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DOE OSTI2025

Basic Research Needs for Inverse Methods for Complex Systems under Uncertainty

Inverse problems, which aim to infer unknown properties of a system using experimental and observational data, are central to addressing many of the U.S. Department of Energy’s (DOE) most critical scientific and engineering challenges. Accurate, computationally efficient, and data-efficient solutions to inverse problems are essential for advancing DOE mission-critical science drivers, including analyzing data from large-scale experimental facilities, optimizing fusion reactor performance, accelerating materials discovery, enhancing geophysical imaging, improving wildfire predictions, and enabling autonomous systems and digital twins. However, these problems are becoming increasingly complex, often involving nonlinear, highdimensional, and interconnected systems and models that span multiple physics and scales, while relying on data with varying quantity, quality, and information content. Compounding these challenges is the uncertainty inherent in DOE-relevant systems, where errors in inputs, noise in data, incompleteness of data, and discrepancies between models and reality constrain the accuracy and precision of solutions. At the same time, the convergence of recent scientific computing trends—scientific machine learning, artificial intelligence, and computing advances such as exascale computing—is creating unprecedented opportunities for tackling these challenges. The cross-cutting nature of inverse problems, combined with their growing complexity and rapidly evolving data and algorithmic demands, strongly motivates the formulation of a prioritized research agenda to maximize their capabilities and impact. In response to this need, DOE’s Advanced Scientific Computing Research (ASCR) program in the Office of Science convened the Workshop on Basic Research Needs for Inverse Problems for Complex Systems Under Uncertainty in June 2025. This workshop brought together experts across disciplines to identify grand challenges and major opportunities in the field. Through collaborative discussions, the workshop defined transformative research directions aimed at addressing the mathematical, statistical, and computational challenges posed by inverse problems under uncertainty. As a result of these efforts, four priority research directions (PRDs) were identified to guide future research and development in this area. These PRDs, summarized below, represent a roadmap for advancing the foundational science and mathematics of inverse problems, enabling robust, scalable, and uncertainty-aware solutions that are critical for DOE applications.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Rapid wavefield forecasting for earthquake early warning via deep sequence to sequence learning

We propose a deep learning model, WaveCastNet, to forecast high-dimensional wavefields. WaveCastNet integrates a convolutional long expressive memory architecture into a sequence-to-sequence forecasting framework, enabling it to model long-term dependencies and multiscale patterns in both space and time. By sharing weights across spatial and temporal dimensions, WaveCastNet requires significantly fewer parameters than more resource-intensive models such as transformers, resulting in faster inference times. Crucially, WaveCastNet also generalizes better than transformers to rare and critical seismic scenarios, such as high-magnitude earthquakes. Here, we show the ability of the model to predict the intensity and timing of destructive ground motions in real time, using simulated data from the San Francisco Bay Area. Furthermore, we demonstrate its zero-shot capabilities by evaluating WaveCastNet on real earthquake data. Our approach does not require estimating earthquake magnitudes and epicenters, steps that are prone to error in conventional methods, nor does it rely on empirical ground-motion models, which often fail to capture strongly heterogeneous wave propagation effects.

Geophysics↗

DOE OSTI2024

Electromagnetic inversion for a baseline conductivity model at the Kemper CarbonSAFE site

Geophysics is one component of a successful monitoring strategy for carbon storage sites. Seismic surveys are a common element of these strategies, with repeat surveys occurring about every 5 years. However, seismic is expensive, the sensitivity to CO2 saturation is limited, and it requires a large footprint on the surface (Yurikov et al., 2022). Electromagnetic (EM) methods offer repeat surveys at a significantly lower cost, the ability to utilize airborne methods to increase coverage, and potentially provide enough information to increase the time between seismic surveys. Specifically, we focus on semi-airborne EM, with a grounded dipole transmitter, and airborne magnetic field receivers as described and modeled in Kohnke et al. (2023).

Kohnke, Colton↗

NASA NTRS2010

Evaluation of Shortwave Infrared Atmospheric Correction for Ocean Color Remote Sensing of Chesapeake Bay

The NASA Moderate Resolution Imaging Spectroradiometer onboard the Aqua platform (MODIS-Aqua) provides a viable data stream for operational water quality monitoring of Chesapeake Bay. Marine geophysical products from MODIS-Aqua depend on the efficacy of the atmospheric correction process, which can be problematic in coastal environments. The operational atmospheric correction algorithm for MODIS-Aqua requires an assumption of negligible near-infrared water-leaving radiance, nL(sub w)(NIR). This assumption progressively degrades with increasing turbidity and, as such, methods exist to account for non-negligible nL(sub w)(NIR) within the atmospheric correction process or to use alternate radiometric bands where the assumption is satisfied, such as those positioned within shortwave infrared (SWIR) region of the spectrum. We evaluated a decade-long time-series of nL(sub w)(lambda) from MODIS-Aqua in Chesapeake Bay derived using NIR and SWIR bands for atmospheric correction. Low signal-to-noise ratios (SNR) for the SWIR bands of MODIS-Aqua added noise errors to the derived radiances, which produced broad, flat frequency distributions of nL(sub w)(lambda) relative to those produced using the NIR bands. The SWIR approach produced an increased number of negative nL(sub w)(lambda) and decreased sample size relative to the NIR approach. Revised vicarious calibration and regional tuning of the scheme to switch between the NIR and SWIR approaches may improve retrievals in Chesapeake Bay, however, poor SNR values for the MODIS-Aqua SWIR bands remain the primary deficiency of the SWIR-based atmospheric correction approach.

Werdell, P. Jeremy↗

NASA NTRS1990

Satellite laser ranging and geological constraints on plate motion

Satellite laser ranging (SLR) observed baseline rates of change were measured and compared with rates determined from sea floor spreading rates and directions, and earth-quake solutions. With the number of years of observation now over six for many of the baselines, the inaccuracy of determining baseline rates of change has diminished so that in some cases it is less than a few mm per year. Thus, a direct comparison between baseline rates of change and rates of change established using geophysical information (called geological rates) is now feasible. In most cases, there is good agreement between the rates determined from SLR and geological rates, but in some cases there appear to be discrepancies. These discrepancies involve many of the data for which one end of the baseline is either Quincy (California), Huahine (French Polynesia), or Simosato (Japan). A method for looking at the discrepancies for these SLR observatories has been devised which makes it possible to calculate the motion not modeled by the geologic information.

Harrison, C. G. A.↗

NASA NTRS2009

Planetary Geologic Mapping Handbook - 2009

Geologic maps present, in an historical context, fundamental syntheses of interpretations of the materials, landforms, structures, and processes that characterize planetary surfaces and shallow subsurfaces (e.g., Varnes, 1974). Such maps also provide a contextual framework for summarizing and evaluating thematic research for a given region or body. In planetary exploration, for example, geologic maps are used for specialized investigations such as targeting regions of interest for data collection and for characterizing sites for landed missions. Whereas most modern terrestrial geologic maps are constructed from regional views provided by remote sensing data and supplemented in detail by field-based observations and measurements, planetary maps have been largely based on analyses of orbital photography. For planetary bodies in particular, geologic maps commonly represent a snapshot of a surface, because they are based on available information at a time when new data are still being acquired. Thus the field of planetary geologic mapping has been evolving rapidly to embrace the use of new data and modern technology and to accommodate the growing needs of planetary exploration. Planetary geologic maps have been published by the U.S. Geological Survey (USGS) since 1962 (Hackman, 1962). Over this time, numerous maps of several planetary bodies have been prepared at a variety of scales and projections using the best available image and topographic bases. Early geologic map bases commonly consisted of hand-mosaicked photographs or airbrushed shaded-relief views and geologic linework was manually drafted using mylar bases and ink drafting pens. Map publishing required a tedious process of scribing, color peel-coat preparation, typesetting, and photo-laboratory work. Beginning in the 1990s, inexpensive computing, display capability and user-friendly illustration software allowed maps to be drawn using digital tools rather than pen and ink, and mylar bases became obsolete. Terrestrial geologic maps published by the USGS now are primarily digital products using geographic information system (GIS) software and file formats. GIS mapping tools permit easy spatial comparison, generation, importation, manipulation, and analysis of multiple raster image, gridded, and vector data sets. GIS software has also permitted the development of project-specific tools and the sharing of geospatial products among researchers. GIS approaches are now being used in planetary geologic mapping as well (e.g., Hare and others, 2009). Guidelines or handbooks on techniques in planetary geologic mapping have been developed periodically (e.g., Wilhelms, 1972, 1990; Tanaka and others, 1994). As records of the heritage of mapping methods and data, these remain extremely useful guides. However, many of the fundamental aspects of earlier mapping handbooks have evolved significantly, and a comprehensive review of currently accepted mapping methodologies is now warranted. As documented in this handbook, such a review incorporates additional guidelines developed in recent years for planetary geologic mapping by the NASA Planetary Geology and Geophysics (PGG) Program s Planetary Cartography and Geologic Mapping Working Group s (PCGMWG) Geologic Mapping Subcommittee (GEMS) on the selection and use of map bases as well as map preparation, review, publication, and distribution. In light of the current boom in planetary exploration and the ongoing rapid evolution of available data for planetary mapping, this handbook is especially timely.

Tanaka, K. L.↗

NASA NTRS2010

Planetary Geologic Mapping Handbook - 2010

Geologic maps present, in an historical context, fundamental syntheses of interpretations of the materials, landforms, structures, and processes that characterize planetary surfaces and shallow subsurfaces. Such maps also provide a contextual framework for summarizing and evaluating thematic research for a given region or body. In planetary exploration, for example, geologic maps are used for specialized investigations such as targeting regions of interest for data collection and for characterizing sites for landed missions. Whereas most modern terrestrial geologic maps are constructed from regional views provided by remote sensing data and supplemented in detail by field-based observations and measurements, planetary maps have been largely based on analyses of orbital photography. For planetary bodies in particular, geologic maps commonly represent a snapshot of a surface, because they are based on available information at a time when new data are still being acquired. Thus the field of planetary geologic mapping has been evolving rapidly to embrace the use of new data and modern technology and to accommodate the growing needs of planetary exploration. Planetary geologic maps have been published by the U.S. Geological Survey (USGS) since 1962. Over this time, numerous maps of several planetary bodies have been prepared at a variety of scales and projections using the best available image and topographic bases. Early geologic map bases commonly consisted of hand-mosaicked photographs or airbrushed shaded-relief views and geologic linework was manually drafted using mylar bases and ink drafting pens. Map publishing required a tedious process of scribing, color peel-coat preparation, typesetting, and photo-laboratory work. Beginning in the 1990s, inexpensive computing, display capability and user-friendly illustration software allowed maps to be drawn using digital tools rather than pen and ink, and mylar bases became obsolete. Terrestrial geologic maps published by the USGS now are primarily digital products using geographic information system (GIS) software and file formats. GIS mapping tools permit easy spatial comparison, generation, importation, manipulation, and analysis of multiple raster image, gridded, and vector data sets. GIS software has also permitted the development of projectspecific tools and the sharing of geospatial products among researchers. GIS approaches are now being used in planetary geologic mapping as well. Guidelines or handbooks on techniques in planetary geologic mapping have been developed periodically. As records of the heritage of mapping methods and data, these remain extremely useful guides. However, many of the fundamental aspects of earlier mapping handbooks have evolved significantly, and a comprehensive review of currently accepted mapping methodologies is now warranted. As documented in this handbook, such a review incorporates additional guidelines developed in recent years for planetary geologic mapping by the NASA Planetary Geology and Geophysics (PGG) Program's Planetary Cartography and Geologic Mapping Working Group's (PCGMWG) Geologic Mapping Subcommittee (GEMS) on the selection and use of map bases as well as map preparation, review, publication, and distribution. In light of the current boom in planetary exploration and the ongoing rapid evolution of available data for planetary mapping, this handbook is especially timely.

Tanaka, K. L.↗

NASA NTRS2012

A Localized Ensemble Kalman Smoother

Numerous geophysical inverse problems prove difficult because the available measurements are indirectly related to the underlying unknown dynamic state and the physics governing the system may involve imperfect models or unobserved parameters. Data assimilation addresses these difficulties by combining the measurements and physical knowledge. The main challenge in such problems usually involves their high dimensionality and the standard statistical methods prove computationally intractable. This paper develops and addresses the theoretical convergence of a new high-dimensional Monte-Carlo approach called the localized ensemble Kalman smoother.

recursive estimation↗

DOE OSTI2024

Quantitative kinetic rules for plastic strain-induced α - ω phase transformation in Zr under high pressure

Plastic strain-induced phase transformations (PTs) and chemical reactions under high pressure are broadly spread in modern technologies, friction and wear, geophysics, and astrogeology. However, because of very heterogeneous fields of plastic strain $E$ p and stress σ tensors and volume fraction c of phases in a sample compressed in a diamond anvil cell (DAC) and impossibility of measurements of σ and $E$ p , there are no strict kinetic equations for them. Here, we develop a kinetic model, finite element method (FEM) approach, and combined FEM-experimental approaches to determine all fields in strongly plastically predeformed Zr compressed in DAC, and specific kinetic equation for α-ω PT consistent with experimental data for the entire sample. Since all fields in the sample are very heterogeneous, data are obtained for numerous complex 7D paths in the space of 3 components of the plastic strain tensor and 4 components of the stress tensor. Kinetic equation depends on accumulated plastic strain (instead of time) and pressure and is independent of plastic strain and deviatoric stress tensors, i.e., it can be applied for various above processes. Our results initiate kinetic studies of strain-induced PTs and provide efforts toward more comprehensive understanding of material behavior in extreme conditions.

36 MATERIALS SCIENCE↗

NASA NTRS1990

Sedimentary Facies Analysis Using AVIRIS Data: A Geophysical Inverse Problem

AVIRIS data can be used to quantitatively analyze and map sedimentary lithofacies. The observed radiance spectra can be reduced to 'apparent reflectance' spectra by topographic and reflectance characterization of several field sites within the image. These apparent reflectance spectra correspond to the true reflectance at each pixel, multiplied by an unknown illumination factor (ranging in value from zero to one). The spatial abundance patterns of spectrally defined lithofacies and the unknown illumination factors can be simultaneously derived using constrained linear spectral unmixing methods. Estimates of the minimum uncertainty in the final results (due to noise, instrument resolutions, degree of illumination and mixing systematics) can be made by forward and inverse modeling. Specific facies studies in the Rattlesnake Hills region of Wyoming illustrate the successful application of these methods.

Boardmann, Joe W.↗

DOE OSTI2025

Multi-frequency progressive refinement for learned inverse scattering

Interpreting scattered acoustic and electromagnetic wave patterns is a computational task that enables remote imaging in a number of important applications, including medical imaging, geophysical exploration, sonar and radar detection, and nondestructive testing of materials. However, accurately and stably recovering an inhomogeneous medium from far-field scattered wave measurements is a computationally difficult problem, due to the nonlinear and non-local nature of the forward scattering process. We design a neural network, called Multi-Frequency Inverse Scattering Network (MFISNet), and a training method to approximate the inverse map from far-field scattered wave measurements at multiple frequencies. We consider three variants of MFISNet, with the strongest performing variant inspired by the recursive linearization method — a commonly used technique for stably inverting scattered wavefield data — that progressively refines the estimate with higher frequency content. MFISNet outperforms past methods in regimes with high-contrast, heterogeneous large objects, and inhomogeneous unknown backgrounds.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1985

Starlette geodynamics - The earth's tidal response

The French Starlette satellite, launched in 1975, had the primary geophysical objective of providing information regarding 'solid' earth and ocean tides. The present paper is concerned with an analysis of the 1980 Starlette laser-ranging data for tides, geodetic parameters, and orbital parameters. The obtained solution represents a simultaneous least squares solution based upon normal equations constructed from seventy 5-day orbital arcs. It is pointed out that this new method has produced far better tidal results than would be achievable on the basis of the previous long periodic mean orbit evolution approach described by Felsentreger et al. (1979). It was possible to recover reasonable tidal values for periods on the Starlette orbit ranging from 6 days to over 90 days.

Williamson, R. G.↗

DOE OSTI2024

Sensitivity of Fine‐Resolution Urban Heat Island Simulations to Soil Moisture Parameterization

ABSTRACT Urban areas experience the impact of natural disasters, such as heatwaves and flash floods, disparately in different neighbourhoods across a city. The demand for precise urban hydrometeorological and hydroclimatological modelling to examine this disparity, and the interacting challenges posed by climate change and urbanisation, has thus surged. The Weather Research and Forecasting (WRF) model has served such operational and research purposes for decades. Recent advancements in WRF, including enhanced numerical schemes and sophisticated urban atmospheric‐hydrological parameterizations, have empowered the simulation of urban geophysical processes at high resolution (~1 km), but even this resolution misses significant urban microclimate variability. This study applies the large‐eddy simulations (LES) mode within WRF, coupled with single‐layer urban canopy models (SLUCM), to enable even finer‐scale modelling (150 m) of the Urban Heat Island (UHI) effect in the Baltimore metropolitan area. We run nine scenarios to evaluate various methods of initializing soil moisture and various spinup lead times, and to assess the impact of WRF's Mosaic approach in depicting subgrid‐scale processes. We evaluate the scenarios by comparing the WRF simulated land surface temperature (LST) against Landsat LST and the WRF simulated hourly 2‐m air temperatures (AT) with observations from eight weather stations across the domain. Results underscore the paramount influence of the lead spinup time on the spatiotemporal distribution of simulated soil moisture, consequently shaping WRF's efficacy in predicting the UHI. Furthermore, interpolating soil moisture‐related parameters from the parent for child domain initialization yields a notable reduction in mean and root‐mean‐squared errors. This improvement was particularly evident in simulations with the longest spinup time, affirming the importance of carefully designing the initialization of soil moisture for improved urban temperature predictions.

Talebpour, Mahdad↗

DOE OSTI2024

Rethinking materials simulations: Blending direct numerical simulations with neural operators

Abstract Materials simulations based on direct numerical solvers are accurate but computationally expensive for predicting materials evolution across length- and time-scales, due to the complexity of the underlying evolution equations, the nature of multiscale spatiotemporal interactions, and the need to reach long-time integration. We develop a method that blends direct numerical solvers with neural operators to accelerate such simulations. This methodology is based on the integration of a community numerical solver with a U-Net neural operator, enhanced by a temporal-conditioning mechanism to enable accurate extrapolation and efficient time-to-solution predictions of the dynamics. We demonstrate the effectiveness of this hybrid framework on simulations of microstructure evolution via the phase-field method. Such simulations exhibit high spatial gradients and the co-evolution of different material phases with simultaneous slow and fast materials dynamics. We establish accurate extrapolation of the coupled solver with large speed-up compared to DNS depending on the hybrid strategy utilized. This methodology is generalizable to a broad range of materials simulations, from solid mechanics to fluid dynamics, geophysics, climate, and more.

36 MATERIALS SCIENCE↗

NASA NTRS2018

Investigating a Firn Aquifer near Helheim Glacier (South-Eastern Greenland) with Magnetic Resonance Soundings and Ground-Penetrating Radar

We apply the magnetic resonance sounding (MRS) method to investigate a firn aquifer in the south-east region of the Greenland ice sheet. Our study aims to delineate and estimate the volume of the recently discovered water stored within the firn (compacted snow) that remains liquid throughout the year. We develop and test successfully amethodology for joint use of MRS and ground-penetrating radar (GPR). This noninvasive geophysical approach is particularly well-adapted to glacier conditions and has a promising future for in situ investigation of water distribution in glaciers. At our field site, MRS showed an aquifer located at variable depths between 20 and 30 m beneath the ice-sheet surface. At the monitoring site, both MRS and GPR show an increase in the water volume stored between April 2015 and July 2016. MRS estimates suggest that the volume increased by approximately 28%.

meltwater↗

NASA NTRS1991

Laboratory and theoretical models of planetary-scale instabilities and waves

Meteorologists and planetary astronomers interested in large-scale planetary and solar circulations recognize the importance of rotation and stratification in determining the character of these flows. The two outstanding problems of interest are: (1) the origins and nature of chaos in baroclinically unstable flows; and (2) the physical mechanisms responsible for high speed zonal winds and banding on the giant planets. The methods used to study these problems, and the insights gained, are useful in more general atmospheric and climate dynamic settings. Because the planetary curvature or beta-effect is crucial in the large scale nonlinear dynamics, the motions of rotating convecting liquids in spherical shells were studied using electrohydrodynamic polarization forces to generate radial gravity and centrally directed buoyancy forces in the laboratory. The Geophysical Fluid Flow Cell (GFFC) experiments performed on Spacelab 3 in 1985 were analyzed. The interpretation and extension of these results have led to the construction of efficient numerical models of rotating convection with an aim to understand the possible generation of zonal banding on Jupiter and the fate of banana cells in rapidly rotating convection as the heating is made strongly supercritical. Efforts to pose baroclinic wave experiments for future space missions using a modified version of the 1985 instrument have led us to develop theoretical and numerical models of baroclinic instability. Some surprising properties of both these models were discovered.

Hart, John E.↗

NASA NTRS1989

Selection of optimum median-filter-based ambiguity removal algorithm parameters for NSCAT

The NASA Scatterometer, NSCAT, is an active spaceborne radar designed to measure the normalized radar backscatter coefficient (sigma0) of the ocean surface. These measurements can, in turn, be used to infer the surface vector wind over the ocean using a geophysical model function. Several ambiguous wind vectors result because of the nature of the model function. A median-filter-based ambiguity removal algorithm will be used by the NSCAT ground data processor to select the best wind vector from the set of ambiguous wind vectors. This process is commonly known as dealiasing or ambiguity removal. The baseline NSCAT ambiguity removal algorithm and the method used to select the set of optimum parameter values are described. An extensive simulation of the NSCAT instrument and ground data processor provides a means of testing the resulting tuned algorithm. This simulation generates the ambiguous wind-field vectors expected from the instrument as it orbits over a set of realistic meoscale wind fields. The ambiguous wind field is then dealiased using the median-based ambiguity removal algorithm. Performance is measured by comparison of the unambiguous wind fields with the true wind fields. Results have shown that the median-filter-based ambiguity removal algorithm satisfies NSCAT mission requirements.

Shaffer, Scott↗

NASA NTRS1995

Visual interface for space and terrestrial analysis

The management of large geophysical and celestial data bases is now, more than ever, the most critical path to timely data analysis. With today's large volume data sets from multiple satellite missions, analysts face the task of defining useful data bases from which data and metadata (information about data) can be extracted readily in a meaningful way. Visualization, following an object-oriented design, is a fundamental method of organizing and handling data. Humans, by nature, easily accept pictorial representations of data. Therefore graphically oriented user interfaces are appealing, as long as they remain simple to produce and use. The Visual Interface for Space and Terrestrial Analysis (VISTA) system, currently under development at the Naval Research Laboratory's Backgrounds Data Center (BDC), has been designed with these goals in mind. Its graphical user interface (GUI) allows the user to perform queries, visualization, and analysis of atmospheric and celestial backgrounds data.

Dombrowski, Edmund G.↗