MatCal: an open-source Python package for material model calibration using inverse problem approaches
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Karlson, Kyle N. [Sandia National Laboratories (SN↗
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Two-dimensional modeling of thermal inversion layers in the middle atmosphere of Mars
There is some evidence that the thermal structure of the martian middle atmosphere may be altered in a significant way by the general circulation motions. Indeed, while it is well known that the circulation in the meridional plane is responsible for the reversal of the latitudinal thermal gradient at the solstice through the adiabatic heating due to sinking motions above the winter pole, here we want to emphasize that a likely by-product effect could be the formation of warm layers, mainly located in the winter hemisphere, and exhibiting an inversion of the vertical thermal gradient.
Theodore, B.↗
Joint Inversion and Forward Modeling of Gravity and Magnetic Data in the Ismenius Region of Mars
The unexpected discovery of remanent crustal magnetism on Mars was one of the most intriguing results from the Mars Global Surveyor mission. The origin of the pattern of magnetization remains elusive. Correlations with gravity and geology have been examined to better understand the nature of the magnetic anomalies. In the area of the Martian dichotomy between 50 and 90 degrees E (here referred to as the Ismenius Area), we find that both the Bouguer and the isostatic gravity anomalies appear to correlate with the magnetic anomalies and a buried fault, and allow for a better constraint on the magnetized crust].
Milbury, C. A.↗
Water Vapor Sensitivity Analysis for AVIRIS Radiactive-Transfer-Model-Based Reflectance Inversion
As with other imaging spectrometers, AVIRIS measures the upwelling specral radiance incident at the sensor. Most research and applications objectives for AVIRIS are based on the molecular absorption and scattering features expressed in the surface reflectance.
AVIRIS Sensitivity Analysis water vapor reflectanc↗
Adjusting a Full Body Model to Mitigate Inverse Kinematics Artifacts in OpenSim
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C. A. Bell↗
Hyperspectral Sounder Spectral Fingerprinting: Using Machine Learning Techniques to Enhance Model-Based Physical Inversion
Different retrieval algorithms have been developed to process top-of-atmosphere (TOA) spectral radiance data provided by hyperspectral infrared sounder missions. Those algorithms are either optimal estimation method (OEM) based schemes with radiative transfer calculation involved in the retrieval process, or machine learning based methods that allow ultra-efficient data procession but lack of radiometric consistency validation based on the directly measured information. Combining both approaches leverages their respective technical advantages, leading to more accurate results. This study introduces a hyperspectral sounder fingerprinting algorithm to explore this hybrid approach. This approach involves the use of a spectral information-based classification method to identify an reference geophysical state and the corresponding radiative kernel. This enables the efficient retrieval of geophysical variables of interest through a radiative kernel-based linear inversion procedure. The fingerprinting method has been applied to analyze a decade-long hyperspectral sounder data record.
Wan Wu↗
Inverse problems in the modeling of vibrations of flexible beams
The formulation and solution of inverse problems for the estimation of parameters which describe damping and other dynamic properties in distributed models for the vibration of flexible structures is considered. Motivated by a slewing beam experiment, the identification of a nonlinear velocity dependent term which models air drag damping in the Euler-Bernoulli equation is investigated. Galerkin techniques are used to generate finite dimensional approximations. Convergence estimates and numerical results are given. The modeling of, and related inverse problems for the dynamics of a high pressure hose line feeding a gas thruster actuator at the tip of a cantilevered beam are then considered. Approximation and convergence are discussed and numerical results involving experimental data are presented.
Banks, H. T.↗
Aerosol Models for the CALIPSO Lidar Inversion Algorithms
We use measurements and models to develop aerosol models for use in the inversion algorithms for the Cloud Aerosol Lidar and Imager Pathfinder Spaceborne Observations (CALIPSO). Radiance measurements and inversions of the AErosol RObotic NETwork (AERONET1, 2) are used to group global atmospheric aerosols using optical and microphysical parameters. This study uses more than 105 records of radiance measurements, aerosol size distributions, and complex refractive indices to generate the optical properties of the aerosol at more 200 sites worldwide. These properties together with the radiance measurements are then classified using classical clustering methods to group the sites according to the type of aerosol with the greatest frequency of occurrence at each site. Six significant clusters are identified: desert dust, biomass burning, urban industrial pollution, rural background, marine, and dirty pollution. Three of these are used in the CALIPSO aerosol models to characterize desert dust, biomass burning, and polluted continental aerosols. The CALIPSO aerosol model also uses the coarse mode of desert dust and the fine mode of biomass burning to build a polluted dust model. For marine aerosol, the CALIPSO aerosol model uses measurements from the SEAS experiment 3. In addition to categorizing the aerosol types, the cluster analysis provides all the column optical and microphysical properties for each cluster.
Omar, Ali H.↗
Improvement of Aerosol Optical Depth Retrieval from MODIS Spectral Reflectance over the Global Ocean Using New Aerosol Models Archived from AERONET Inversion Data and Tri-axial Ellipsoidal Dust Database
New over-ocean aerosol models are developed by integrating the inversion data from the Aerosol Robotic Network (AERONET) sun/sky radiometers with a database for the optical properties of tri-axial ellipsoid particles. The new aerosol models allow more accurate retrieval of aerosol optical depth (AOD) from the Moderate Resolution Imaging Spectroradiometer (MODIS) in the case of high AOD (AOD greater than 0.3). The aerosol models are categorized by using the fine-mode fraction (FMF) at 550 nm and the singlescattering albedo (SSA) at 440 nm from the AERONET inversion data to include a variety of aerosol types found around the globe. For each aerosol model, the changes in the aerosol optical properties (AOPs) as functions of AOD are considered to better represent aerosol characteristics. Comparisons of AODs between AERONET and MODIS for the period from 2003 to 2010 show that the use of the new aerosol models enhances the AOD accuracy with a Pearson coefficient of 0.93 and a regression slope of 0.99 compared to 0.92 and 0.85 calculated using the MODIS Collection 5 data. Moreover, the percentage of data within an expected error of +/-(0.03 + 0.05xAOD) is increased from 62 percent to 64 percent for overall data and from 39 percent to 51 percent for AOD greater than 0.3. Errors in the retrieved AOD are further characterized with respect to the Angstrom exponent (AE), scattering angle, SSA, and air mass factor (AMF). Due to more realistic AOPs assumptions, the new algorithm generally reduces systematic errors in the retrieved AODs compared with the current operational algorithm. In particular, the underestimation of fine-dominated AOD and the scattering angle dependence of dust-dominated AOD are significantly mitigated as results of the new algorithm's improved treatment of aerosol size distribution and dust particle nonsphericity.
aerosol optical depth↗
Directional and polarimetric effects in the optical domain
Papers focused on land surface, atmospheric, and ocean properties are reported. Specific comments pertaining to polarization, models and inversion, and measurements, are given. Recommendations are: continued research into the application potential of the BRDF (Bidirectional Reflectance Distribution Function) and polarization properties of ground surface and atmospheric targets; three dimensional models, which account for the statistical behavior of remotely sensed data, should be extended and inverted in order to support analysis of data potentially covering rolling terrain such that pixels represent heterogeneous mixtures of surface cover types and project ground footprints with sizes between 10 to 6 km, the ground pixel sizes of planned future sensors; available reflectance models should be further validated by means of multi dimensional (directional, spectral, temporal) field data and existing models should be intercompared in more depth to evaluate their performance and limitations; existing methods for model inversion should be validated in more depth in order to quantify the practical limitations and the expected accuracy of the parameters retrieved and new approaches should be developed based upon apriori knowledge of plant canopy development and spectral BRDF properties; there is a need to establish a protocol of validation and intercomparison of the indices and compositing techniques which have been proposed during these last years.
Vanderbilt, V. C.↗
Unifying Radiative Transfer Models in Computer Graphics and Remote Sensing, Part II: A Differentiable, Polarimetric Forward Model and Validation
The constellation of Earth-observing satellites continuously collects measurements of scattered radiance, which must be transformed into geophysical parameters in order to answer fundamental scientific questions about the Earth. Retrieval of these parameters requires highly flexible, accurate, and fast forward and inverse radiative transfer models. Existing forward models used by the remote sensing community are typically accurate and fast, but sacrifice flexibility by assuming the atmosphere or ocean is composed of plane-parallel layers. Monte Carlo forward models can handle more complex scenarios such as 3D spatial heterogeneity, but are relatively slower. We propose looking to the computer graphics community for inspiration to improve the statistical efficiency of Monte Carlo forward models and explore new approaches to inverse models for remote sensing. In Part 2 of this work, we demonstrate that Monte Carlo forward models in computer graphics are capable of sufficient accuracy for remote sensing by extending Mitsuba 3, a forward and inverse modeling framework recently developed in the computer graphics community, to simulate simple atmosphere-ocean systems and show that our framework is capable of achieving error on par with codes currently used by the remote sensing community on benchmark results.
Radiative transfer↗
Latent and sensible heat flux estimated from ERS-1 data
Two issues regarding surface latent and sensible heat flux are addressed: its value in low wind speed conditions over the tropical oceans,and its determination solely from satellite observations. The investigation is performed with an oceanic mixed layer model operated in an 'inverse' mode. The 'normal' model is forced with the surface heat and radiative fluxes and produces the SST evolution, whereas the 'inverse' model produces the latent sensible heat flux given the SST and surface radiative flux as input. The results indicate that at low wind speeds there exists a minimum latent sensible heat flux of about 80 to 100 W/sq m. Sensitivity studies show that the latent sensible heat flux is very sensitive to random errors in the forcing SST time series. The implications of this strong sensitivity in regards to the use of satellite measurements to supply the forcing SST are discussed.
Iacobellis, S. F.↗
Mapping From an Instrumented Glove to a Robot Hand
An algorithm has been developed to solve the problem of mapping from (1) a glove instrumented with joint-angle sensors to (2) an anthropomorphic robot hand. Such a mapping is needed to generate control signals to make the robot hand mimic the configuration of the hand of a human attempting to control the robot. The mapping problem is complicated by uncertainties in sensor locations caused by variations in sizes and shapes of hands and variations in the fit of the glove. The present mapping algorithm is robust in the face of these uncertainties, largely because it includes a calibration sub-algorithm that inherently adapts the mapping to the specific hand and glove, without need for measuring the hand and without regard for goodness of fit. The algorithm utilizes a forward-kinematics model of the glove derived from documentation provided by the manufacturer of the glove. In this case, forward-kinematics model signifies a mathematical model of the glove fingertip positions as functions of the sensor readings. More specifically, given the sensor readings, the forward-kinematics model calculates the glove fingertip positions in a Cartesian reference frame nominally attached to the palm. The algorithm also utilizes an inverse-kinematics model of the robot hand. In this case, inverse-kinematics model signifies a mathematical model of the robot finger-joint angles as functions of the robot fingertip positions. Again, more specifically, the inverse-kinematics model calculates the finger-joint commands needed to place the fingertips at specified positions in a Cartesian reference frame that is attached to the palm of the robot hand and that nominally corresponds to the Cartesian reference frame attached to the palm of the glove. Initially, because of the aforementioned uncertainties, the glove fingertip positions calculated by the forwardkinematics model in the glove Cartesian reference frame cannot be expected to match the robot fingertip positions in the robot-hand Cartesian reference frame. A calibration must be performed to make the glove and robot-hand fingertip positions correspond more precisely. The calibration procedure involves a few simple hand poses designed to provide well-defined fingertip positions. One of the poses is a fist. In each of the other poses, a finger touches the thumb. The calibration subalgorithm uses the sensor readings from these poses to modify the kinematical models to make the two sets of fingertip positions agree more closely.
Goza, Michael↗
Latent Twins
Over the past decade, scientific machine learning has transformed the development of mathematical and computational frameworks for analyzing, modeling, and predicting complex systems. From inverse problems to numerical partial differential equations (PDEs), dynamical systems, and model reduction, these advances have pushed the boundaries of what can be simulated. Yet they have often progressed in parallel, with representation learning and algorithmic solution methods evolving largely as separate pipelines. With Latent Twins, we propose a unifying mathematical framework that creates a hidden surrogate in latent space for the underlying equations. Whereas digital twins mirror physical systems in the digital world, Latent Twins mirror mathematical systems in a learned latent space governed by operators. Through this lens, classical modeling, inversion, model reduction, and operator approximation all emerge as special cases of a single principle. We establish the fundamental approximation properties of Latent Twins for both ordinary differential equations (ODEs) and PDEs and demonstrate the framework across three representative settings: (i) canonical ODEs, capturing diverse dynamical regimes; (ii) a PDE benchmark using the shallow-water equations, contrasting Latent Twin simulations with deep operator network and forecasts with a four-dimensional variational method baseline; and (iii) a challenging real-data geopotential reanalysis dataset, reconstructing and forecasting from sparse, noisy observations. Latent Twins provide a compact, interpretable surrogate for solution operators that evaluate across arbitrary time gaps in a single-shot, while remaining compatible with scientific pipelines such as assimilation, control, and uncertainty quantification. Looking forward, this framework offers scalable, theory-grounded surrogates that bridge data-driven representation learning and classical scientific modeling across disciplines.
Latent Twins↗
Non-Thermal Hard X-Ray Emission in Galaxy Clusters Observed with the BeppoSAX PDS
We study the X-ray emission in a Sample of galaxy clusters using the BeppoSAX PDS instrument in the 20 - 80 keV energy band. We estimate the non-thermal hard X-ray cluster emission (HXR) by modeling the thermal contribution from the cluster gas and the non-thermal contamination from the unobscured AGN in the clusters. We also evaluate the systematic uncertainties due to the background fluctuations. Assuming negligible contamination from the obscured AGN, the resulting non-thermal component is detected at a 2 sigma level in approx. 50% of the non-significantly AGN-contaminated clusters: A2142, A2199, A2256, A3376, Coma, Ophiuchus and Virgo. The data are consistent with a scenario whereby relaxed clusters have no hard X-ray component of non-thermal origin, whereas merger clusters do. The co-added spectrum of the above clusters indicates a power-law spectrum for the HXR with a photon index of 2.8+0.3-0.4 in the 12 - 115 keV band, and we find indication that it has extended distribution. These indications argue against significant contamination from obscured AGN, which have harder spectra and centrally concentrated distribution. These results are supportive of the assumption of the merger shock acceleration of electrons in clusters, which has been proposed as a possible origin of the non-thermal hard X-ray emission models. Assuming that the Cosmic Microwave Background photons experience Inverse Compton scattering from the merger-accelerated relativistic electrons, and thus produce the observed HXR, the measured hard X-ray slope corresponds to a differential momentum spectra of the relativistic electrons with a slope of mu = 3.8 - 5.0. In presence of cluster magnetic fields this relativistic electron population produces synchrotron emission with a spectral index of 1.4 - 2.1, consistent with radio halo observations of merger clusters. Thus both hard X-ray and radio observations of merger clusters are consistent with the Inverse Compton model. The observed slope of HXR is also consistent with that predicted by the non-thermal bremsstrahlung, which chus cannot be ruled by the fit to the current data, even though this model requires an extreme, untenable cluster energetics. Assuming centrally concentrated distribution of HXR, the data requires a harder slope for the HXR spectrum, which is consistent with secondary electron models, but this model yields a worse fit to the PDS data and thus seems to be disfavored over the primary electron Inverse Compton model.
Nevalainen, J.↗
Inversion of canopy reflectance models for estimation of vegetation parameters
One of the keys to successful remote sensing of vegetation is to be able to estimate important agronomic parameters like leaf area index (LAI) and biomass (BM) from the bidirectional canopy reflectance (CR) data obtained by a space-shuttle or satellite borne sensor. One approach for such an estimation is through inversion of CR models which relate these parameters to CR. The feasibility of this approach was shown. The overall objective of the research carried out was to address heretofore uninvestigated but important fundamental issues, develop the inversion technique further, and delineate its strengths and limitations.
Goel, Narendra S.↗
Linearization of manipulator dynamics using spatial operators
Linearized dynamics models for manipulators are useful in robot analysis, motion planning, and control applications. Techniques from the spatial operator algebra are used to obtain closed form operator expressions for two types of linearized dynamics models, the linearized inverse and forward dynamics models. Spatially recursive algorithms of O(n) and O(n-squared) complexity for the computation of the perturbation vector and coefficient matrices for the linearized inverse dynamics model are developed first. Subsequently, operator factorization and inversion identities are used to develop corresponding closed-form expressions for the linearized forward dynamics model (LFDM). Once again, these are used to develop algorithms of O(n) and O(n-squared) complexity for the computation of the perturbation vector and the coefficient matrices. The algorithms for the LFDM do not require the explicit computation of the mass matrix nor its numerical inversion and are also of lower complexity than the conventional O(n-cubed) algorithms.
Jain, A.↗
Flight instrument and telemetry response and its inversion
Mathematical models of rate gyros, servo accelerometers, pressure transducers, and telemetry systems were derived and their parameters were obtained from laboratory tests. Analog computer simulations were used extensively for verification of the validity for fast and large input signals. An optimal inversion method was derived to reconstruct input signals from noisy output signals and a computer program was prepared.
Weinberger, M. R.↗