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DOE OSTI2025

Demonstrate new plasticity models for doped UO 2 that capture dislocation mechanisms

In light water reactors, fuel vendors are investigating the use of dopants to modify the properties of UO 2 pellets, with the goal of improving pellet-cladding mechanical interactions during operation. Dopants are expected to ‘soften’ the pellets; that is, the doped pellets have higher plastic deformation than conventional UO 2 . This leads to a reduction in the severity of mechanical pellet-cladding interactions, helping to reduce the hoop strain on the cladding. By minimizing the strain exerted by the pellet on the cladding, it is anticipated that cladding performance under accident conditions can be enhanced (i.e., lowering the risk of burst during a LOCA). Dopants such as chromium (Cr) promote grain growth during pellet fabrication, leading to larger grains; therefore, understanding the link between chemistry, microstructure and mechanical deformation (enhanced creep rates) behavior of UO 2 is critical to helping operators further substantiate the benefits of doping UO 2 . Historically, the nuclear energy industry has relied on empirical models to make assessments of performance. Compared to empirical models, mechanistic physics-based models provide benefits, such as, fewer data points for validation and better extrapolation where experimental data is scarce or non-existent. In this report, Bayesian inference techniques have been applied to a previously developed lower length-scale-informed diffusional creep model. The objective is to i) infer lower-length-scale parameter distributions from available experiment and then ii) determine the uncertainties in the measurable quantity (in this case creep rates) after propagating the inferred lower length scale parameter uncertainties. The approach requires many evaluations of the model, which becomes computationally insurmountable; therefore, a neural-network model is trained to data obtained by sampling the full model over the most important parameters. This neural-network is then used in the Bayesian inference approach to determine probability distributions in the parameter values that represent the uncertainty in the model given what is known from the experiments (posterior). A significant reduction compared to conservative initial (prior) uncertainties is achieved through inference against the experimental data, demonstrating the efficacy of this approach. Furthermore, by accounting for uncertainties in the experimental conditions and sample non-stoichiometry, it is possible to resolve apparent discrepancies in experimental measurements within a self-consistent grain boundary (Coble) creep model that is sensitive to chemistry. This work has been written up and submitted to Nuclear Technology for a special issue on accelerated fuel qualification (AFQ). This uncertainty quantification (UQ) work not only improves the diffusional model, while accounting for uncertainty, but also establishes a framework which can readily be applied to the mechanistic models of dislocation deformation developed in this study. The most likely values from the Bayesian analysis are incorporated into our UO 2 diffusional creep model and a lower length scale-informed irradiation UO 2 creep mechanistic model to generate a dataset. This dataset has been provided to our INL collaborators for training an artificial neural network surrogate model, which will be implemented in the BISON fuel performance code to assess how the results differ from those currently obtained using a fully empirical model and that of using the nominal (uncalibrated) atomic scale parameters in our mechanistic model. Plastic deformation (creep and glide) in UO 2 is a complex phenomenon, governed by multiple underlying processes such as local defect concentrations, applied stresses, and microstructural characteristics. Consequently, there is a need for a meso-scale model with polycrystalline resolution capable of extrapolating to large grain sizes applicable to doped UO 2 , where data is limited and the model can help bridge the knowledge gap. By integrating atomistic data into the polycrystal LApx code, it becomes possible to predict dislocation climb and glide plasticity that simple analytical models cannot accurately represent. The application of atomic-scale data within LApx demonstrated the importance of climb and glide mechanisms in reproducing high-stress UO 2 behavior. Behaviors such as this are crucial to capture and implement in BISON, as parts of the fuel pellet can reach temperatures where glide can occur before pellet cracking. This model which captures dislocation based mechanisms for UO 2 is then used to stand up the doped model accounting for larger grain sizes. It was found that larger grain sizes can lead to enhanced deformation rates in the glide regime, and therefore can help with the pellet cladding mechanical interaction. Therefore if the fuel pellet reaches conditions (stress/temperature) where glide is active, the enhanced creep rates for larger grains in the glide regime (doped UO 2 ) can help with pellet cladding mechanical interactions. Plastic deformation in UO 2 involves multiple mechanisms, including diffusional creep, dislocation climb, and glide. This milestone contains two parts: (1) UQ of a pre-existing lower length scale informed mechanistic diffusional creep model, and (2) development of a new LApx based model for dislocation-mediated creep mechanisms in UO 2 , with application to large-grain doped UO 2 .

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2025

Ensemble‐Based Spatially Distributed CLM5 Hydrological Parameter Estimation for the Continental United States

Abstract One of the major challenges in large‐domain hydrological modeling efforts lies in the estimation of spatially distributed hydrological parameters while simultaneously accounting for their associated uncertainties. Addressing this challenge is particularly difficult in ungauged locations. With growing societal demands for large‐scale streamflow projections to inform water resource management and long‐term planning, evaluating and constraining hydrological parameter uncertainty is increasingly vital. This study introduces a hybrid regionalization approach to enhance hydrological predictions of the Community Land Model version 5 (CLM5) across the Continental United States (CONUS), with a total of 50,629 1/8° grid cells. This hybrid method combines the strengths of two existing techniques: parameter regionalization and streamflow signature regionalization. It identifies ensemble behavioral parameters for each 1/8° grid cell across the CONUS domain, tailored to three distinct streamflow signatures focused on low flows, high flows, and annual water balance. Evaluating this hybrid method for 464 CAMELS (Catchment Attributes and Meteorology for Large‐sample Studies) basins demonstrates a significant improvement in CLM5 hydrological predictions, even in challenging arid regions. In CONUS applications, the derived spatially distributed parameter sets capture both spatial continuity and variation of parameters, highlighting their heterogeneous nature within specific regions. Overall, this hybrid regionalization approach offers a promising solution to the complex task of improving hydrological modeling over large domains for important hydrological applications.

CLM5↗

DOE OSTI2025

$\mathrm{SageNet}$: Fast Neural Network Emulation of the Stiff-amplified Gravitational Waves from Inflation

Accurate modeling of the inflationary gravitational waves (GWs) requires time-consuming, iterative numerical integrations of differential equations to take into account their backreaction on the expansion history. To improve computational efficiency while preserving accuracy, we present the Stiff-amplified Gravitational-wave Emulator Network (SageNet), a deep learning framework designed to replace conventional numerical solvers (code available at https://github.com/YifangLuo/SageNet). SageNet employs a long short-term memory architecture to emulate the present-day energy density spectrum of the inflationary GWs with possible stiff amplification, Ω GW (f). Trained on a data set of 25,689 numerically generated solutions, SageNet allows accurate reconstructions of Ω GW (f) and generalizes well to a wide range of cosmological parameters; 90.9% of the test emulations with randomly distributed parameters exhibit errors of under 4%. In addition, SageNet demonstrates its ability to learn and reproduce the artificial, adaptive sampling patterns in numerical calculations, which implement denser sampling of frequencies around changes in spectral indices in Ω GW (f). The dual capability of learning both physical and artificial features of the numerical GW spectra establishes SageNet as a robust alternative to exact numerical methods. Finally, our benchmark tests show that SageNet reduces the computation time from tens of seconds to milliseconds, achieving a speedup of ∼10 4 times over standard CPU-based numerical solvers with the potential for further acceleration on GPU hardware. These capabilities make SageNet a powerful tool for accelerating Bayesian inference procedures for extended cosmological models. In a broad sense, the SageNet framework offers a fast, accurate, and generalizable solution to modeling cosmological observables whose theoretical predictions demand costly differential equation solvers.

Astronomy data modeling↗

DOE OSTI2024

Distributed quantum sensing of multiple phases with fewer photons

Abstract Distributed quantum metrology has drawn intense interest as it outperforms the optimal classical counterparts in estimating multiple distributed parameters. However, most schemes so far have required entangled resources consisting of photon numbers equal to or more than the parameter numbers, which is a fairly demanding requirement as the number of nodes increases. Here, we present a distributed quantum sensing scenario in which quantum-enhanced sensitivity can be achieved with fewer photons than the number of parameters. As an experimental demonstration, using a two-photon entangled state, we estimate four phases distributed 3 km away from the central node, resulting in a 2.2 dB sensitivity enhancement from the standard quantum limit. Our results show that the Heisenberg scaling can be achieved even when using fewer photons than the number of parameters. We believe our scheme will open a pathway to perform large-scale distributed quantum sensing with currently available entangled sources.

Science & Technology - Other Topics↗

DOE OSTI2026

Modelling the Sensitivity of Yukon River Biogeochemical Dynamics to Environmental and Chemical Drivers: Implications for Dissolved Organic Carbon

Riverine dissolved organic carbon (DOC) is a critical biogeochemical component that transmits information from Arctic soils to the Arctic Ocean, significantly influencing carbon dynamics in this unique ecosystem. As DOC travels downstream, it undergoes transformations that alter its composition and fate. The Yukon River serves as an effective testbed for modelling these dynamics, offering sufficient scale to capture key biogeochemical processes while having a simpler hydrology than other major Arctic rivers, as well as long-term DOC observational data for model validation. To investigate DOC transformations during transit in the Yukon River, we adapted our Arctic Riverine Organic Macromolecular Model by applying regional-specific parameterisations. Our model simulates the transport and transformation of 15 organic macromolecules, including CDOM (coloured dissolved organic matter), proteins, polysaccharides, lipids, lignin phenols, and humic substances. Initial DOC concentrations were derived from observed soil organic carbon stocks in the surrounding watershed, while chemical transformations and hydrological dynamics were modelled along the river's course. Sensitivity and uncertainty analyses were conducted using a Monte Carlo approach under two experimental setups. Results revealed that variability in DOC and CDOM concentrations at the river mouth were predominantly driven by initial DOC concentration (~70% of variability explained) and dilution at confluence points (~10%). The refractory fraction of DOC explained 21%–88% of the variability in 14 macromolecular concentrations and ranked in the top five sensitive parameters for all outputs when a uniform parameter distribution was assumed. However, when a more likely variability was applied to this parameter, its influence on DOC and CDOM decreased. Given that refractory DOC accounts for ~80% of total DOC in Arctic Rivers, this suggests that most DOC resists degradation and retains its chemical composition during transport to the coastal environment. River velocity, which determines residence time, explained 8%–47% of the variability in protein, polysaccharide, lipid, pigments, and lignin phenols at the river mouth. In contrast, chemical turnover times contributed only 1%–5% to output variability. Our findings underscore the need for improved land-specific headwater observations, including seasonal soil moisture and lateral transport dynamics that control the initial tributary-specific DOC inputs. With accelerated permafrost thaw and increasing river discharge, extending our model to other Arctic River systems and seasons will enhance understanding of Arctic riverine carbon fluxes and their contributions to the Arctic Ocean.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Astrometric microlensing probes of the isolated neutron star population with Roman

Notoriously hard to detect and study, isolated neutron stars (NSs) might provide valuable answers to fundamental questions about stellar evolution and explosion physics. With the upcoming Roman Space Telescope, scheduled for launch in 2026, a new and powerful channel for their detection will become available: astrometric microlensing. We set out to create a realistic sample of simulated gravitational microlensing events as observed by Roman with the Galactic Bulge Time Domain Survey. We focus in particular on the population of NS lenses, which has until now been largely understudied. We used dedicated Galactic models tailored for application to microlensing by compact objects. In addition to populations of stars, white dwarfs, and black holes, we simulated four different NS populations with Maxwellian natal kick distributions: v = (150, 250, 350, 450) km/s. For each simulation, we applied projected Roman precision, cadence, and detectability criteria. We found that the parameter space log10 t E –log 10 θ E , which will be accessible to Roman observations, is efficient for the classification of stellar remnants. We found a feature in this space that is characteristic of NSs; using this feature, optimal samples of NS candidates can be constructed from Roman -like datasets. We describe the dependence of the observable parameter distributions on the assumed mean kick velocities. As the effects of natal kicks are very complex and mutually counteracting, we suggest that more detailed studies focused on the dynamics of NSs are needed in anticipation of Roman and future surveys. We estimate that Roman will observe approximately 11 000 microlensing events, including ~100 with NS lenses, whose photometric and astrometric signals are detectable; the event yield decreases by 38% when gap-filling low-cadence observations are not included. We make all simulated microlensing event datasets publicly available in preparation for Roman data.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Simulation Studies on the Interactions of Electron Beam with Wastewater

The manufactured chemical pollutants, like 1,4 dioxane and PFAS (per- and polyfluroralkyl substances), found in the underground water and/or drinking water are challenging to be removed or biodegraded. Energetic electrons are capable of mediating and removing them. This paper utilizes FLUKA code to evaluate the beam-wastewater interaction effects with different energy, space and divergence distributions of the electron beam. With 8 MeV average energy, the electron beam exits from a 0.0127 cm thick titanium window, travels through a 4.3 cm distance air and a second 0.0127 cm thick stainless water container window with 2.43 cm radius, and finally is injected into the water area, where the volume of water is around 75 cubic cm. The distribution parameters of the electron beam are from the GPT (General Particle Tracer) simulations for UITF (Upgraded Injector Test Facility) in Jefferson lab. By varying the distributions, several measurements including the dose (or energy deposition) distribution, electron fluence, photon fluence are scored and compared. Taking the comparisons into consideration, this paper is aiming to find better electron beams for the wastewater irradiation.

Li, X.↗

DOE OSTI2022

Updates and Validation for the n+ 63,65 Cu Cross Sections [Slides]

The RRR and URR parameters for 63,65 Cu have been optimized to transmission and capture data. Several data sets have been newly incorporated in this evaluation. The angular distribution parameters have been adopted from differential measurements, as was done in ENDF/B-V. The performance of this evaluation in the integral benchmark calculations is favorable, and the validation is ongoing.

07 ISOTOPE AND RADIATION SOURCES↗

DOE OSTI2021

Simulation Studies on the Interactions of Electron Beam with Wastewater

Li, X.↗

DOE OSTI2024

The Aemulus Project. VI. Emulation of Beyond-standard Galaxy Clustering Statistics to Improve Cosmological Constraints

Abstract There is untapped cosmological information in galaxy redshift surveys in the nonlinear regime. In this work, we use the Aemulus suite of cosmological N -body simulations to construct Gaussian process emulators of galaxy clustering statistics at small scales (0.1–50 h −1 Mpc) in order to constrain cosmological and galaxy bias parameters. In addition to standard statistics—the projected correlation function w p ( r p ), the redshift-space monopole of the correlation function ξ 0 ( s ), and the quadrupole ξ 2 ( s )—we emulate statistics that include information about the local environment, namely the underdensity probability function P U ( s ) and the density-marked correlation function M ( s ). This extends the model of Aemulus III for redshift-space distortions by including new statistics sensitive to galaxy assembly bias. In recovery tests, we find that the beyond-standard statistics significantly increase the constraining power on cosmological parameters of interest: including P U ( s ) and M ( s ) improves the precision of our constraints on Ω m by 27%, σ 8 by 19%, and the growth of structure parameter, f σ 8 , by 12% compared to standard statistics. We additionally find that scales below ∼6 h −1 Mpc contain as much information as larger scales. The density-sensitive statistics also contribute to constraining halo occupation distribution parameters and a flexible environment-dependent assembly bias model, which is important for extracting the small-scale cosmological information as well as understanding the galaxy–halo connection. This analysis demonstrates the potential of emulating beyond-standard clustering statistics at small scales to constrain the growth of structure as a test of cosmic acceleration.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Joint estimation of biogeochemical model parameters from multiple experiments: A bayesian approach applied to mercury methylation

Here, to characterize complex biogeochemical systems, results from multiple experiments, where each targets a specific subprocess, are commonly combined. The resulting datasets are interpreted through the calibration of biogeochemical models for process inference and predictions. Commonly used calibration approaches of fitting datasets from individual experiments to subprocess models one at a time is prone to missing information shared between datasets and incomplete uncertainty propagation. We propose a Bayesian joint-fitting scheme addressing the above-mentioned concerns by jointly fitting all the available datasets, thus calibrating the entire biogeochemical model in one go using Markov Chain Monte Carlo (MCMC). The identification of null spaces in the parameter distributions from MCMC guided the simplification of certain subprocess models. For example, fast kinetic sorption was replaced by equilibrium sorption, and Monod demethylation was replaced by first-order demethylation. Joint fitting of datasets resulted in complete uncertainty propagation with parameter estimates informed by all available data.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Revisiting constraints on asymmetric dark matter from collapse in white dwarf stars

The runaway collapse phase of a small dark matter cluster inside a white dwarf star encompasses a reversible stage, where heat can be transferred back and forth between nuclear and dark matter. Induced nuclear burning phases are stable and early carbon depletion undermines previous claims of type Ia supernova ignition. Instead, mini black holes are formed at the center of the star that either evaporate or accrete stellar material until a macroscopic sub-Chandrasekhar-mass black hole is formed. In the latter case, a 0.1 to 1 second lasting electromagnetic transient signal can be detected upon ejection of the white dwarf’s potential magnetic field. Binary systems that transmute to black holes and subsequently merge emit gravitational waves. Advanced LIGO should detect one such sub-Chandrasekhar binary black hole inspiral per year, while future Einstein telescope-like facilities will detect thousands per year. The effective spin parameter distribution is peaked at 0.2 and permits future studies to disentangle from primordial sub-Chandrasekhar black holes. Such signatures are compatible with current direct detection constraints, as well as with neutron star constraints in the case of bosonic dark matter, even though they remain in conflict with the fermionic case for part of the parameter space.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Parameter uncertainties for imperfect surrogate models in the low-noise regime

Abstract Bayesian regression determines model parameters by minimizing the expected loss, an upper bound to the true generalization error. However, this loss ignores model form error, or misspecification, meaning parameter uncertainties are significantly underestimated and vanish in the large data limit. As misspecification is the main source of uncertainty for surrogate models of low-noise calculations, such as those arising in atomistic simulation, predictive uncertainties are systematically underestimated. We analyze the true generalization error of misspecified, near-deterministic surrogate models, a regime of broad relevance in science and engineering. We show that posterior parameter distributions must cover every training point to avoid a divergence in the generalization error and design a compatible ansatz which incurs minimal overhead for linear models. The approach is demonstrated on model problems before application to thousand-dimensional datasets in atomistic machine learning. Our efficient misspecification-aware scheme gives accurate prediction and bounding of test errors in terms of parameter uncertainties, allowing this important source of uncertainty to be incorporated in multi-scale computational workflows.

Swinburne, Thomas D. (ORCID:0000000232554257)↗

DOE OSTI2022

The Novel Scaling of Tsallis Parameters from the Transverse Momentum Spectra of Charged Particles in Heavy-Ion Collisions

The transverse momentum (pT) spectra of charged particles measured in Au + Au collisions from the beam energy scan (BES) program, Cu + Cu collisions at sNN=62.4, 200 GeV at the RHIC and Pb + Pb, Xe + Xe collisions at the LHC are investigated in the framework of Tsallis thermodynamics. The theory can describe the experimental data well for all the collision systems, energies and centralities investigated. The collision energy and centrality dependence of the Tsallis distribution parameters, i.e., the temperature T and the nonextensive parameter q, for the A + A collisions are also studied and discussed. A novel scaling between the temperature divided by the natural logarithm of collision energy (T/lns) and the nonextensive parameter q is presented.

Tao, Junqi↗

DOE OSTI2021

Validation Metrics for Fixed Effects and Mixed-Effects Calibration

The modern scientific process often involves the development of a predictive computational model. To improve its accuracy, a computational model can be calibrated to a set of experimental data. A variety of validation metrics can be used to quantify this process. Some of these metrics have direct physical interpretations and a history of use, while others, especially those for probabilistic data, are more difficult to interpret. In this work, a variety of validation metrics are used to quantify the accuracy of different calibration methods. Frequentist and Bayesian perspectives are used with both fixed effects and mixed-effects statistical models. Through a quantitative comparison of the resulting distributions, the most accurate calibration method can be selected. Two examples are included which compare the results of various validation metrics for different calibration methods. It is quantitatively shown that, in the presence of significant laboratory biases, a fixed effects calibration is significantly less accurate than a mixed-effects calibration. This is because the mixed-effects statistical model better characterizes the underlying parameter distributions than the fixed effects model. The results suggest that validation metrics can be used to select the most accurate calibration model for a particular empirical model with corresponding experimental data.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Candidate strongly lensed type Ia supernovae in the Zwicky Transient Facility archive

Gravitationally lensed type Ia supernovae (glSNe Ia) are unique astronomical tools that can be used to study cosmological parameters, distributions of dark matter, the astrophysics of the supernovae, and the intervening lensing galaxies themselves. A small number of highly magnified glSNe Ia have been discovered by ground-based telescopes such as the Zwicky Transient Facility (ZTF), but simulations predict that a fainter, undetected population may also exist. We present a systematic search for glSNe Ia in the ZTF archive of alerts distributed from June 1 2019 to September 1 2022. Using the AMPEL platform, we developed a pipeline that distinguishes candidate glSNe Ia from other variable sources. Initial cuts were applied to the ZTF alert photometry (with constraints on the peak absolute magnitude and the distance to a catalogue-matched galaxy, as examples) before forced photometry was obtained for the remaining candidates. Additional cuts were applied to refine the candidates based on their light curve colours, lens galaxy colours, and the resulting parameters from fits to the SALT2 SN Ia template. The candidates were also cross-matched with the DESI spectroscopic catalogue. Seven transients were identified that passed all the cuts and had an associated galaxy DESI redshift, which we present as glSN Ia candidates. Although superluminous supernovae (SLSNe) cannot be fully rejected as contaminants, two events, ZTF19abpjicm and ZTF22aahmovu, are significantly different from typical SLSNe and their light curves can be modelled as two-image glSN Ia systems. From this two-image modelling, we estimate time delays of 22 ± 3 and 34 ± 1 days for the two events, respectively, which suggests that we have uncovered a population of glSNe Ia with longer time delays. The pipeline is efficient and sensitive enough to parse full alert streams. It is currently being applied to the live ZTF alert stream to identify and follow-up future candidates while active. This pipeline could be the foundation for glSNe Ia searches in future surveys, such as the Rubin Observatory Legacy Survey of Space and Time.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Efficacy of a portable, moderate-resolution, fast-scanning differential mobility analyzer for ambient aerosol size distribution measurements

Abstract. Ambient aerosol size distributions obtained with a compact scanning mobility analyzer, the “Spider” differential mobility analyzer (DMA), are compared to those obtained with a conventional mobility analyzer, with specific attention to the effect of mobility resolution on the measured size distribution parameters. The Spider is a 12 cm diameter radial differential mobility analyzer that spans the 10–500 nm size range with 30 s mobility scans. It achieves its compact size by operating at a nominal mobility resolution R=3 (sheath flow = 0.9 L min−1; aerosol flow = 0.3 L min−1) in place of the higher ratio of sheath flow to aerosol flow commonly used. The question addressed here is whether the lower resolution is sufficient to capture key characteristics of ambient aerosol size distributions. The Spider, operated at R=3 with 30 s up- and downscans, was co-located with a TSI 3081 long-column mobility analyzer, operated at R=10 with a 360 s sampling duty cycle. Ambient aerosol data were collected over 26 consecutive days of continuous operation, in Pasadena, CA. Over the 17–500 nm size range, the two instruments exhibit excellent correlation in the total particle number concentrations and geometric mean diameters, with regression slopes of 1.13 and 1.00, respectively. Our results suggest that particle sizing at a lower resolution than typically employed may be sufficient to obtain key properties of ambient size distributions, at least for these two moments of the size distribution. Moreover, it enables better counting statistics, as the wider transfer function for a given aerosol flow rate results in a higher counting rate.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

System and method for reasoning about the optimality of a configuration parameter of a distributed system

Embodiments provide a system and method for reasoning about the optimality of a configuration parameter of a distributed system. During operation, the system obtains a multi-layer graph for a system with a plurality of components, wherein the multi-layer graph comprises a configuration subgraph, a vulnerability subgraph, and a dependency subgraph. The system determines, based on the multi-layer graph, constraint relationships associated with configuration parameters for the components, wherein the constraint relationships include security constraints and functionality constraints. The system computes an unsatisfiable core which comprises a set of mutually incompatible constraints. The system resolves, based on a strategy and over multiple iterations, the unsatisfiable core by analyzing one pair of mutually incompatible constraints per a respective iteration, to obtain a new unsatisfiable core which comprises a smaller number of mutually incompatible constraints than the computed unsatisfiable core or a previously computed unsatisfiable core from a most recent iteration.

Soroush, Hamed↗