamorphic rocks.

Kis, K. I.↗

NASA NTRS1986

Analysis of harmonic spline gravity models for Venus and Mars

Methodology utilizing harmonic splines for determining the true gravity field from Line-Of-Sight (LOS) acceleration data from planetary spacecraft missions was tested. As is well known, the LOS data incorporate errors in the zero reference level that appear to be inherent in the processing procedure used to obtain the LOS vectors. The proposed method offers a solution to this problem. The harmonic spline program was converted from the VAX 11/780 to the Ridge 32C computer. The problem with the matrix inversion routine that improved inversion of the data matrices used in the Optimum Estimate program for global Earth studies was solved. The problem of obtaining a successful matrix inversion for a single rev supplemented by data for the two adjacent revs still remains.

Bowin, Carl↗

NASA NTRS1990

Spatial operator approach to flexible manipulator inverse and forward dynamics

This study extends to flexible multibody manipulators the recent results of the author on the use of spatially recursive filtering and smoothing techniques for robot arm dynamics. The configuration analyzed is that of a mechanical system of flexible bodies joined together by articulated joints. The inverse and forward dynamics problems are solved using the techniques of spatially recursive Kalman filtering and smoothing. The algorithms are easily developed using a set of identities associated with mass matrix factorization and inversion. The identities are easily derived using a spatial operator algebra developed by the author.

Rodriguez, G.↗

NASA NTRS1986

Numerical pole assignment by eigenvalue Jacobian inversion

A numerical procedure for solving the linear pole placement problem is developed which operates by the inversion of an analytically determined eigenvalue Jacobian matrix. Attention is given to convergence characteristics and pathological situations. It is not concluded that the algorithm developed is suitable for computer-aided control system design with particular reference to the scan platform pointing control system for the Galileo spacecraft.

Sevaston, George E.↗

NASA NTRS2003

Fully Nonlinear Modeling and Analysis of Precision Membranes

High precision membranes are used in many current space applications. This paper presents a fully nonlinear membrane theory with forward and inverse analyses of high precision membrane structures. The fully nonlinear membrane theory is derived from Jaumann strains and stresses, exact coordinate transformations, the concept of local relative displacements, and orthogonal virtual rotations. In this theory, energy and Newtonian formulations are fully correlated, and every structural term can be interpreted in terms of vectors. Fully nonlinear ordinary differential equations (ODES) governing the large static deformations of known axisymmetric membranes under known axisymmetric loading (i.e., forward problems) are presented as first-order ODES, and a method for obtaining numerically exact solutions using the multiple shooting procedure is shown. A method for obtaining the undeformed geometry of any axisymmetric membrane with a known inflated geometry and a known internal pressure (i.e., inverse problems) is also derived. Numerical results from forward analysis are verified using results in the literature, and results from inverse analysis are verified using known exact solutions and solutions from the forward analysis. Results show that the membrane theory and the proposed numerical methods for solving nonlinear forward and inverse membrane problems are accurate.

Pai, P. Frank↗

NASA NTRS1992

Kinematics of an in-parallel actuated manipulator based on the Stewart platform mechanism

This paper presents kinematic equations and solutions for an in-parallel actuated robotic mechanism based on Stewart's platform. These equations are required for inverse position and resolved rate (inverse velocity) platform control. NASA LaRC has a Vehicle Emulator System (VES) platform designed by MIT which is based on Stewart's platform. The inverse position solution is straight-forward and computationally inexpensive. Given the desired position and orientation of the moving platform with respect to the base, the lengths of the prismatic leg actuators are calculated. The forward position solution is more complicated and theoretically has 16 solutions. The position and orientation of the moving platform with respect to the base is calculated given the leg actuator lengths. Two methods are pursued in this paper to solve this problem. The resolved rate (inverse velocity) solution is derived. Given the desired Cartesian velocity of the end-effector, the required leg actuator rates are calculated. The Newton-Raphson Jacobian matrix resulting from the second forward position kinematics solution is a modified inverse Jacobian matrix. Examples and simulations are given for the VES.

Williams, Robert L., II↗

NASA NTRS1993

Steady induction effects in geomagnetism. Part 1B: Geomagnetic estimation of steady surficial core motions: A non-linear inverse problem

The problem of estimating a steady fluid velocity field near the top of Earth's core which induces the secular variation (SV) indicated by models of the observed geomagnetic field is examined in the source-free mantle/frozen-flux core (SFI/VFFC) approximation. This inverse problem is non-linear because solutions of the forward problem are deterministically chaotic. The SFM/FFC approximation is inexact, and neither the models nor the observations they represent are either complete or perfect. A method is developed for solving the non-linear inverse motional induction problem posed by the hypothesis of (piecewise, statistically) steady core surface flow and the supposition of a complete initial geomagnetic condition. The method features iterative solution of the weighted, linearized least-squares problem and admits optional biases favoring surficially geostrophic flow and/or spatially simple flow. Two types of weights are advanced radial field weights for fitting the evolution of the broad-scale portion of the radial field component near Earth's surface implied by the models, and generalized weights for fitting the evolution of the broad-scale portion of the scalar potential specified by the models.

Voorhies, Coerte V.↗

DOE OSTI2025

Real-Time Bayesian Inference at Extreme Scale: A Digital Twin for Tsunami Early Warning Applied to the Cascadia Subduction Zone

We present a Bayesian inversion-based digital twin that employs acoustic pressure data from seafloor sensors, along with 3D coupled acoustic–gravity wave equations, to infer earthquake-induced spatiotemporal seafloor motion in real time and forecast tsunami propagation toward coastlines for early warning with quantified uncertainties. Our target is the Cascadia subduction zone, with one billion parameters. Computing the posterior mean alone would require 50 years on a 512 GPU machine. Instead, exploiting the shift invariance of the parameter-to-observable map and devising novel parallel algorithms, we induce a fast offline–online decomposition. The offline component requires just one adjoint wave propagation per sensor; using MFEM, we scale this part of the computation to the full El Capitan system (43,520 GPUs) with 92% weak parallel efficiency. Moreover, given real-time data, the online component exactly solves the Bayesian inverse and forecasting problems in 0.2 seconds on a modest GPU system, a ten-billion-fold speedup.

97 MATHEMATICS AND COMPUTING↗