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DOE OSTI2025

GenAI4UQ: A software for forward and inverse uncertainty quantification using conditional generative AI

We introduce GenAI4UQ, a software package for forward and inverse uncertainty quantification in model calibration, parameter estimation, and ensemble forecasting. GenAI4UQ leverages a generative AI-based conditional modeling framework to address limitations of traditional inverse modeling techniques, such as Markov Chain Monte Carlo (MCMC) methods. By replacing computationally intensive iterative processes with a direct, learned mapping, GenAI4UQ enables efficient calibration of input parameters and generation of predictions directly from observations. The software supports rapid ensemble forecasting with robust uncertainty quantification while maintaining computational and storage efficiency. Built-in auto-tuning of hyperparameters simplifies model training, ensuring accessibility for users with varying expertise. Its versatile conditional generative framework is applicable across diverse scientific domains. While GenAI4UQ offers significant advantages in flexibility and efficiency, users should interpret its uncertainty estimates with caution in data-sparse scenarios, as the model may overestimate uncertainty—an effect common to all surrogate-based approaches including MCMC with surrogate models. Despite this, GenAI4UQ transforms inverse modeling by providing a fast, reliable, and user-friendly solution. It empowers researchers and practitioners to quickly estimate parameter distributions and generate model predictions for new observations, facilitating efficient decision-making and advancing the state of uncertainty quantification in computational modeling.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Construction of Inverse Metal–Zeolite Interfaces via Area-Selective Atomic Layer Deposition

The spatial confinement at metal–zeolite interfaces offers a powerful knob to steer the selectivity of chemical reactions on metal catalysts. However, encapsulating metal catalysts into small-pore zeolites remains a challenging task. Here, we demonstrate an inverse design of metal–zeolite interfaces, “metal-on-zeolite,” constructed by area-selective atomic layer deposition. This inverse design bypasses the intrinsic synthetic issues associated with metal encapsulation, offering a potential solution for the fabrication of task-specific metal–zeolite interfaces for desired catalytic applications. Infrared spectroscopy and several probe reactions confirmed the spatial confinement effects at the inverse metal–zeolite interfaces.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Double-Atom Catalysts Featuring Inverse Sandwich Structure for CO 2 Reduction Reaction: A Synergetic First-Principles and Machine Learning Investigation

Electrocatalytic CO 2 reduction reactions (CO 2 RR) based on scalable and highly efficient catalysis provide an attractive strategy for reducing CO 2 emissions. Here in this work, we combined first-principles density functional theory (DFT) and machine learning (ML) to comprehensively explore the potential of double-atom catalysts (DACs) featuring an inverse sandwich structure anchored on defective graphene (gra) to catalyze CO 2 RR to generate C 1 products. We started with five homonuclear M 2 ⊥gra (M = Co, Ni, Rh, Ir, and Pt), followed by 127 heteronuclear MM'⊥gra (M = Co, Ni, Rh, Ir, and Pt, M' = Sc–Au). Stable DACs were screened by evaluating their binding energy, formation energy, and dissolution potential of metal atoms, as well as conducting first-principles molecular dynamics simulations with and without solvent water molecules. Based on DFT calculations, Rh 2 ⊥gra DAC was found to outperform the other four homonuclear DACs and the Rh-based single- and double-atom catalysts of noninverse sandwich structures. Out of the 127 heteronuclear DACs, 14 were found to be stable and have good catalytic performance. An ML approach was adopted to correlate key factors with the activity and stability of the DACs, including the sum of radii of metal and ligand atoms (d M–M' , d M–C , and d M'–C ), the sum and difference of electronegativity of two metal atoms (P M + P M' , P M – P M '), the sum and difference of first ionization energy of two metal atoms (I M + I M' , I M – I M '), the sum and difference of electron affinity of two metal atoms (A M + A M' , A M – A M '), and the number of d-electrons of the two metal atoms (Nd). The obtained ML models were further used to predict 154 potential electrocatalysts out of 784 possible DACs featuring the same inverse sandwich configuration. Overall, this work not only identified promising CO 2 RR DACs featuring the reported inverse sandwich structure but also provided insights into key atomic characteristics associated with high CO 2 RR activity.

30 DIRECT ENERGY CONVERSION↗

DOE OSTI2026

Interfacial Inversion of Stealth Surfactants

Amphiphilic macromolecular surfactants segregate to liquid–liquid interfaces, thereby reducing the interfacial tension and free energy. Here, we investigated “stealth surfactants” in the form of core–shell bottlebrush polymers comprised of pH-responsive diblock copolymer side chains forming a hydrophilic core and a hydrophobic shell, enabling solubility in oil. At liquid–liquid interfaces, these polymers undergo a structural “inversion”, with hydrophilic blocks segregating into the aqueous phase and hydrophobic blocks residing in the oil phase. The reconfiguration kinetics and surfactant properties are influenced by multiple factors, including the molecular weights of the backbone and side chain components, the hydrophilic-to-hydrophobic balance of the side chains, and the pH of the aqueous phase. An observed nonmonotonic dependence of interfacial tension with time is attributed to a progressive structural inversion, where the projected area of the macromolecule onto the interface decreases. To validate this inversion hypothesis, interfacial properties were characterized by sum-frequency generation vibrational spectroscopy, which revealed configurational changes of the core–shell bottlebrush polymers at the fluid interface and revealed a pH-dependent interfacial coverage. Coarse-grained molecular dynamics simulations supported these experimental findings, showing that the pH-responsive core and hydrophobic shell assume a time-averaged configuration with orientations parallel and perpendicular to the plane of the interface, respectively. These findings open routes to design multistimuli-responsive polymeric surfactants and compatibilizers, expanding their potential applications in advanced interfacial systems.

Stealth surfactants↗

DOE OSTI2021

Adjoint-Based Inversion of Geodetic Data for Sources of Deformation and Strain

An adjoint-based formulation leads to a particularly efficient approach for inverting geodetic measurements for the source of the deformation. Specifically, the quantities necessary to iteratively improve the fit to the observations can be computed with just three forward calculations, one to obtain the current residuals, another to solve the adjoint problem, and a third to compute the step length. An inversion algorithm utilizing the adjoint-based gradient is applied to a set of Interferometric Synthetic Aperture Radar (InSAR) data gathered between 2016 and 2018 over the Tulare Basin in California's Central Valley. Because the measured deformation is due to groundwater withdrawal, a penalty function is included in the inversion to avoid placing aquifer volume change in locations that are far from any documented wells. The solution of the inverse problem provides estimates of aquifer compaction that provide a match to the observed range changes while honoring the well data. The solution indicates an average aquifer volume loss of 2.17 km 3 /year over the two year period from January 2016 to January 2018, encompassing one drought year (2016) and one wet year (2017). Finally, this magnitude of lost volume is compatible with the 3.1 km 3 /year decrease in water volume for the entire Central Valley, estimated from GRACE satellite gravity data.

58 GEOSCIENCES↗

DOE OSTI2022

Controlling inversion disorder in a stoichiometric spinel magnet

In the study of frustrated quantum magnets, it is essential to be able to control the nature and degree of site disorder during the growth process, as many measurement techniques are incapable of distinguishing between site disorder and frustration-induced spin disorder. Pyrochlore-structured spinel oxides can serve as model systems of geometrically frustrated three-dimensional quantum magnets; however, the nature of the magnetism in one well-studied spinel, ZnFe 2 O 4 , remains unclear. Here, we demonstrate simultaneous control of both stoichiometry and inversion disorder in the growth of ZnFe 2 O 4 single crystals, directly yielding a revised understanding of both the collective spin behavior and lattice symmetry. Crystals grown in the stoichiometric limit with minimal site inversion disorder contravene all the previously suggested exotic spin phases in ZnFe 2 O 4 . Furthermore, the structure is confirmed on the F$\bar{4}$3m space group with broken inversion symmetry that induces antiferroelectricity. The effective tuning of magnetic behavior by site disorder in the presence of robust antiferroelectricity makes ZnFe 2 O 4 of special interest to multiferroic devices.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Inversion technique to obtain local ion temperature profiles for an axisymmetric plasma with toroidal and radial velocities

A matrix inversion technique is derived to calculate local ion temperature from line-integrated measurements of an extended emission source in an axisymmetric plasma which exactly corrects for both toroidal velocity and radial velocity components. Local emissivity and toroidal velocity can be directly recovered from line-integrated spectroscopic measurements, but an independent measurement of the radial velocity is necessary to complete the temperature inversion. The extension of this technique to handle the radial velocity is relevant for magnetic reconnection and merging compression devices where temperature inversion from spectroscopic measurements is desired. A simulation demonstrates the effects of radial velocity on the determination of ion temperature.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2026

Implementation of Pfirsch–Schlüter parallel flow in x-ray imaging crystal spectrometer inversion analysis

The x-ray imaging crystal spectrometer (XICS) tomographic inversion code for Wendelstein 7-X (W7-X) has been modified to consider the effects of parallel flows and has been applied to analyze measurements taken during recent experimental campaigns. Previous analysis neglected the effects of parallel flows due to the primarily perpendicular geometry of the sightlines and the small magnitude predicted by neoclassical theory. To reconsider these effects, the incompressibility condition for plasma flows is used to calculate the parallel Pfirsch–Schlüter flow component for the equilibrium configuration. By incorporating this condition along with the geometry of the sightlines—i.e. the fractional contributions of perpendicular and parallel flows—, an updated expression for the measured flow is used for the profile inversion. Application of this modified inversion code to data from W7-X shows that the magnitude of the radial electric field and the flux surface averaged perpendicular flow are reduced by approximately a factor of 2 and brought into better agreement with neoclassical predictions and charge exchange recombination spectroscopy measurements.

Pfirsch–Schlüter flows↗

DOE OSTI2025

Coefficient-to-Basis Network: a fine-tunable operator learning framework for inverse problems with adaptive discretizations and theoretical guarantees

We propose a Coefficient-to-Basis Network (C2BNet), a novel framework for solving inverse problems within the operator learning paradigm. C2BNet efficiently adapts to different discretizations through fine-tuning, using a pre-trained model to significantly reduce computational cost while maintaining high accuracy. Unlike traditional approaches that require retraining from scratch for new discretizations, our method enables seamless adaptation without sacrificing predictive performance. Furthermore, we establish theoretical approximation and generalization error bounds for C2BNet by exploiting low-dimensional structures in the underlying datasets. Our analysis demonstrates that C2BNet adapts to low-dimensional structures without relying on explicit encoding mechanisms, highlighting its robustness and efficiency. To validate our theoretical findings, we conducted extensive numerical experiments that showcase the superior performance of C2BNet on several inverse problems. The results confirm that C2BNet effectively balances computational efficiency and accuracy, making it a promising tool to solve inverse problems in scientific computing and engineering applications.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Multiscale Data-Driven Seismic Full-Waveform Inversion With Field Data Study

Seismic full-waveform inversion (FWI), which uses iterative methods to estimate high-resolution subsurface models from seismograms, is a powerful imaging technique in exploration geophysics. In recent years, the computational cost of FWI has grown exponentially due to the increasing size and resolution of seismic data. Moreover, it is a nonconvex problem and can encounter local minima due to the limited accuracy of the initial velocity models or the absence of low frequencies in the measurements. To overcome these computational issues, we develop a multiscale data-driven FWI method based on fully convolutional networks (FCNs). In preparing the training data, we first develop a real-time style transform method to create a large set of synthetic subsurface velocity models from natural images. We then develop two convolutional neural networks with encoder-decoder structures to reconstruct the low- and high-frequency components of the subsurface velocity models, separately. To validate the performance of our data-driven inversion method and the effectiveness of the synthesized training set, we compare it with conventional physics-based waveform inversion approaches using both synthetic and field data. Finally, these numerical results demonstrate that, once our model is fully trained, it can significantly reduce the computation time and yield more accurate subsurface velocity models in comparison with conventional FWI.

58 GEOSCIENCES↗

DOE OSTI2021

Inverse Biot–Savart Optimization for Superconducting Accelerator Magnets

Superconducting (SC) magnets for accelerator concepts are often synthesized by numerically optimizing magnetic field waveforms, a process that requires a subsequent solution of a constrained inverse problem to identify suitable SC magnet windings. When the desired field distribution is intuitive, the inverse process is facilitated by seeding preconceived coil distributions into design optimization methods for refinement. With more complex magnetic field distributions, an initial design may be unknown, and topology optimization tools are required to synthesize current distributions without a priori guidance from a subject matter expert. In this work, we develop a constrained inverse Biot-Savart topology optimization methodology that synthesizes optimal distributions of current density in racetrack-like SC coils. The problem structure is exploited through a computationally efficient quadratic programming formulation, and the method is applied to recently published magnetic field waveforms for a recirculating proton phase shifter, a proton therapy gantry, and dipole magnets with sharp field transitions. The method and results herein identify novel winding configurations that can help magnet designers bring accelerator concepts to fruition.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

A Framework for Inverse Prediction Using Functional Response Data

Inverse prediction models have commonly been developed to handle scalar data from physical experiments. However, it is not uncommon for data to be collected in functional form. When data are collected in functional form, it must be aggregated to fit the form of traditional methods, which often results in a loss of information. For expensive experiments, this loss of information can be costly. In this study, we introduce the functional inverse prediction (FIP) framework, a general approach which uses the full information in functional response data to provide inverse predictions with probabilistic prediction uncertainties obtained with the bootstrap. The FIP framework is a general methodology that can be modified by practitioners to accommodate many different applications and types of data. We demonstrate the framework, highlighting points of flexibility, with a simulation example and applications to weather data and to nuclear forensics. Results show how functional models can improve the accuracy and precision of predictions.

42 ENGINEERING↗

DOE OSTI2021

Inversion technique to obtain local ion temperature profiles for an axisymmetric plasma with toroidal and radial velocities

ion temperature↗

DOE OSTI2022

Acoustic Impedance Inversions for Offshore CO 2 Storage: South Georgia Embayment, United States

This study builds and expands on previous CO 2 storage resource assessment studies of the southeastern offshore Atlantic margin by providing a detailed evaluation on how rock porosities and permeabilities are distributed across the Upper Cretaceous strata restricted to the South Georgia Embayment (SGE). Using legacy industry two-dimensional seismic reflection and well data, this assessment is the first application of multiple seismic inversion techniques in this area. This workflow provides a reliable and repeatable model-based inversion which gives an improved image to discriminate lithology and predict porosity. The workflow is applicable to future CO 2 storage resource assessment studies elsewhere. The inversion results indicate that distinct porosity and permeability regimes are present and distributed in the Upper Cretaceous strata within the SGE. The impedance and porosity relationships show well-founded and reliable correlation. These relationships reveal low impedance coincident to the high porosity intervals which are proposed as potential reservoir intervals for CO 2 storage. In addition, the result shows that the Upper Cretaceous strata have two main potential reservoirs in the lower part. These are overlain by a thick impermeable interval, mostly shale, which has high impedance, low porosity, and low permeability and extends within the SGE. This result is in agreement with a previous study that also proposed two significant storage reservoirs for CO 2 in the Upper Cretaceous strata. Since porosity distribution is estimated using multiple methods, it follows the trends of seismic signature and structures of the Upper Cretaceous strata. The extracted values of porosity, ranging from 15 to 36%, and permeability, ranging from 1 to 100 mD, are close to the measured values from the well core data at the Upper Cretaceous strata interval.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

Geometry of conformal manifolds and the inversion formula

Families of conformal field theories are naturally endowed with a Riemannian geometry which is locally encoded by correlation functions of exactly marginal operators. We show that the curvature of such conformal manifolds can be computed using Euclidean and Lorentzian inversion formulae, which combine the operator content of the conformal field theory into an analytic function. Analogously, operators of fixed dimension define bundles over the conformal manifold whose curvatures can also be computed using inversion formulae. These results relate curvatures to integrated four-point correlation functions which are sensitive only to the behavior of the theory at separated points. We apply these inversion formulae to derive convergent sum rules expressing the curvature in terms of the spectrum of local operators and their three-point function coefficients. We further show that the curvature can smoothly diverge only if a conserved current appears in the spectrum, or if the theory develops a continuum. We verify our results explicitly in 2d examples. In particular, for 2d (2,2) superconformal field theories we derive a lower bound on the scalar curvature, which is saturated by free theories when the central charge is a multiple of three.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

A combined experimental and numerical approach that eliminates the non-uniqueness associated with the Johnson-Cook parameters obtained using inverse methods

Abstract Johnson-Cook constitutive model is a commonly used material model for machining simulations. The model includes five parameters that capture the initial yield stress, strain-hardening, strain-rate hardening, and thermal softening behavior of the material. These parameters are difficult to determine using experiments since the conditions observed during machining (such as high strain-rates of the order of $$10^5$$ 10 5 /sec - $$10^6$$ 10 6 /sec) are challenging to recreate in the laboratory. To address this problem, several researchers have recently proposed inverse approaches where a combination of experiments and analytical models are used to predict the Johnson-Cook parameters. The errors between the measured cutting forces, chip thicknesses and temperatures and those predicted by analytical models are minimized and the parameters are determined. In this work, it is shown that only two of the five Johnson-Cook parameters can be determined uniquely using inverse approaches. Two different algorithms, namely, Adaptive Memory Programming for Global Optimization (AMPGO) and Particle Swarm Optimization (PSO), are used for this purpose. The extended Oxley’s model is used as the analytical tool for optimization. For determining a parameter’s value, a large range for each parameter is provided as an input to the algorithms. The algorithms converge to several different sets of values for the five Johnson-Cook parameters when all the five parameters are considered as unknown in the optimization algorithm. All of these sets, however, yield the same chip shape and cutting forces in FEM simulations. Further analyses show that only the strain-rate and thermal softening parameters can be determined uniquely and the three parameters present in the strain-hardening term of the Johnson-Cook model cannot be determined uniquely using the inverse method. A combined experimental and numerical approach is proposed to eliminate this determine all parameters uniquely.

42 ENGINEERING↗

DOE OSTI2024

Monitoring spatiotemporal evolution of fractures during hydraulic stimulations at the first EGS collab testbed using anisotropic elastic-waveform inversion

The EGS Collab project acquired continuous active-source seismic monitoring (CASSM) data before, during, and after hydraulic stimulations at the first testbed at the depth of 4850 ft (1478 m) at the Sanford Underground Research Facility in Lead, South Dakota, for monitoring fracture creation and evolution. CASSM acquisition was conducted using 24 hydrophones, 18 accelerometers, and 17 piezoelectric sources within four fracture-parallel wells and two orthogonal wells. 3D anisotropic traveltime tomography and anisotropic elastic-waveform inversion of the campaign cross-borehole seismic data show that the rock within the stimulation region is a heterogeneous horizontal transverse isotropic medium. Here we use these inversion results as the initial models and apply 3D anisotropic first-arrival traveltime tomography and 3D anisotropic elastic-waveform inversion to the CASSM data acquired after each stimulation in May, 2018 and December, 2018. We observe the spatiotemporal evolution of seismic velocities and anisotropic parameters caused by hydraulic fracture stimulations, showing the regions of rock alternation caused by hydraulic fracture stimulation.

15 GEOTHERMAL ENERGY↗

DOE OSTI2025

Time inversion symmetry in the Dirac and Schrödinger-Pauli theories

The Schrödinger-Pauli theory is generally believed to give a faithful representation of the nonrelativistic and weakly relativistic limit of the Dirac theory. However, the Schrödinger-Pauli theory is fundamentally incomplete in its account of broken time inversion symmetry, e.g., in magnetically ordered systems. Here, in the Dirac theory of the electron, magnetic order breaks time inversion symmetry even in the nonrelativistic limit, whereas time inversion symmetry is effectively preserved in the Schrödinger-Pauli theory in the absence of spin-orbit coupling. In the Dirac theory, the Berry curvature $1/(2m^2 c^2)$ is thus an intrinsic property of nonrelativistic electrons similar to the well-known spin magnetic moment $e\hbar/(2m)$, while this result is missed by the nonrelativistic or weakly relativistic Schrödinger-Pauli equation. In ferromagnetically ordered systems, the intrinsic Berry curvature yields a contribution to the anomalous Hall conductivity independent of spin-orbit coupling.

Winkler, R. [Northern Illinois Univ., DeKalb, IL (↗