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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↗

DOE OSTI2026

Uncertainty quantification for inverse problems with application to ptychographic reconstruction

Inverse problems in imaging are commonly solved by optimization or learned surrogates that return a single reconstruction, while uncertainty information is often unavailable. In many experimental settings, however, uncertainty is required to assess reliability, guide downstream analysis, and prioritize additional measurements. In this note, we present a compact uncertainty-quantification framework based on local objective curvature, and then specialize it to ptychographic reconstruction. We further show how repeated reconstructions can be aggregated in a statistically principled way, including a practical implementation path for PtychoNN.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1988

An exact inverse method for subsonic flows

A new inverse method for the aerodynamic design of airfoils is presented for subcritical flows. The pressure distribution in this method can be prescribed as a function of the arclength of the still unknown body. It is shown that this inverse problem is mathematically equivalent to solving only one nonlinear boundary value problem subject to known Dirichlet data on the boundary.

Daripa, Prabir↗

NASA NTRS1992

The double universal joint wrist on a manipulator: Solution of inverse position kinematics and singularity analysis

This paper presents three methods to solve the inverse position kinematics position problem of the double universal joint attached to a manipulator: (1) an analytical solution for two specific cases; (2) an approximate closed form solution based on ignoring the wrist offset; and (3) an iterative method which repeats closed form position and orientation calculations until the solution is achieved. Several manipulators are used to demonstrate the solution methods: cartesian, cylindrical, spherical, and an anthropomorphic articulated arm, based on the Flight Telerobotic Servicer (FTS) arm. A singularity analysis is presented for the double universal joint wrist attached to the above manipulator arms. While the double universal joint wrist standing alone is singularity-free in orientation, the singularity analysis indicates the presence of coupled position/orientation singularities of the spherical and articulated manipulators with the wrist. The cartesian and cylindrical manipulators with the double universal joint wrist were found to be singularity-free. The methods of this paper can be implemented in a real-time controller for manipulators with the double universal joint wrist. Such mechanically dextrous systems could be used in telerobotic and industrial applications, but further work is required to avoid the singularities.

Williams, Robert L., III↗

NASA NTRS1993

Simultaneous solution for core magnetic field and fluid flow beneath an electrically conducting mantle

The effects of laterally homogeneous mantle electrical conductivity were included in steady, frozen-flux core surface flow estimation along with refinements in method and weighting. The refined method allows simultaneous solution for both the initial radial geomagnetic field component at the core-mantle boundary (CMB) and the sub-adjacent fluid motion; it also features Gauss' method for solving the non-linear inverse problem associated with steady motional induction. The tradeoff between spatial complexity of the derived flows and misfit to the weighted Definitive Geomagnetic Reference Field models (DGRF's) is studied for various mantle conductivity profiles. For simple flow and a fixed initial geomagnetic condition, a fairly high deep-mantle conductivity performs better than either insulating or weakly conducting profiles; however, a thin, very high conductivity layer at the base of the mantle performs almost as well. Simultaneous solution for both initial geomagnetic field and flow reduces the misfit per degree of freedom even more than does changing the mantle conductivity profile. Moreover, when both core field and flow are estimated, the performance of the solutions and the derived flows become insensitive to the conductivity profile.

Voorhies, Coerte V.↗

NASA NTRS1993

Steady induction effects in geomagnetism. Part 1C: Geomagnetic estimation of steady surficial core motions: Application to the definitive geomagnetic reference field models

In the source-free mantle/frozen-flux core magnetic earth model, the non-linear inverse steady motional induction problem was solved using the method presented in Part 1B. How that method was applied to estimate steady, broad-scale fluid velocity fields near the top of Earth's core that induce the secular change indicated by the Definitive Geomagnetic Reference Field (DGRF) models from 1945 to 1980 are described. Special attention is given to the derivation of weight matrices for the DGRF models because the weights determine the apparent significance of the residual secular change. The derived weight matrices also enable estimation of the secular change signal-to-noise ratio characterizing the DGRF models. Two types of weights were derived in 1987-88: radial field weights for fitting the evolution of the broad-scale portion of the radial geomagnetic field component at Earth's surface implied by the DGRF's, and general weights for fitting the evolution of the broad-scale portion of the scalar potential specified by these models. The difference is non-trivial because not all the geomagnetic data represented by the DGRF's constrain the radial field component. For radial field weights (or general weights), a quantitatively acceptable explication of broad-scale secular change relative to the 1980 Magsat epoch must account for 99.94271 percent (or 99.98784 percent) of the total weighted variance accumulated therein. Tolerable normalized root-mean-square weighted residuals of 2.394 percent (or 1.103 percent) are less than the 7 percent errors expected in the source-free mantle/frozen-flux core approximation.

Voorhies, Coerte V.↗

NASA NTRS2010

Electrical Capacitance Volume Tomography with High-Contrast Dielectrics

The Electrical Capacitance Volume Tomography (ECVT) system has been designed to complement the tools created to sense the presence of water in nonconductive spacecraft materials, by helping to not only find the approximate location of moisture but also its quantity and depth. The ECVT system has been created for use with a new image reconstruction algorithm capable of imaging high-contrast dielectric distributions. Rather than relying solely on mutual capacitance readings as is done in traditional electrical capacitance tomography applications, this method reconstructs high-resolution images using only the self-capacitance measurements. The image reconstruction method assumes that the material under inspection consists of a binary dielectric distribution, with either a high relative dielectric value representing the water or a low dielectric value for the background material. By constraining the unknown dielectric material to one of two values, the inverse math problem that must be solved to generate the image is no longer ill-determined. The image resolution becomes limited only by the accuracy and resolution of the measurement circuitry. Images were reconstructed using this method with both synthetic and real data acquired using an aluminum structure inserted at different positions within the sensing region. The cuboid geometry of the system has two parallel planes of 16 conductors arranged in a 4 4 pattern. The electrode geometry consists of parallel planes of copper conductors, connected through custom-built switch electronics, to a commercially available capacitance to digital converter. The figure shows two 4 4 arrays of electrodes milled from square sections of copper-clad circuit-board material and mounted on two pieces of glass-filled plastic backing, which were cut to approximately square shapes, 10 cm on a side. Each electrode is placed on 2.0-cm centers. The parallel arrays were mounted with the electrode arrays approximately 3 cm apart. The open ends were surrounded by a metal guard to reduce the sensitivity of the electrodes to outside interference and to help maintain the spacing between the arrays. Other uses for this innovation potentially include quantifying the amount of commodity remaining in the fuel and oxidizer tanks while on-orbit without having to fire spacecraft engines. Another orbit application is moisture sensing in plant-growth experiments because microgravity causes moisture in soil to distribute itself in unusual ways. At the moment, the hardware and image reconstruction technique may only be of interest to people involved in nondestructive evaluation. The reconstructed image takes almost a full week to reproduce with existing computer power. However, because computer power and speeds follows Moore s Law, execution times are likely to become acceptable within the next five to eight years. The code was written in Mathematica for dedicated use with the ECVT system. In its present form, it is not suitable to be used directly as a consumer product. However, the code could be likely improved by rewriting it in a compiled language such as C or Fortran.

Nurge, Mark↗

NASA NTRS2022

P- and L-Band Retrieval of Subsurface Soil Moisture and Temperature Profiles as First-Order Polynomial Function

This paper demonstrates the potential use of P and L band passive measurements to determine root zone soil moisture (SM) and soil temperature(ST). SM and ST data have been taken as a function of depth during the NASA GSFC PLEX19 experiment in the summer of 2019 at Beltsville, MD, USA. Using these data, a coherent model has been used to compute H and V brightness temperatures at frequencies of 0.8 and 1.4 GHz with an observation angle of 35 degrees. These synthetic brightness data are then used to estimate the SM and ST profiles which are represented by linear polynomials. The inversion problem is formulated as a least square problem that is solved by a global optimization method known as the Adaptive Simulated Annealing(ASA) method. Four inversion examples having different SM and ST profiles are presented. Selected results show that the standard deviation between the retrieved and measured data is less than 0.077 cm3/cm3 for SM, and 2.245 °C for ST.

Ming Li↗

DOE OSTI2026

FIRM: federated image reconstruction using multimodal tomographic data

Here, we propose a federated algorithm for reconstructing images using multimodal tomographic data sourced from dispersed locations, addressing the challenges of traditional unimodal approaches that are prone to noise and reduced image quality, as well as the limitations of centralized multimodal approaches that require extensive data transfer, leading to significant communication overhead, storage demands, and potential data privacy concerns. Our approach formulates a joint inverse optimization problem incorporating multimodality constraints and solves it in a federated framework through local gradient computations complemented by lightweight central operations, thereby ensuring data decentralization. Leveraging the connection between our federated algorithm and the quadratic penalty method, we introduce an adaptive step-size rule with guaranteed sublinear convergence. Numerical results demonstrate superior computational efficiency and improved image reconstruction quality compared to existing approaches.

federated algorithm↗

DOE OSTI2025

Characterizing the hadronization of parton showers using the HOMER method

We update the HOMER method, a technique to solve a restricted version of the inverse problem of hadronization – extracting the Lund string fragmentation function f(z) from data using only observable information. Here, we demonstrate its utility by extracting f(z) from synthetic Pythia simulations using high-level observables constructed on an event-by-event basis, such as multiplicities and shape variables. Four cases of increasing complexity are considered, corresponding to e + e − collisions at a center-of-mass energy of 90 ≥ v producing either a string stretched between a $q$ and $\bar{q}$ containing no gluons; the same string containing one gluon g with fixed kinematics; the same but the gluon has varying kinematics; and the most realistic case, strings with an unrestricted number of gluons that is the end-result of a parton shower. We demonstrate the extraction of f(z) in each case, with the result of only a relatively modest degradation in performance of the HOMER method with the increased complexity of the string system.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS1981

The design and analysis of low-speed airfoils

PROFILE program solves diverse and inverse airfoil-flow problems. It combines conformational mapping method for design of airfoils with prescribed velocity-distribution characteristics, panel method for potential-flow analysis, and boundary-layer method. PROFILE is written in FORTRAN IV for implementation on CDC 6000-series computer.

Eppler, R.↗

NASA NTRS1989

On trajectory generation for flexible space crane: Inverse dynamics analysis by LATDYN

For future in-space construction facility, one or more space cranes capable of manipulating and positioning large and massive spacecraft components will be needed. Inverse dynamics was extensively studied as a basis for trajectory generation and control of robot manipulators. The focus here is on trajectory generation in the gross-motion phase of space crane operation. Inverse dynamics of the flexible crane body is much more complex and intricate as compared with rigid robot link. To model and solve the space crane's inverse dynamics problem, LATDYN program which employs a three-dimensional finite element formulation for the multibody truss-type structures will be used. The formulation is oriented toward a joint dominated structure which is suitable for the proposed space crane concept. To track a planned trajectory, procedures will be developed to obtain the actuation profile and dynamics envelope which are pertinent to the design and performance requirements of the space crane concept.

Chen, G.-S.↗

NASA NTRS1989

Kinematics, controls, and path planning results for a redundant manipulator

The inverse kinematics solution, a modal position control algorithm, and path planning results for a 7 degree of freedom manipulator are presented. The redundant arm consists of two links with shoulder and elbow joints and a spherical wrist. The inverse kinematics problem for tip position is solved and the redundant joint is identified. It is also shown that a locus of tip positions exists in which there are kinematic limitations on self-motion. A computationally simple modal position control algorithm has been developed which guarantees a nearly constant closed-loop dynamic response throughout the workspace. If all closed-loop poles are assigned to the same location, the algorithm can be implemented with very little computation. To further reduce the required computation, the modal gains are updated only at discrete time intervals. Criteria are developed for the frequency of these updates. For commanding manipulator movements, a 5th-order spline which minimizes jerk provides a smooth tip-space path. Schemes for deriving a corresponding joint-space trajectory are discussed. Modifying the trajectory to avoid joint torque saturation when a tip payload is added is also considered. Simulation results are presented.

Gretz, Bruce↗

NASA NTRS1990

A high temperature thermal diffusivity determination procedure for solids and liquids

A new method for measuring the thermal diffusivity of materials at high temperatures is presented. The method is applicable to solids on Earth, and to liquids in the reduced gravity environment of space. It is especially suited to levitated liquid metals at elevated temperatures where thermal diffusivity data is not available. The method is applied in two parts, such that lumped analysis is valid in the first part, and Fourier's law of conduction is valid in the second. In both parts, the spherical specimen is assumed to have been heated to a desired temperature and cooled. An inverse conduction problem is then formulated and solved using Laplace transformation techniques. Using this solution, sample sizes, and experimentally obtained surface temperature history, the thermal diffusivity is determined by minimizing a function that satisifies the heat balance at the surface. Minimization is performed using a modified quasilinearization algorithm. Accuracy is very sensitive to error in the temperature data and increases with better curve fits to the temperature data. An error analysis is also performed, and the effect of errors in the various parameters on the evaluated thermal diffusivity is determined. An experimental study for solids on Earth is suggested, before development for implementation in space.

Bayazitoglu, Yildiz↗

NASA NTRS1994

Coupled 2-dimensional cascade theory for noise and unsteady aerodynamics of blade row interaction in turbofans. Volume 1: Theory development and parametric studies

Typical analytical models for interaction between rotor and stator in a turbofan analyze the effect of wakes from the rotor impinging on the stator, producing unsteady loading, and thereby generating noise. Reflection/transmission characteristics of the rotor are sometimes added in a separate calculation. In those models, there is a one-to-one relationship between wake harmonics and noise harmonics; that is, the BPF (blade passing frequency) wake harmonic causes only the BPF noise harmonic, etc. This report presents a more complete model in which flow tangency boundary conditions are satisfied on two cascades in relative motion for several harmonics simultaneously. By an extension of S.N. Smith's code for two dimensional flat plate cascades, the noise generation/frequency scattering/blade row reflection problem is solved in a single matrix inversion. It is found that the BPF harmonic excitation of the stator scatters considerable energy in the higher BPF harmonics due to relative motion between the blade rows. Furthermore, when swirl between the rotor and stator is modeled, a 'mode trapping' effect occurs which explains observations on fans operating at rotational speeds below BFP cuton: the BPF mode amplifies between blade rows by multiple reflections but cannot escape to the inlet and exit ducts. However, energy scattered into higher harmonics does propagate and dominates the spectrum at two and three times BPF. This report presents the complete derivation of the theory, comparison with a previous (more limited) coupled rotor/stator interaction theory due to Kaji and Okazaki, exploration of the mode trapping phenomenon, and parametric studies showing the effects of vane/blade ratio and rotor/stator interaction. For generality, the analysis applies to stages where the rotor is either upstream or downstream of the stator and to counter rotation stages. The theory has been coded in a FORTRAN program called CUP2D, documented in Volume 2 of this report. It is concluded that the new features of this analysis - unsteady coupling, frequency scattering, and flow turning between rotor and stator - have a profound effect on noise generation caused by rotor/stator interaction. Treating rotors and stators as isolated cascades is not adequate for noise analysis and prediction.

Hanson, Donald B.↗

NASA NTRSDate not supplied

Total Variation Majorization Minimization (TV-MM) Approach to Radiometer Brightness Temperature Gridding and Reconstruction

This paper presents the implementation of an algorithm to enhance the image resolution of the Earth's surface brightness temperature (T B ) data measured by radiometers such as the one onboard of the Soil Moisture Active Passive (SMAP) mission. A key step in radiometer T B processing is the conversion of the swath-based calibrated antenna temperature (T A ) measurements to the Level 3 Earth-centered grid. The simplest algorithm to transform this data from swath to gridded format is called drop-in-the-bucket which simply averages surrounding noisy T A samples to form a T B value at the gridded location. This method reduces noise, however produces low resolution products. To obtain a higher resolution product, SMAP uses other techniques such the Backus-Gilbert (BG) algorithm, which is the conventional method used in microwave radiometry. Although this method performs the required interpolation, it is not effective in denoising and removing blurring effects due to antenna filtering of the radiometer image data. Our motivation for this development is to further improve the resolution through post-processing of the radiometer T B image, a highly cost-effective method of image enhancement. The approach adapted in this work is based on the minimization of the Total Variation (TV) regularized objective function that is used extensively in solving general ill-posed linear inverse problems in image processing. Since the TV-based objective function is convex but not everywhere differentiable, there exists many numerical algorithms that can estimate the solution and the one selected for this work is called Majorization- Minimization (MM). By applying this algorithm, simulation experiments were performed based on synthetic data from the Geophysical model as well as real SMAP data to demonstrate the effectiveness of the technique. Results were then compared against the BG method.

Wing Lee↗

NASA NTRS1991

Identification of dynamic characteristics of flexible rotors as dynamic inverse problem

The problem of dynamic and balancing of flexible rotors were considered, which were set and solved as the problem of the identification of flexible rotor systems, which is the same as the inverse problem of the oscillation theory dealing with the task of the identifying the outside influences and system parameters on the basis of the known laws of motion. This approach to the problem allows the disclosure the picture of disbalances throughout the rotor-under-test (which traditional methods of flexible rotor balancing, based on natural oscillations, could not provide), and identify dynamic characteristics of the system, which correspond to a selected mathematical model. Eventually, various methods of balancing were developed depending on the special features of the machines as to their design, technology, and operation specifications. Also, theoretical and practical methods are given for the flexible rotor balancing at far from critical rotation frequencies, which does not necessarily require the knowledge forms of oscillation, dissipation, and elasticity and inertia characteristics, and to use testing masses.

Roisman, W. P.↗

NASA NTRS1991

Trajectory optimization and guidance for a hypersonic vehicle

The optimal ascent problem for a hypersonic vehicle is formulated as an inverse dynamic problem. This formulation is essential in solving the trajectory optimization problem via the nonlinear programming approach. Both minimum-fuel and minimax type of performance indices are considered. The results reveal important features of the optimal trajectory and controls, and they are subsequently used to construct a nonlinear feedback midcourse control law. This control law not only greatly simplifies the difficult constrained optimization problem and yields improved solutions, but is also suitable for onboard implementation. Finally, off-nominal trajectory guidance is addressed using combination of feedback compensation and onboard generation of control through the inverse dynamics approach.

Lu, Ping↗