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DOE OSTI2025

Karhunen–Loève deep learning method for surrogate modeling and approximate Bayesian parameter estimation

We evaluate the performance of the Karhunen-Loève Deep Neural Network (KL-DNN) framework for surrogate modeling and approximate Bayesian parameter estimation in partial differential equation models. In the surrogate model, the Karhunen-Loève (KL) expansions are used for the dimensionality reduction of the number of unknown parameters and variables, and a deep neural network is employed to relate the reduced space of parameters to that of the state variables. The KL-DNN surrogate model is used to formulate a maximum-a-posteriori-like least-squares problem, which is randomized to draw samples of the posterior distribution of the parameters. We test the proposed framework for a hypothetical unconfined aquifer via comparison with the forward MODFLOW and inverse PEST++ iterative ensemble smoother (IES) solutions as well as the state-of-the-art Fourier neural operator (FNO) and deep operator networks (DeepONets) operator learning surrogate models. Our results show that the KL-DNN surrogate model outperforms FNO and DeepONet for forward predictions. For solving inverse problems, the randomized algorithm provides the same or more accurate Bayesian predictions of the parameters than IES as evidenced by the higher log-predictive probability of both the estimated parameter field and the forecast hydraulic head. The posterior mean obtained from the randomized algorithm is closer to the reference parameter field than that obtained with FNO as the maximum a posteriori estimate.

Approximate Bayesian inference↗

DOE OSTI2021

Multi-device Studies of Pedestal Physics and Confinement in the I-mode Regime

This paper describes joint ITPA studies of the I-mode regime, which features an edge thermal barrier but with L-mode-like particle and impurity transport, and without ELMs. The regime has been demonstrated on Alcator C-Mod, ASDEX Upgrade and DIII-D tokamaks, over a wide range of device parameters and pedestal conditions, including low collisionality. Access to I-mode is independent of heating method (neutral beam injection, ICRH and/or ECRH). Normalized energy confinement H98y,2 ≥ 1 has been achieved for a range of 3≤q95≤4.9 and scales favourably with power. Changes in turbulence in the pedestal region accompany the transition from L-mode to I-mode. The L-I threshold increases with plasma density and current, and with device size, but weakly with BT. The upper limit of power for I-modes increases with toroidal field, and is largest on Alcator C-Mod at B > 5 T. Issues for extrapolation to ITER and other future fusion devices are discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Stellarator optimization for good magnetic surfaces at the same time as quasisymmetry

A method is demonstrated to optimize a stellarator's geometry to eliminate magnetic islands and achieve other desired physics properties at the same time. For many physics quantities that have been used in stellarator optimization, including quasisymmetry, neoclassical transport, and magnetohydrodynamic stability, it is convenient to use a magnetic equilibrium representation that assures the existence of magnetic surfaces. However, this representation hides the possible presence of magnetic islands, which are typically undesirable. To include both surface-based objectives and island widths in a single optimization, two fixed-boundary equilibrium calculations are run at each iteration of the optimization: one that enforces the existence of magnetic surfaces (the Variational Moments Equilibrium Code) [S. P. Hirshman and J. C. Whitson, Phys. Fluids 26, 3553 (1983)] and one that does not (the Stepped Pressure Equilibrium Code) [Hudson et al., Phys. Plasmas 19, 112502 (2012)]. By penalizing the island residues in the objective function, the two magnetic field representations are brought into agreement during the optimization. Here, an example is presented in which, particularly on the surface where quasisymmetry was targeted, quasisymmetry is achieved more accurately than in previously published examples.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Simulating self-powered neutron detector responses to infer burnup-induced power distribution perturbations in next-generation light water reactors

Understanding how 3D power distribution will be monitored throughout reactor core volumetric space in next-generation nuclear power reactors is crucial to the design, deployment, and licensing of these reactors. Although numerous techniques exist for 3D power distribution monitoring based on the response of both in situ and ex situ sensors currently implemented or proposed for use in the US reactor fleet, crucial details about these techniques are often unclear. The publicly available documentation does not include information such as how well these techniques are characterized and optimized in their implementations and the levels of uncertainty in the inferred 3D power distribution. The work described herein investigated a recently developed 3D power distribution inferencing method as applied to two next-generation reactor simulations: (1) the NuScale small modular reactor design and (2) the Westinghouse AP1000 design, both of which contain in-core strings of vanadium self-powered neutron detectors (SPNDs). This investigation considered a range of SPND string sensor densities, as well as a range of 3D power distribution axial segment sizes. In this work, SPND response simulation is informed by neutron flux calculations in representative homogenized cores. For the different sensor densities and power distribution axial segment sizes in these simulations, the average solution error, solver iterations, and run time were tracked to parameterize the sensor-core configuration.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2021

Encoder–decoder neural network for solving the nonlinear Fokker–Planck–Landau collision operator in XGC

An encoder–decoder neural network has been used to examine the possibility for acceleration of a partial integro-differential equation, the Fokker–Planck–Landau collision operator. This is part of the governing equation in the massively parallel particle-in-cell code XGC, which is used to study turbulence in fusion energy devices. The neural network emphasizes physics-inspired learning, where it is taught to respect physical conservation constraints of the collision operator by including them in the training loss, along with the ℓ 2 loss. In particular, network architectures used for the computer vision task of semantic segmentation have been used for training. A penalization method is used to enforce the ‘soft’ constraints of the system and integrate error in the conservation properties into the loss function. During training, quantities representing the particle density, momentum and energy for all species of the system are calculated at each configuration vertex, mirroring the procedure in XGC. This simple training has produced a median relative loss, across configuration space, of the order of 10 –4 , which is low enough if the error is of random nature, but not if it is of drift nature in time steps. The run time for the current Picard iterative solver of the operator is O(n 2 ), where n is the number of plasma species. As the XGC1 code begins to attack problems including a larger number of species, the collision operator will become expensive computationally, making the neural network solver even more important, especially since its training only scales as O(n). Here, a wide enough range of collisionality has been considered in the training data to ensure the full domain of collision physics is captured. An advanced technique to decrease the losses further will be subject of a subsequent report. Eventual work will include expansion of the network to include multiple plasma species.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

A Dirac R-matrix calculation for the electron-impact excitation of W +

Abstract Aims : tungsten has been chosen for use as a plasma facing component in the divertor for the ITER experiment, and is currently being used on existing tokamaks such as JET. W + plays an integral role in assessing the impurity influx from plasma facing component of tokamaks and subsequent redeposition. Together with previously calculated a neutral tungsten electron-impact dataset this study allows us to determine neighbouring spectral lines in the same wavelength window of the spectrometer, and detect if there is strong blending of overlapping lines between these two ion stages as well as providing ionisation per photon ratios for both species. The new data is to be used for tungsten erosion/redeposition diagnostics. Methods : a significantly modified version of the GRASP0 atomic structure code in conjunction with DARC (Dirac Atomic R -matrix Code) are used to calculate the Einstein A coefficients and collisional rates used to generate a synthetic W II spectrum. The W II spectrum is compared against tungsten spectral emission experiments. Results : this study is used to model the spectrum of W ii , providing the predictive capability of identifying spectral lines from recent experiments. These results provide an integral part of impurity influx and redeposition determination, as the ionisation rates may be used to calculate S/XB ratios.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2025

Distributed Stochastic Optimization of a Neural Representation Network for Time-Space Tomography Reconstruction

4D time-space reconstruction of dynamic events or deforming objects using X-ray computed tomography (CT) is an important inverse problem in non-destructive evaluation. Conventional back-projection based reconstruction methods assume that the object remains static for the duration of several tens or hundreds of X-ray projection measurement images (reconstruction of consecutive limited-angle CT scans). However, this is an unrealistic assumption for many in-situ experiments that causes spurious artifacts and inaccurate morphological reconstructions of the object. To solve this problem, we propose to perform a 4D time-space reconstruction using a distributed implicit neural representation (DINR) network that is trained using a novel distributed stochastic training algorithm. Our DINR network learns to reconstruct the object at its output by iterative optimization of its network parameters such that the measured projection images best match the output of the CT forward measurement model. Here, we use a forward measurement model that is a function of the DINR outputs at a sparsely sampled set of continuous valued 4D object coordinates. Unlike previous neural representation architectures that forward and back propagate through dense voxel grids that sample the object's entire time-space coordinates, we only propagate through the DINR at a small subset of object coordinates in each iteration resulting in an order-of-magnitude reduction in memory and compute for training. DINR leverages distributed computation across several compute nodes and GPUs to produce high-fidelity 4D time-space reconstructions. We use both simulated parallel-beam and experimental cone-beam X-ray CT datasets to demonstrate the superior performance of our approach.

36 MATERIALS SCIENCE↗

DOE OSTI2026

ReMU: regional minimal updating for model-based derivative-free optimization

Derivative-free optimization (DFO) problems are optimization problems where derivative information is unavailable or extremely difficult to obtain. Model-based DFO solvers have been applied extensively in scientific computing. Powell's NEWUOA (2004) [Powell, The NEWUOA software for unconstrained optimization without derivatives, in Large-Scale Nonlinear Optimization, Nonconvex Optimization and its Applications Vol. 83, G. Di Pillo and M. Roma, eds., Springer, 2006, pp. 255–297] and Wild's POUNDerS (2014) [Wild, Solving derivative-free nonlinear least squares problems with POUNDERS, in Advances and Trends in Optimization with Engineering Applications, T. Terlaky, M.F. Anjos, and S. Ahmed, eds., SIAM, 2017, pp. 529–540] explore the numerical power of the minimal norm Hessian (MNH) model for DFO and contributed to the open discussion on building better models with fewer data to achieve faster numerical convergence. Another decade later, we propose the regional minimal updating (ReMU) models, and extend the previous models into a broader class, including the H 2 norm models [Xie and Yuan, Least H 2 norm updating of quadratic interpolation models for derivative-free trust-region algorithms, IMA J. Numer. Anal. 46 (2025), pp. 21–50]. This paper shows motivation behind ReMU models, computational details, theoretical and numerical results on particular extreme points and the barycentre of ReMU's weight coefficient region, and the associated KKT matrix error and distance. Novel metrics, such as the truncated Newton step error, are proposed to numerically understand the new models' properties. A new algorithmic strategy, based on iteratively adjusting the ReMU model type, is also proposed, and shows numerical advantages by combining and switching between the barycentric model and the classic least Frobenius norm model in an online fashion.

derivative-free trust-region methods↗

DOE OSTI2021

Numerical Simulations of Noisy Variational Quantum Eigensolver Ansatz Circuits

This is a case study of the variational quantum eigensolver (VQE) method using numerical simulations to test the influence of noise on the accuracy of the underlying circuit ansatz. We investigate a computational chemistry application of VQE to calculate the electronic ground state and its energy for Sodium Hydride (NaH), a prototypical two-electron problem. Using a one-parameter ansatz derived from unitary coupled cluster (UCC) theory, we simulate the effects of noise on the energy expectation value and variance with respect to the ansatz parameter. These numerical simulations provide insights into the accuracy of the prepared quantum state and the efficiency of the classical optimizer that iteratively refines the ansatz. We conduct a comparative study between analytical results derived for the UCC ansatz in the absence of noise and the noisy numerical simulation results obtained using an isotropic depolarizing noise model for each gate. We also compare the relative increase in noise on logically equivalent UCC ansatz circuits generated by randomized compiling. Notably, we observe that the intrinsic variance in the energy due to the simplicity of the ansatz itself compares with the noise induced by the bare circuit.

Gowrishankar, Meenambika↗

DOE OSTI2021

Alpha particle channeling in ITER

Alpha particle channeling, the attempt to extract energy from high-energy fusion alpha particles using a combination of high- and low-frequency waves introduced in the plasma with antennae, is studied using a guiding center code. We examine the effect of the combination of cooling caused by a cyclotron mode, particle diffusion due to Alfvén modes introduced for ash removal, the inclusion of microturbulent diffusion, and the slowing down of the alpha particles on electrons. Induced cooling is achieved with a cyclotron resonance, producing additional losses of particles above 3.5 MeV in an amount about equal to the prompt loss. The removal of the low-energy cooled particles by additional modes or by microturbulent diffusion is the hardest challenge for alpha channeling. The cooled alpha particles remain deep in the plasma center, so for this removal, the method used must be capable of providing transport from the plasma center to the edge without also causing losses of high-energy particles.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Temporal Explosion Source Processes of Declared Nuclear Tests in the Democratic People’s Republic of Korea

In this work we highlight a preliminary temporal source analysis of the six declared Democratic People's Republic of Korea (DPRK) nuclear tests. We use regional seismic data to estimate relative source time functions (RSTFs) via iterative time-domain deconvolution (Ammon, 2006; Pippin, 2022) of vertical-component ground motions recorded within 2000 km of the source region. Since RSTFs are ideally independent of site and propagation effects, their amplitude spectrum is equivalent to the source spectral ratio, but they also retain phase information. We compare observed RSTFs (in the time and frequency domains) with synthetic RSTFs derived from the Mueller & Murphy (1971) explosion source model. The resolution of these time functions varies, however, we generally obtain high-quality results within the limitations of the recording broadband instrumentation. The results indicate that this method effectively preserves source time-history information that can be used for temporal analysis of remote nuclear explosions. This preliminary analysis is intended to assess the viability of using time-domain deconvolution methods for extracting temporal source information.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

DOE OSTI2020

Effect of Computational Schemes on Coupled Flow and Geo-Mechanical Modeling of CO 2 Leakage through a Compromised Well

Carbon capture, utilization, and storage (CCUS) describes a set of technically viable processes to separate carbon dioxide (CO 2 ) from industrial byproduct streams and inject it into deep geologic formations for long-term storage. Legacy wells located within the spatial domain of new injection and production activities represent potential pathways for fluids (i.e., CO 2 and aqueous phase) to leak through compromised components (e.g., through fractures or micro-annulus pathways). The finite element (FE) method is a well-established numerical approach to simulate the coupling between multi-phase fluid flow and solid phase deformation interactions that occur in a compromised well system. We assumed the spatial domain consists of a three-phases system: a solid, liquid, and gas phase. For flow in the two fluids phases, we considered two sets of primary variables: the first considering capillary pressure and gas pressure (PP) scheme, and the second considering liquid pressure and gas saturation (PS) scheme. Fluid phases were coupled with the solid phase using the full coupling (i.e., monolithic coupling) and iterative coupling (i.e., sequential coupling) approaches. The challenge of achieving numerical stability in the coupled formulation in heterogeneous media was addressed using the mass lumping and the upwinding techniques. Numerical results were compared with three benchmark problems to assess the performance of coupled FE solutions: 1D Terzaghi’s consolidation, Liakopoulos experiments, and the Kueper and Frind experiments. We found good agreement between our results and the three benchmark problems. For the Kueper and Frind test, the PP scheme successfully captured the observed experimental response of the non-aqueous phase infiltration, in contrast to the PS scheme. These exercises demonstrate the importance of fluid phase primary variable selection for heterogeneous porous media. We then applied the developed model to the hypothetical case of leakage along a compromised well representing a heterogeneous media. Considering the mass lumping and the upwinding techniques, both the monotonic and the sequential coupling provided identical results, but mass lumping was needed to avoid numerical instabilities in the sequential coupling. Additionally, in the monolithic coupling, the magnitude of primary variables in the coupled solution without mass lumping and the upwinding is higher, which is essential for the risk-based analyses.

deformation flow↗

DOE OSTI2020

Template-Assisted, Seed-Mediated Synthesis of Hierarchically Mesoporous Core–Shell UiO-66: Enhancing Adsorption Capacity and Catalytic Activity through Iterative Growth

A hierarchically mesoporous (HM) UiO-66-F 4 shell with ~8 nm mesopores can be iteratively grown on top of UiO-66 nanoparticle (NP) seeds over several cycles templated by Pluronic F-127 micelles. Presumably, the Pluronic micelles that were formed in water can surround UiO-66 NPs to facilitate the overgrowth of an HM-UiO-66-F 4 shell in the presence of Zr IV precursors and BDC-F 4 linkers. The UiO-66 NP seeds play an important role in directing the continuous growth of the HM-UiO-66-F 4 shell, as only a nonporous phase was obtained in their absence. Furthermore, this template-assisted, seed-mediated method can be extended to produce other UiO-66-X (X = (OH) 2 , (COOH) 2 , etc.) shells, demonstrating its generality for the UiO-66 family of metal–organic frameworks. Notably, the incorporation of mesopores into the thrice-overgrown UiO-66@HM|3rd-UiO-66-F 4 materials leads to impressive enhancements in the per-mass uptake capacity of Direct Blue 86, a large anionic dye: 320% better than the parent UiO-66 seeds and 150% better than that for a [UiO-66 + UiO-66-F 4 ] physical mixture at the same mass proportion. Similar enhancements were also observed in the catalyzed oxidation of thioanisole.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Multi–Modular Design of Stable Pore–Space–Partitioned Metal–Organic Frameworks for Gas Separation Applications

Pore space partition (PSP) is an effective materials design method for developing high-performance small-pore materials for storage and separation of gas molecules. The continued success of PSP depends on broad availability and judicious choice of pore-partition ligands and better understanding of each structural module on stability and sorption properties. Here, by using substructural bioisosteric strategy (sub-BIS), a dramatic expansion of pore-partitioned materials is targeted by using ditopic dipyridyl ligands with non-aromatic cores or extenders, as well as by expanding heterometallic clusters to uncommon nickel–vanadium and nickel–indium clusters rarely known before in porous materials. The dual-module iterative refinement of pore-partition ligands and trimers leads to remarkable enhancement of chemical stability and porosity. Here a family of 23 pore-partitioned materials synthesized from five pore-partition ligands and seven types of trimeric clusters is reported. New materials with such compositionally and structurally diverse framework modules reveal key factors that dictate stability, porosity, and gas separation properties. Among these, materials based on heterometallic vanadium–nickel trimeric clusters give rise to the highest long-term hydrolytic stability and remarkable uptake capacity for CO 2 , C 2 H 2 /C 2 H 4 /C 2 H 6 , and C 3 H 6 /C 3 H 8 hydrocarbon gases. Here, the breakthrough experiment shows the potential application of new materials for separating gas mixtures such as C 2 H 2 /CO 2 .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

SymbolFit: Automatic Parametric Modeling with Symbolic Regression

We introduce SymbolFit (API: https://github.com/hftsoi/symbolfit), a framework that automates parametric modeling by using symbolic regression to perform a machine-search for functions that fit the data while simultaneously providing uncertainty estimates in a single run. Traditionally, constructing a parametric model to accurately describe binned data has been a manual and iterative process, requiring an adequate functional form to be determined before the fit can be performed. The main challenge arises when the appropriate functional forms cannot be derived from first principles, especially when there is no underlying true closed-form function for the distribution. In this work, we develop a framework that automates and streamlines the process by utilizing symbolic regression, a machine learning technique that explores a vast space of candidate functions without requiring a predefined functional form because the functional form itself is treated as a trainable parameter, making the process far more efficient and effortless than traditional regression methods. We demonstrate the framework in high-energy physics experiments at the CERN Large Hadron Collider (LHC) using five real proton-proton collision datasets from new physics searches, including background modeling in resonance searches for high-mass dijet, trijet, paired-dijet, diphoton, and dimuon events. We show that our framework can flexibly and efficiently generate a wide range of candidate functions that fit a nontrivial distribution well using a simple fit configuration that varies only by random seed, and that the same fit configuration, which defines a vast function space, can also be applied to distributions of different shapes, whereas achieving a comparable result with traditional methods would have required extensive manual effort.

Tsoi, Ho Fung [Univ. of Pennsylvania, Philadelphia↗

DOE OSTI2021

NRC Multiphysics Analysis Capability Deployment FY21: Part 3

This report details the progress and activities of Idaho National Laboratory (INL) on the Nuclear Regulatory Commission (NRC) project “Development and Modeling Support for Advanced Non-Light Water Reactors.” The deliverables completed for this report are: Deliverable 1c: the capability to model gas mixtures was added to Pronghorn. A test problem mimicking the conditions achieved in a depressurized loss of forced cooling (DLOFC) event was solved with both RELAP-5 and Pronghorn. Pronghorn employed a finite vol ume method with the Kurganov-Tadmor discretization. The comparison between the mass fraction spatial profiles computed with RELAP-5 and Pronghorn clearly shows the presence of numerical artifacts (i.e., overly diffusive behavior at low Mach numbers). We confirmed that the problem disappears at higher Mach numbers. We recommend future work on the implementation of a low Mach finite volume formulation to better treat low Mach number problems. Deliverable 2a: we demonstrated two approaches to model the radiation/conduction/natural convection heat transfer across a stagnant gas for the PBMR-400 design using Pronghorn. The first approach is based on the net radiation method, which relies on the computation of view factors with the Multiphysics Object-Oriented Simulation Environment (MOOSE) ray tracing capability. The second method is a traditional thermal resistance approach. The test problems include both 2D and 3D geometries. In all cases, the results show very good agreement during a DLOFC transient. This confirms that the faster thermal resistance method produces solutions that are equivalent to the net radiation method for this geometry. Deliverable 3d: we demonstrated the use of the advection kernel for the delayed neutron precursor equation in Griffin with a 2D MSFR model. The results appear physical but further verification is recommended. We also recommend the addition of conjugate heat transfer to compute the temperatures and model the thermomechanic behavior of the reflectors and other structures. Significant memory and performance issues were encountered in the 3D axisymmetric model. Future work is recommended in this area. Task 8g: this task allows multidimensional MOOSE applications to be coupled to system codes (RELAP-7 and SAM). We implemented a faster multiphysics iteration coupling algorithm, which provides an overall 6× acceleration of the 3D-1D coupling of the core multidi- mensional fluid flow solver and the 1D primary and secondary loop model.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2026

Advancing Artificial Intelligence with Liquid Argon Neutrino Experiments (Technical Report)

The grant allowed two main contributions: 1) The development of a first successful demonstration of the employment of Optimal Transport in liquid argon time projection chamber neutrino detectors. Optimal Transport, used in other contexts and specifically with LHC calorimetric data, was adapted to address a key particle identification challenge in LArTPCs: the separation of pi0 backgrounds from single-electrons produced in charged-current electron neutrino interactions. The work, leveraging ML methods such as k-nearest-neighbor (kNN) and support-vector-machine (SVM), showed an increase in background rejection of a factor of two or more. Work is now ongoing to incorporate this development in physics analyses for LArTPC experiments and more broadly expand the use of OT in LArTPC detectors including DUNE. This work was done in collaboration with the phenomenology group led by Nathaniel Craig at UCSB. 2) The deployment of NuGraph2, a graph neural network developed for LArTPC reconstruction, in the MicroBooNE experiment. NuGraph2 uses novel graph-neural-network methods on the rather simple LArTPC inputs of reconstructed hits, greatly simplifying the workflow compared to the use of waveform or signal-deconvolved wire ROIs. The network performed particle classification and was shown to address many challenging problems in LArTPC imaging including track-shower separation and the identification of protons and charged pions from primary muons. Our group collaborated with Giuseppe Cerati (FNAL scientist) who is one of the core developers of NuGraph2 to integrate this tool in MicroBooNE’s analysis framework. This consisted in tow key contributions: a) Studying performance on real data, which came with several months of iterations because the MC-trained version of the network was found to show significant bias that our group investigated and addressed. b) Integrating the output hit labeling of NuGraph2 into the existing particle tracking and shower reconstruction code. As a result of this work led by our team NuGraph2 is now enabling a suite of new analyses which benefit from enhanced capabilities and thus broader physics reach. The grant supported primarily the salary of UCSB graduate student Chuyue “Michaelia” Fang as well as partial summer salary support for PI Caratelli. Some funds were used for travel by Michaelia to ML related schools and conferences.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

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↗