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NASA NTRS1999

Preview-Based Stable-Inversion for Output Tracking

Stable Inversion techniques can be used to achieve high-accuracy output tracking. However, for nonminimum phase systems, the inverse is non-causal - hence the inverse has to be pre-computed using a pre-specified desired-output trajectory. This requirement for pre-specification of the desired output restricts the use of inversion-based approaches to trajectory planning problems (for nonminimum phase systems). In the present article, it is shown that preview information of the desired output can be used to achieve online inversion-based output tracking of linear systems. The amount of preview-time needed is quantified in terms of the tracking error and the internal dynamics of the system (zeros of the system). The methodology is applied to the online output tracking of a flexible structure and experimental results are presented.

Zou, Qing-Ze↗

NASA NTRS1985

Shoot inversion-induced ethylene in Pharbitis nil induces the release of apical dominance by restricting shoot elongation

Shoot inversion induces outgrowth of the highest lateral bud (HLB) adjacent to the bend in the stem in Pharbitis nil. In order to determine whether or not ethylene produced by shoot inversion plays a direct role in promoting or inhibiting bud outgrowth, comparisons were made of endogenous levels of ethylene in the HLB and HLB node of plants with and without inverted shoots. That no changes were found suggests that the control of apical dominance does not involve the direction action of ethylene. This conclusion is further supported by evidence that the direct application of ethylene inhibitors or ethrel to inactive or induced lateral buds has no significant effect on bud outgrowth. The hypothesis that ethylene evolved during shoot inversion indirectly promotes the outgrowth of the highest lateral bud (HLB) in restricting terminal bud (TB) growth is found to be supported by the following observations: (1) the restriction of TB growth appears to occur before the beginning of HLB outgrowth; (2) the treatment of the inverted portion of the shoot with AgNO3, an inhibitor of ethylene action, dramatically eliminates both the restriction of TB growth and the promotion of HLB outgrowth which usually accompany shoot inversion; and (3) the treatment of the upper shoot of an upright plant with ethrel mimics shoot inversion by retarding upper shoot growth and inducing outgrowth of the lateral bud basipetal to the treated region.

NASA Discipline Plant Biology↗

NASA NTRS2009

Chemical Source Inversion using Assimilated Constituent Observations in an Idealized Two-dimensional System

We present a source inversion technique for chemical constituents that uses assimilated constituent observations rather than directly using the observations. The method is tested with a simple model problem, which is a two-dimensional Fourier-Galerkin transport model combined with a Kalman filter for data assimilation. Inversion is carried out using a Green's function method and observations are simulated from a true state with added Gaussian noise. The forecast state uses the same spectral spectral model, but differs by an unbiased Gaussian model error, and emissions models with constant errors. The numerical experiments employ both simulated in situ and satellite observation networks. Source inversion was carried out by either direct use of synthetically generated observations with added noise, or by first assimilating the observations and using the analyses to extract observations. We have conducted 20 identical twin experiments for each set of source and observation configurations, and find that in the limiting cases of a very few localized observations, or an extremely large observation network there is little advantage to carrying out assimilation first. However, in intermediate observation densities, there decreases in source inversion error standard deviation using the Kalman filter algorithm followed by Green's function inversion by 50% to 95%.

Tangborn, Andrew↗

NASA NTRS2019

Implementation and Testing of Inverse Kinematics on Robotic Arm

COSIE (Coronal Spectrographic Imager in the Extreme Ultraviolet) is a proposed solar tracking ISS imaging payload that will help bridge the theoretical gap between the physics of the low corona and the heliosphere. This scientific instrument requires high pointing accuracy, on the order of arc seconds. The instrument is mounted on to a three revolute joint robotic arm in order to track the roll, pitch and yaw motion of the Sun. The goal of this project is to construct a prototype model of the robotic arm and implement the proposed analytical inverse kinematics algorithm. In robotics, the inverse kinematics problem is solving for the set of joint angles that achieve the desired end effect or location and/or orientation. In this case, orientation is the focus. Depending on the configuration, multiple sets of joint angle solutions may exist. Due to the complexity of robotics, typically iterative methods are used to solve for the joint angle solution sets. However, in this case, an analytical solution exists. A small robotic arm representative of the full size hardware was constructed. The inverse kinematics algorithm, originally in MATLAB/Simulink, was converted into C in order to interface with the motors. This C software was implemented on a Windows PC and micro-controller, and serial communication between the two was established, allowing the motors to be directly controlled by the inverse kinematics algorithm. Testing the inverse kinematics on a physical system will allow the validity and accuracy of the analytic solution to be verified.

Franz, Carter↗

NASA NTRS2019

Is There an Optimal CO2 Partial Column for Flux Inversions?

The fidelity of flux estimates from an atmospheric inversion depends on the ability of atmospheric transport models to simulate the measured quantity. For species such as CO2, with surface fluxes and a large network of surface measurements, this means correctly simulating the dynamics of the planetary boundary layer (PBL), which is one of the most uncertain aspects of atmospheric transport modeling. In contrast, the simulated total column average mole fraction of CO2 (XCO2) is largely insensitive to simulated PBL dynamics. Therefore, measurements of XCO2 provided by current and future short wave infrared (SWIR) greenhouse gas (GHG) satellites such as GOSAT and the OCO family would seem to be more appropriate to flux inversions, as far as minimizing transport model errors (the "noise") is concerned. Unfortunately, the flux-induced variation of CO2 (the "signal") is the largest within the PBL and smallest in XCO2. Therefore, assimilating XCO2 as opposed to PBL CO2 need not give us the strongest "signal to noise" in flux inversions. Recent work on GOSAT and OCO2 retrievals suggest that SWIR satellite spectra may be used to estimate a lower partial column CO2, which could be assimilated in a flux inversion, instead of XCO2.Here we report on a study to assess whether there is an optimal partial column average CO2, intermediate between PBL CO2 and XCO2, whose assimilation might yield the best signal to noise in flux inversions, where (as before) "signal" is the flux-induced variation and "noise" is the error in transport modeling. We simulate atmospheric CO2 with five different global transport models and a common surface CO2 flux over ten years. We consider the spread across the five models to be a proxy for transport model error (the "noise"), and the common variation of CO2 in all five models to be a proxy for the "signal". We compare these signals and noises at different spatiotemporal scales for different partial column specifications to investigate whether there exists an optimal partial column that has large surface flux-driven variations and yet is relatively insensitive to errors in transport models. Finally, we comment on the feasibility of estimating such a partial column from current and future SWIR GHG satellites in the light of recent work on vertically resolved CO2 from current SWIR GHG satellites.

Basu, Sourish↗

NASA NTRS2021

Inversion of Magnetic Measurements of the Swarm A Satellite of the Bangui Magnetic Anomaly

We wanted to make a satellite altitude magnetic anomaly map of the large magnetic anomaly in the Central African Republic, the Bangui magnetic anomaly, with data from the Swarm satellites. In the first part of our study, we summarize the earlier investigations and their interpretation. In the second we discuss our data processing applied to produce a magnetic anomaly map. We used the IGRF 12th to remove the long-wavelength regional anomalies. We will use an inverse procedure, which always requires a solution of the direct problem, and a horizontal polygonal prism given in the Descartes coordinate system. For this, reason the total magnetic anomaly was transformed into the Descartes coordinate system. The magnetization and its direction were used from our previous paper. The inverse problem is solved by the Simplex procedure. Our selected polygon has 14 geometrical parameters however, the inverse problem that is the numerical determination of the minimum problem is solved in the 14 dimensions. The result of our inverse problem was the 12 horizontal coordinates and the two upper and lower data of the polygon. The origin of the Bangui anomaly has been discussed in several scientific reports, either as a deep crustal tectonic feature or the result of a large external impactor. However, according to our inversion computations we cannot make any unambiguous finding for the origin of this feature. The inaccuracy in our total anomaly map is given by the Gaussian error propagation.

KI Kis↗

DOE OSTI2025

AutoTandemML: Active Learning Enhanced Tandem Neural Networks for Inverse Design Problems

Inverse design in science and engineering involves determining optimal design parameters that achieve desired performance outcomes, a process often hindered by the complexity and high dimensionality of design spaces, leading to significant computational costs. To tackle this challenge, we propose a novel hybrid approach that combines active learning with Tandem Neural Networks to enhance the efficiency and effectiveness of solving inverse design problems. Active learning allows to selectively sample the most informative data points, reducing the required dataset size without compromising accuracy. We investigate this approach using three benchmark problems: airfoil inverse design, photonic surface inverse design, and scalar boundary condition reconstruction in diffusion partial differential equations. We demonstrate that integrating active learning with Tandem Neural Networks outperforms standard approaches across the benchmark suite, achieving better accuracy with fewer training samples.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

SAGIPS: a physics-inspired scalable asynchronous generative inverse-problem solver

Abstract Solving large-scale inverse problems using deep-learning algorithms have become an essential part of modern research and industrial applications. The complexity of the underlying inverse problem may require the utilization of high performance computing systems which poses a challenge on the algorithmic design of the inverse problem solver. Most deep learning algorithms require, due to their design, custom parallelization techniques in order to be resource efficient while showing a reasonable convergence. In this paper we introduce a S calable A synchronous G enerative I nverse P roblem S olver (SAGIPS) on high-performance computing systems. We present a workflow that utilizes an asynchronous ring-allreduce algorithm to transfer the gradients of the generator network across multiple GPUs. Experiments with a scientific proxy application demonstrate that SAGIPS shows near linear weak scaling, together with a convergence quality that is comparable to traditional methods. The approach presented here allows leveraging Generative Adverserial Network across multiple GPUs, promising advancements in solving complex inverse problems at scale.

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 OSTI2024

Stability and Convergence of Solutions to Stochastic Inverse Problems Using Approximate Probability Densities

Data-consistent inversion is designed to solve a class of stochastic inverse problems where the solution is a pullback of a probability measure specified on the outputs of a quantities of interest (QoI) map. Here, this work presents stability and convergence results for the case where finite QoI data result in an approximation of the solution as a density. Given their popularity in the literature, separate results are proven for three different approaches to measuring discrepancies between probability measures: f-divergences, integral probability metrics, and L p metrics. In the context of integral probability metrics, we also introduce a pullback probability metric that is well-suited for data-consistent inversion. This fills a theoretical gap in the convergence and stability results for data-consistent inversion that have mostly focused on convergence of solutions associated with approximate maps. Numerical results are included to illustrate key theoretical results with intuitive and reproducible test problems that include a demonstration of convergence in the measure-theoretic "almost" sense.

97 MATHEMATICS AND COMPUTING↗

NASA NTRSDate not supplied

NASA’s Prototype Spectral Water Inversion Processor and Emulator (SWIPE): Towards Global Coastal and Inland Water Quality and Algal Biodiversity Monitoring

Degradation of Earth’s inland water resources due to anthropogenic perturbations and climate anomalies at both local and global scales continues to place human health at substantial risk. There is now a growing necessity to develop pragmatic approaches that allow timely and effective extrapolation of local processes, to spatially resolved global products, and to promote operational and sustainable resource policy management. This presentation will provide updates on NASA’s prototype open-source aquatic modeling platform, Spectral Water Inversion Processor and Emulator (SWIPE), which is a comprehensive, multi-faceted modeling platform for both forward and inverse modeling of diverse aquatic ecosystems from the benthos to top-of-atmosphere (TOA). SWIPE provides a cohesive application which leverages recent advancements in particle modeling, Big Data analytics, and machine learning to develop a high-fidelity synthetic training ground for sensitivity studies and algorithm development for multispectral or upcoming hyperspectral missions. Some of the prominent features of SWIPE to be discussed include: 1. Advanced hyperspectral modeling of globally diverse algal and non-algal particles using a novel two-layer coated sphere scattering model and radiative transfer modeling, 2. Massive, highly detailed synthetic spectral libraries of Analysis-Ready-Data (ARD) which include spectral libraries of particle microphysics, water biogeophysical and optical properties, as well as surface and TOA reflectances at 1 nm resolution, 3. An ensemble of pre-built analytic, machine learning, and deep learning inversion algorithms for various water quality and biodiversity related retrieval parameters and uncertainty quantification, 4. Sensor-agnostic water quality inversion at wide ranging spatial and spectral resolutions including a codebase for seamless application in the Google Earth Engine and NASA Earth Exchange (NEX) for planetary scale analysis. SWIPE will be a fully open-source platform based in python with comprehensive documentation, tutorials, and options for distributed computing on high performance computing clusters or on single, local machines. Further, we will discuss how we envision SWIPE contributing towards a global analysis of coastal and inland water quality dynamics.

top-of-atmosphere (TOA)↗

NASA NTRSDate not supplied

Modified Cascading Generalized Inverse Control Allocation

The current aviation revolution towards electric propulsion aircraft (e.g., electric vertical takeoff-and-landing) brings unique control challenges. These vehicles are typically over-actuated (more effectors than desired control outcomes), may require control strategies for the three phases of flight (hover, transition and cruise), and currently have limited electric power availability. These vehicle challenges bring the need for optimal control allocation to the forefront of research. A leading control allocation algorithm, used in current flight vehicles, is the Cascading Generalized Inverse (CGI). Unfortunately, the Cascading Generalized Inverse algorithm is unable to achieve some desired outcomes, it intermittently provides non-optimal allocations, and it may fail to preserve moment direction near maximal achievable outcomes. In this research, the shortcomings of the Cascading Generalized Inverse algorithm are addressed by augmenting the algorithm with Scalar Difference Quadratic unsaturation identification and location at each iteration. Rigorous theory is shown that the Modified Cascading Generalized Inverse performs better at obtaining optimal allocations for all attainable outcomes. Numerical case studies for over-actuated vehicles demonstrate resolution to the aforementioned deficiencies.

Control Allocation↗

NASA NTRSDate not supplied

Modified Cascading Generalized Inverse Control Allocation

Control Allocation↗

NASA NTRS2017

Imaging a Free-Geometry Magma Reservoir Using FEM-Based Linear Inverse Modeling of InSAR Data: Application to Rabaul Caldera, Papua New Guinea

We test an innovative inversion scheme using Green’s functions from an array of pressure sources embedded in finite-element method (FEM) models to image, without assuming an a-priori geometry, the composite and complex shape of a volcano deformation source. We invert interferometric synthetic aperture radar (InSAR) data to estimate the pressurization and shape of the magma reservoir of Rabaul caldera, Papua New Guinea. The results image the extended shallow magmatic system responsible for a broad and long-term subsidence of the caldera between 2007 February and 2010 December. Elastic FEM solutions are integrated into the regularized linear inversion of InSAR data of volcano surface displacements in order to obtain a 3-D image of the source of deformation. The Green’s function matrix is constructed from a library of forward line-of-sight displacement solutions for a grid of cubic elementary deformation sources. Each source is sequentially generated by removing the corresponding cubic elements from a common meshed domain and simulating the injection of a fluid mass flux into the cavity, which results in a pressurization and volumetric change of the fluidfilled cavity. The use of a single mesh for the generation of all FEM models avoids the computationally expensive process of non-linear inversion and remeshing a variable geometry domain. Without assuming an a-priori source geometry other than the configuration of the 3-D grid that generates the library of Green’s functions, the geodetic data dictate the geometry of the magma reservoir as a 3-D distribution of pressure (or flux of magma) within the source array. The inversion of InSAR data of Rabaul caldera shows a distribution of interconnected sources forming an amorphous, shallow magmatic system elongated under two opposite sides of the caldera. The marginal areas at the sides of the imaged magmatic system are the possible feeding reservoirs of the ongoing Tavurvur volcano eruption of andesitic products on the east side and of the past Vulcan volcano eruptions of more evolved materials on the west side. The interconnection and spatial distributions of sources correspond to the petrography of the volcanic products described in the literature and to the dynamics of the single and twin eruptions that characterize the caldera. The ability to image the complex geometry of deformation sources in both space and time can improve our ability to monitor active volcanoes, widen our understanding of the dynamics of active volcanic systems and improve the predictions of eruptions.

Inverse theory↗

NASA NTRS2017

Imaging the Complex Geometry of a Magma Reservoir Using Fem-Based Linear Inverse Modeling of InSAR Data: Application to Rabaul Caldera, Papua New Guinea

We test an innovative inversion scheme using Green’s functions from an array of pressure sources embedded in finite-element method (FEM) models to image, without assuming an a-priori geometry, the composite and complex shape of a volcano deformation source. We invert interferometric synthetic aperture radar (InSAR) data to estimate the pressurization and shape of the magma reservoir of Rabaul caldera, Papua New Guinea. The results image the extended shallow magmatic system responsible for a broad and long-term subsidence of the caldera between 2007 February and 2010 December. Elastic FEM solutions are integrated into the regularized linear inversion of InSAR data of volcano surface displacements in order to obtain a 3-D image of the source of deformation. The Green’s function matrix is constructed from a library of forward line-of-sight displacement solutions for a grid of cubic elementary deformation sources. Each source is sequentially generated by removing the corresponding cubic elements from a common meshed domain and simulating the injection of a fluid mass flux into the cavity, which results in a pressurization and volumetric change of the fluid-filled cavity. The use of a single mesh for the generation of all FEM models avoids the computationally expensive process of non-linear inversion and remeshing a variable geometry domain. Without assuming an a-priori source geometry other than the configuration of the 3-D grid that generates the library of Green’s functions, the geodetic data dictate the geometry of the magma reservoir as a 3-D distribution of pressure (or flux of magma) within the source array. The inversion of InSAR data of Rabaul caldera shows a distribution of interconnected sources forming an amorphous, shallow magmatic system elongated under two opposite sides of the caldera. The marginal areas at the sides of the imaged magmatic system are the possible feeding reservoirs of the ongoing Tavurvur volcano eruption of andesitic products on the east side and of the past Vulcan volcano eruptions of more evolved materials on the west side. The interconnection and spatial distributions of sources correspond to the petrography of the volcanic products described in the literature and to the dynamics of the single and twin eruptions that characterize the caldera. The ability to image the complex geometry of deformation sources in both space and time can improve our ability to monitor active volcanoes, widen our understanding of the dynamics of active volcanic systems and improve the predictions of eruptions.

Inverse theory↗

NASA NTRSDate not supplied

Forward and Inverse Models for Satellite Remote Sensors using Principal Component Analysis

Satellite remote sensors such as AIRS on Aqua, CrIS on S-NPP, NOAA20 and JPSS-2, IASI on Metop A, B, and C make millions of observations each day with thousands of spectral channels for each observation; this poses challenges for efficiently inversion of the inherently large dataset as needed to retrieve atmospheric and surface properties. This presentation will illustrate the use of Principal Component Analysis (PCA) to speed up radiative transfer forward model calculations and to stabilize the inversion algorithms. A Principal Component-based radiative transfer model (PCRTM) developed at NASA Langley Research Center can simulate top of atmosphere (TOA) radiance or reflectance spectra from 50 cm-1 to 50000 cm-1 (200 m to 0.20 m quickly and accurately. PCRTM demonstrated very high accuracy relative to reference line-by-line radiative transfer models and it saves orders of magnitude computational time. Examples of the PCRTM model developed for hyperspectral sensors such as AIRS, CrIS, IASI, NAST-I, SHIS, CPF, TEMPO, SBG, OMI, and SCIAMACHY will be presented. In addition to using the PCRTM as forward model, the NASA Langley developed inversion algorithm also uses PCA to compress the state vector into a compressed dimension to speed up and stabilize the inversion process. Examples of retrieved atmospheric temperature, water vapor, CO2, CO, CH4, N2O, and O3 profiles, cloud properties (optical depth, size, phase, and height), and surface properties (surface emissivity spectra and skin temperatures) will be presented. This algorithm is being transitioned to the NASA Sounder SIPS and NASA's Goddard Earth Sciences Data and Information Services Center (GES DISC).

forward model↗

DOE OSTI2025

Physically constrained 3D diffusion for inverse design of fiber-reinforced polymer composite materials

Designing fiber-reinforced polymer composites (FRPCs) with a tailored nonlinear stress-strain response is crucial for applications such as energy absorption in crash structures, flexible robotics, and impact-resistant protective gear. However, the inherent complexities of composite materials and the multitude of parameters involved, render traditional design and optimization methods inadequate for achieving effective inverse design of composites. In this paper, we present an AI-based inverse design framework that effectively and efficiently generates FRPCs with targeted nonlinear stress-strain responses. We introduce a physically constrained diffusion model (PC3D_Diffusion) capable of managing the complexities of composite materials and producing detailed, high-quality designs. We propose a loss-guided, learning-free approach to generate physically feasible microstructure designs by explicitly enforcing physical constraints during the generation process. For training purposes, 1.35 million FRPC samples were created, and their corresponding stress-strain curves were computed using established physics-based computational models. The results show that PC3D_Diffusion consistently generates high-quality designs with tailored mechanical behaviors, while guaranteeing compliance with the physical constraints. PC3D_Diffusion advances FRPC inverse design and may facilitate the inverse design of other 3D materials, offering potential applications in industries reliant on materials with custom mechanical properties.

Xu, Pei [Clemson Univ., SC (United States)]↗

DOE OSTI2025

Abrupt structural transition in exotic molybdenum isotopes unveils an isospin-symmetric island of inversion

Like electrons in atoms, protons and neutrons in nuclei occupy orbitals in a shell structure with energy gaps at magic numbers. Radioactive-beam experiments revealed the disappearance of magic numbers in some neutron-rich isotopes. In these nuclei, configurations involving particles excited across the shell gap gain correlation energy, becoming the ground state. Neutron-rich regions of the nuclear chart that exhibit this property are known as “Islands of Inversion”. Here we present the lifetime measurement of the first 2 + states in 84 Mo (N = Z) and 86 Mo (N = Z + 2) revealing an unexpected sharp structural change between them defining the edge of the region of deformation around 80 Zr. Similarly to the neutron-rich N = 40 Island of Inversion near 64 Cr where cross-shell excitations dominate, we identify this region as an Island of Inversion with symmetrical proton and neutron excitations that we term “Isospin-Symmetric Island of Inversion”. Three-nucleon forces are suggested to drive Mo isotope structural changes.

experimental nuclear physics↗