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DOE OSTI2026

Classical-Quantum Algorithm for Solving Stochastic Programs

Stochastic programming provides a rigorous mathematical framework for making decisions under uncertainty in a risk-aware manner. Two-stage stochastic programming is, perhaps, the simplest form of this framework. Here the first-stage variables represent decisions that must be made "here and now" in the face of uncertainty, while the second-stage variables are decisions made after uncertain events. However, the broad adoption of stochastic programming has been hindered by computational challenges caused by the two-stage stochastic programming formulation which requires solving an ensemble of optimization problems. Using quantum amplitude estimation (QAE), quantum computers have shown the theoretic ability to compute expectations with Monte-Carlo methods with quadratically fewer samples than classical methods. In this work, we present a quantum algorithm for computing the expectation term using QAE for given first-stage decisions. Further, we detail methods of computing gradient information from the quantum calculation enabling the application of classical gradient-based optimization techniques. The result is a classical-quantum hybrid method of solving two-stage stochastic programs. These techniques are demonstrated with computational experiments based an engineering optimization problem.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Robust Optimal Experimental Design of Infinite-Dimensional Bayesian Nonlinear Inverse Problems

Abstract. We consider robust optimal experimental design (ROED) for nonlinear Bayesian inverse problems governed by partial differential equations (PDEs). An optimal design is one that maximizes some utility quantifying the quality of the solution of an inverse problem. However, the optimal design is dependent on elements of the inverse problem such as the simulation model, the prior, or the measurement error model. ROED aims to produce an optimal design that is aware of the additional uncertainties encoded in the inverse problem and remains optimal even after variations in them. We follow a worst-case scenario approach to develop a new framework for robust optimal design of nonlinear Bayesian inverse problems. The proposed framework (a) is scalable and designed for infinite-dimensional Bayesian nonlinear inverse problems constrained by PDEs; (b) develops efficient approximations of the utility, namely the expected information gain; (c) employs eigenvalue sensitivity techniques to develop analytical forms and efficient evaluation methods of the gradient of the utility with respect to the uncertainties against which we wish to be robust; and (d) employs a probabilistic optimization paradigm that properly defines and efficiently solves the resulting combinatorial max-min optimization problem. The effectiveness of the proposed approach is illustrated for optimal sensor placement problem in an inverse problem governed by an elliptic PDE.

Chowdhary, Abhijit↗

DOE OSTI2026

Low Activity Waste Glass Optimization with Property Models from Machine Learning, Part 2: Experimental Validation and Active Learning

The United States Department of Energy is responsible for managing legacy nuclear waste stored in underground tanks at the Hanford Site. To treat the waste, it is planned as the current baseline to separately vitrify low-activity waste (LAW) and high-level waste fractions. Previously, machine learning (ML) based glass property models (e.g., chemical durability, viscosity, electrical conductivity and SO3 solubility) were developed with prediction uncertainties. A waste glass optimization approach was then established to enable the capability of using these ML models in LAW glass formulation. In this study, the previous ML models were first experimentally validated, and the results were incorporated back into the database to update the ML models. The updated models and formulations showed increased waste loading while reducing the failure rate, demonstrating improved predictive accuracy, reduced uncertainties, and the effectiveness of active learning in guiding high-dimensional, nonlinear LAW glass design. This represents the first experimental validation of ML based LAW glass formulation, with practical benefits such as higher waste loading, shorter mission duration, and lower operational risk.

Lu, Xiaonan (ORCID:0000000179708148)↗

DOE OSTI2020

Calibration of energy density functionals with deformed nuclei

Nuclear density functional theory is the prevalent theoretical framework for accurately describing nuclear properties at the scale of the entire chart of nuclides. Given an energy functional and a many-body scheme (e.g., single- or multireference level), the predictive power of the theory depends strongly on how the parameters of the energy functionals have been calibrated with experimental data. Expanded algorithms and computing power have enabled recent optimization protocols to include data in deformed nuclei in order to optimize the coupling constants of the energy functional. The primary motivation of this work is to test the robustness of such protocols with respect to some of the technical and numerical details of the underlying calculations, especially when the calibration explores a large parameter space. To this end, we quantify the effect of these uncertainties on both the optimization and statistical emulation of composite objective functions. We also emphasize that Bayesian calibration can provide better estimates of the theoretical errors used to define objective functions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Sensitivity and Uncertainty Quantification of Transition Scenario Simulations

This report documents the first collective attempt at developing and applying capabilities to quantify uncertainties, assess parametric sensitivities, and optimize multiple parameters and metrics in fuel cycle simulations generated by the SA&I Campaign. To do this, external codes that were designed to perform sensitivity analysis and uncertainty quantification (SA&UQ) needed to be coupled to the SA&I Campaign’s nuclear fuel cycle simulators (NFCS). In FY20, two approaches were pursued: 1) coupling Cyclus to an ORNL-internal code called MOT (Metaheuristic Optimization Tool) and 2) coupling DYMOND to the opensource SA&UQ tool kit Dakota. The primary objective of having these NFCS/SA&UQ coupled capabilities is to better inform DOE-NE and other stakeholders on the results generated from the NFCS. For a given set of fuel cycle strategies, policies, and technology assumptions that make up a fuel cycle scenario, these NFCS have traditionally been used by the SA&I Campaign to provide quantitative answers in terms of year-by-year mass flows, infrastructure requirements, costs, etc. With these newly developed coupled capabilities, the SA&I Campaign can now efficiently simulate hundreds or thousands of these scenarios, sample large ranges of parameters and assumptions, and use the unique features of the SA&UQ tools to process the data. This enables providing answers with known and propagated uncertainties, determining the sensitivity of important metrics to different parameters and assumptions, quantifying how much fuel cycle and technology parameters impact each other, and producing optimized fuel cycle strategies for single and multiple variables. To demonstrate these new capabilities, the Cyclus/MOT was used to model several scenarios ranging from simple fleet retirements to transitions to advanced reactors. Specifically, for a transition scenario from LWRs to SFRs and advanced LWRs, uncertainty quantification, sensitivity analysis, and optimization studies were applied to cases involving single and multiple parameter (input) and single and multiple metric (output) variations. In addition, a similar transition scenario was modeled to demonstrate how to optimize the reprocessing capacity parameter to minimize two performance metrics while taking into account uncertainties from two other parameters. Lastly, a depletion module based on SCALE/ORIGEN was added in Cyclus to simulate the third scenario that was designed to quantify the impact of the modeling assumption that all LWR used nuclear fuel have the same burnup. The newly developed DYMOND/Dakota capability was also applied to a transition scenario from the existing fleet to small modular reactors and fast reactors. This particular scenario involves not only explicit isotopic depletion via ORIGEN-2, but also includes multirecycling and utilizing the criticality search feature to determine the fresh fuel composition of recycled fuel, a feature unique to the DYMOND NFCS. A large database of simulations were run with 4 main parameters that were sampled: start date of reprocessing, reprocessing capacity, energy demand growth rate, and advanced reactor share of the fleet. The 4 main metrics were uranium consumption, enrichment requirements, waste generation, and levelized cost of electricity using data from the Cost Basis Report. The demonstrated SA&UQ results include those that inform on how to choose parameters to avoid “failed” scenarios, Sobol’ indices that inform on the importance of various parameters individually and synergistically, and Analysis of Variance (ANOVA) studies that decompose parameter ranges into groups and informs on whether variations are statistically significant.

Feng, B.↗

DOE OSTI2024

AEOLUS: Advances in Experimental Design, Optimal Control, and Learning for Uncertain Complex Systems

Sustained advances in the mathematics of modeling and simulation have resulted in the capability today for routine simulation of a number of large scale complex DOE-relevant systems. As remarkable as this capability for solving the so-called forward problem is, it is typically only the first step-an inner loop within an outer loop that explores the simulation model's parameter space and decision space to characterize uncertainty in the model's predictions, learn unknown model parameters from data, design the most informative experiments, determine optimal control strategies, and create optimal designs. Broadly, what unifies all of these outer loop problems is that they are, in one form or another, optimization problems over parameter/control/design space that are constrained by complex uncertain models. To fully realize the power of scientific simulation as a basis for scientific discovery, technological innovation, and rational decision-making, it is imperative to move beyond simulation to tackle the outer loop of optimization for learning from data, experimental design, and control with complex uncertain models. When the models under consideration are large-scale and complex, and when the optimization variable and uncertain parameter spaces are high (or infinite) dimensional, this constitutes a grand challenge of the highest order, and is intractable with conventional methods. To overcome these challenges, the AEOLUS Center was established to develop a unified mathematical, computational, and statistical framework for (1) Learning predictive models from complex data via Bayesian inference and optimization, and (2) Optimizing experiments, processes, and designs using the resulting uncertain models. These problems are intractable with conventional methods, for several reasons: (1) The simulation problems that govern the inner loops of the optimization problems are expensive to execute (due to severe nonlinearity, heterogeneity, multiphysics/multiscale coupling); (2) The optimization variable and uncertain parameter spaces are high dimensional, often stemming from discretizations of infinite dimensional fields such as initial conditions, sources, or material properties. We argue that the key to overcoming these challenges is to develop new mathematical, computational, and statistical methods that exploit the structure of the Bayesian inference and optimization problems mediated by their underlying complex uncertain models. This structure includes the regularity, sparsity, geometry, low intrinsic dimensionality, and multifidelity nature of the maps from uncertain parameter/optimization variable spaces to the specific objectives targeted: Bayesian inference, optimal experimental design, and optimal control design. Black box methods developed as generic tools are incapable of exploiting this structure. To be successful, we must create, integrate, and cross-fertilize ideas across multiple areas of applied math--including approximation theory, Bayesian inference, data science, experimental design, information theory, machine learning, model reduction, optimal control theory, parallel algorithms, PDE-constrained optimization, randomized algorithms, stochastic optimization, and uncertainty quantification--all while exploiting the structure of the problems at hand. With this goal in mind, we have marshaled a team of leading authorities in these areas. While the methods we develop will be broadly applicable across a wide spectrum of DOE problems in which experiments inform models and the systems those models describe must be optimized under uncertainty, we have chosen a specific area, advanced manufacturing and materials, to drive our work. AMM is characterized by complex models across multiple scales, and is a rich source of challenging problems in inference, experimental design, and optimal control, requiring multifaceted and integrated advances in applied mathematics. As such, AMM serves as an excellent vehicle to motivate and demonstrate the advances in applied mathematics developed by our center.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Renewable electricity capacity planning with uncertainty at multiple scales

Abstract We formulate and compare optimization models of investment in renewable generation using a suite of social planning models that compute optimal generation capacity investments for a hydro-dominated electricity system where inflow uncertainty results in a risk of energy shortage. The models optimize the expected cost of capacity expansion and operation allowing for investments in hydro, geothermal, solar, wind, and thermal plant, as well as battery storage for smoothing load profiles. A novel feature is the integration of uncertain seasonal hydroelectric energy supply and short-term variability in renewable supply in a two-stage stochastic programming framework. The models are applied to data from the New Zealand electricity system and used to estimate the costs of moving to a 100% renewable electricity system by 2035. We also explore the outcomes obtained when applying different forms of CO 2 constraint that limit respectively non-renewable capacity, non-renewable generation, and CO 2 emissions on average, almost surely, or in a chance-constrained setting, and show how our models can be used to investigate the merits of a proposed pumped-hydro scheme in New Zealand’s South Island.

Ferris, Michael C.↗

DOE OSTI2021

Data-driven optimization of mixed-integer bi-level multi-follower integrated planning and scheduling problems under demand uncertainty

The coordination of interconnected elements across the different layers of the supply chain is essential for all industrial processes and the key to optimal decision-making. Yet, the modeling and optimization of such interdependent systems are still burdensome. Here we address the simultaneous modeling and optimization of medium-term planning and short-term scheduling problems under demand uncertainty using mixed-integer bi-level multi-follower programming and data-driven optimization. Bi-level multi-follower programs model the natural hierarchy between different layers of supply chain management holistically, while scenario analysis and data-driven optimization allow us to retrieve the guaranteed feasible solutions of the integrated formulation under various demand considerations. We address the data-driven optimization of this challenging class of problems using the DOMINO framework, which was initially developed to solve single-leader single-follower bi-level optimization problems to guaranteed feasibility. This framework is extended to solve single-leader multi-follower stochastic formulations and its performance is characterized by well-known single and multi-product process scheduling case studies. Through our data-driven algorithmic approach, we present guaranteed feasible solutions to linear and nonlinear mixed-integer bi-level formulations of simultaneous planning and scheduling problems and further characterize the effects of the scheduling level complexity on the solution performance, which spans over several hundred continuous and binary variables, and thousands of constraints.

42 ENGINEERING↗

DOE OSTI2020

The Convolutional Multiple Whole Profile (CMWP) Fitting Method, a Global Optimization Procedure for Microstructure Determination

The analysis of line broadening in X-ray and neutron diffraction patterns using profile functions constructed on the basis of well-established physical principles and TEM observations of lattice defects has proven to be a powerful tool for characterizing microstructures in crystalline materials. These principles are applied in the convolutional multiple-whole-profile (CMWP) procedure to determine dislocation densities, crystallite size, stacking fault and twin boundary densities, and intergranular strains. The different lattice defect contributions to line broadening are separated by considering the hkl dependence of strain anisotropy, planar defect broadening and peak shifts, and the defect dependent profile shapes. The Levenberg–Marquardt (LM) peak fitting procedure can be used successfully to determine crystal defect types and densities as long as the diffraction patterns are relatively simple. However, in more complicated cases like hexagonal materials or multiple-phase patterns, using the LM procedure alone may cause uncertainties. Here, we extended the CMWP procedure by including a Monte Carlo statistical method where the LM and a Monte Carlo algorithm were combined in an alternating manner. The updated CMWP procedure eliminated uncertainties and provided global optimized parameters of the microstructure in good correlation with electron microscopy methods.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Learning and Fast Adaptation for Grid Emergency Control via Deep Meta Reinforcement Learning

As power systems are undergoing a significant transformation with more uncertainties, less inertia and closer to operation limits, there is increasing risk of large outages. Thus, there is an imperative need to enhance grid emergency control to maintain system reliability and security. Towards this end, great progress has been made in developing deep reinforcement learning (DRL) based grid control solutions in recent years. However, existing DRL-based solutions have two main limitations: 1) they cannot handle well with a wide range of grid operation conditions, system parameters, and contingencies; 2) they generally lack the ability to fast adapt to new grid operation conditions, system parameters, and contingencies, limiting their applicability for real-world applications. Here, in this paper, we mitigate these limitations by developing a novel deep meta-reinforcement learning (DMRL) algorithm. The DMRL combines the meta strategy optimization together with DRL, and trains policies modulated by a latent space that can quickly adapt to new scenarios. We test the developed DMRL algorithm on the IEEE 300-bus system. We demonstrate fast adaptation of the meta-trained DRL polices with latent variables to new operating conditions and scenarios using the proposed method, which achieves superior performance compared to the state-of-the-art DRL and model predictive control (MPC) methods.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2023

Isotherm modeling and techno-economic analysis of a TSA moving bed process using a tetraamine-appended MOF for NGCC applications

Tetraamine-appended metal-organic frameworks (MOF) are a new family of amine-functionalized MOF materials that show potential for CO 2 capture from flue gas conditions relevant to natural gas combined cycle (NGCC) power plants. This work presents isotherm modeling of the tetraamine-appended MOF Mg 2 (dobpdc)(3-4-3)(dobpdc 4- =4,4'-dioxidobiphenyl-3,3'dicarboxylate;3-4-3=N,N'bis(3-aminopropyl)-1,4-diaminobutane), process modeling, scale up, and a techno-economic optimization of a moving bed Temperature Swing Adsorption (TSA) process for carbon capture using this sorbent. This MOF exhibits a unique two-step CO 2 adsorption profile in three different pressure ranges. Thus, arctangent-based logistic functions and, quadratic and Langmuir models were employed to represent such isotherm behavior. The results of the isotherm model show good fitting vs the experimental data with an RMSE of 0.41. Here, to model the carbon capture process, the isotherm model was embedded into a moving bed contactor model, and this was used to simulate a TSA CO 2 capture cycle and evaluate cost-optimal designs considering flue gas from a -650 MWe NGCC power plant. The capital cost model consists of CAPEX correlations for reactors, compressors, ducting, etc., while the operating costs include steam, water, chemicals, and electricity (following NETL's quality guidelines for energy systems studies). A techno-economic optimization of the capture system was performed by using NETL's Framework for the Optimization and Quantification of Uncertainty and Surrogates tool (FOQUS). Results suggest that a moving bed carbon capture system with tetraamine-appended MOF can be competitive compared to conventional MEA solvent-based capture processes for NGCC plants, when a heat recovery efficiency of at least 40% is achieved, and MOF materials can be produced at a cost below -$9/kg.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Data-Driven Optimization of Pixelated CdZnTe Spectrometers for Uranium Enrichment Assay

Here, in recent work [Vavrek et al. (2025)], we developed the performance optimization framework spectre-ml for gamma spectrometers with variable performance across many readout channels. The framework uses non-negative matrix factorization (NMF) and clustering to learn groups of similarly-performing channels and sweep through various learned channel combinations to optimize the performance tradeoff of including worse-performing channels for better total efficiency. In this work, we integrate the pyGEM uranium enrichment assay code with our spectre-ml framework, and show that the U-235 enrichment relative uncertainty can be directly used as an optimization target. We find that this optimization reduces relative uncertainties after a 30 -minute measurement by an average of 20%, as tested on six different H3D M400 CdZnTe spectrometers, which can significantly improve uranium non-destructive assay measurement times in nuclear safeguards contexts. Additionally, this work demonstrates that the spect re-ml optimization framework can accommodate arbitrary end-user spectroscopic analysis code and performance metrics, enabling future optimizations for complex Pu spectra.

Gamma-ray detection↗

DOE OSTI2024

Multistage Stochastic optimization for mid-term integrated generation and maintenance scheduling of cascaded hydroelectric system with renewable energy uncertainty

The uncertainties resulting from the escalating penetration of renewable energy resources pose severe challenges to the efficient operation of modern power systems. Hydroelectricity is characterized by its flexibility, controllability, and reliability, and thus becomes one of the most ideal energy resources to hedge against such uncertainties. This paper studies the mid-term integrated generation and maintenance scheduling of a cascaded hydroelectric system (CHS) consisting of multiple cascaded reservoirs and hydroelectric units. To precisely describe the mid-term water regulation policies, the hydraulic coupling relationship and water-energy nexus of CHS are incorporated into the proposed optimization model. The uncertainties of natural water inflow and the power outputs of wind/solar energy generation are taken into consideration and captured via a stochastic process modeled by a scenario tree. A multistage stochastic optimization (MSO) approach is developed to coordinate the complementary operations of multiple energy resources, by optimizing the mid-term water resource management, generation scheduling, and maintenance scheduling of CHS. The proposed MSO model is formulated as a large-scale mixed-integer linear program that presents significant computational intractability. To address this issue, a tailored Benders decomposition algorithm is developed. Two real-world case studies are conducted to demonstrate the capability and characteristics of the proposed model and algorithm. The computational results show that the proposed MSO model can exploit the flexibility of hydroelectricity to efficiently respond to variable wind and solar power, and reserve water resources for the generation in peak months to reduce the consumption of fossil fuel. Furthermore, the proposed solution approach also exhibits promising computational efficiency when handling large-scale models.

13 HYDRO ENERGY↗

DOE OSTI2024

Projective Integral Updates for High-Dimensional Variational Inference

Variational inference is an approximation framework for Bayesian inference that seeks to improve quantified uncertainty in predictions by optimizing a simplified distribution over parameters to stand in for the full posterior. Capturing model variations that remain consistent with training data enables more robust predictions by reducing parameter sensitivity. This work introduces a fixed-point optimization for variational inference that is applicable when every feasible log density can be expressed as a linear combination of functions from a given basis. In such cases, the optimizer becomes a fixed-point of projective integral updates. When the basis spans univariate quadratics in each parameter, the feasible distributions are Gaussian mean-fields and the projective integral updates yield quasi-Newton variational Bayes (QNVB). Other bases and updates are also possible. Since these updates require high-dimensional integration, this work begins by proposing an efficient quasirandom sequence of quadratures for mean-field distributions. Each iterate of the sequence contains two evaluation points that combine to correctly integrate all univariate quadratic functions and, if the mean-field factors are symmetric, all univariate cubics. More importantly, averaging results over short subsequences achieves periodic exactness on a much larger space of multivariate polynomials of quadratic total degree. The corresponding variational updates require four loss evaluations with standard (not second-order) backpropagation to eliminate error terms from over half of all multivariate quadratic basis functions. Furthermore, this integration technique is motivated by first proposing stochastic blocked mean-field quadratures, which may be useful in other contexts. A PyTorch implementation of QNVB allows for better control over model uncertainty during training than competing methods. Experiments demonstrate superior generalizability for multiple learning problems and architectures.

Gaussian mean-field↗

DOE OSTI2022

Tri-level hybrid interval-stochastic optimal scheduling for flexible residential loads under GAN-assisted multiple uncertainties

Various building loads, such as heating, ventilation, and air conditioners (HVACs), electric water heaters (EWHs), and electric vehicles (EVs), can introduce opportunities for improving the flexibility of electricity consumption while satisfying the needs of building owners as well as benefiting the resilience of distribution system. To utilize such flexibility, a tri-level distribution market framework is established, including residential consumers, load aggregators (LAs), and the distribution system operator (DSO). In this work, the uncertainties from all three levels are considered. The random consumption behavior at the consumer level is modeled as a Gaussian noise that is also aggregated and transmitted to the LA level. The weather temperature in the LA level is forecasted as an interval, and the photovoltaic (PV) power in the market-clearing level is modeled by a set of power scenarios generated by Generative Adversarial Networks (GANs). Then, a hybrid interval-stochastic programming is proposed to transform the uncertain problems in the first two levels into deterministic ones. For real-time implementations, a rolling horizon optimization (RHO) scheme is employed to continuously optimize the power consumption based on the latest operating information. Finally, case studies on a modified IEEE 69-bus system validate the effectiveness of the proposed uncertainty modeling strategies and the RHO scheme.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2022

Parametric dynamic mode decomposition for reduced order modeling

Dynamic Mode Decomposition (DMD) is a model-order reduction approach, whereby spatial modes of fixed temporal frequencies are extracted from numerical or experimental data sets. The DMD low-rank or reduced operator is typically obtained by singular value decomposition of the temporal data sets. For parameter-dependent models, as found in many multi-query applications such as uncertainty quantification or design optimization, the only parametric DMD technique developed was a stacked approach, with data sets at multiple parameter values were aggregated together, increasing the computational work needed to devise low-rank dynamical reduced-order models. Here in this paper, we present two novel approach to carry out parametric DMD: one based on the interpolation of the reduced-order DMD eigen-pair and the other based on the interpolation of the reduced DMD (Koopman) operator. Numerical results are presented for diffusion-dominated nonlinear dynamical problems, including a multiphysics radiative transfer example. All three parametric DMD approaches are compared.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

ECLEIRS: Exact conservation law embedded identification of reduced states for parameterized nonlinear conservation laws from sparse and noisy data

Multi-query applications such as parameter estimation, uncertainty quantification and design optimization for parameterized partial differential equation (PDE) systems are expensive. While reduced/latent state dynamics approaches for parameterized PDEs offer a viable alternative, these approaches rely on high-quality data and struggle with highly sparse spatiotemporal noisy measurements typically obtained from experiments. Furthermore, there is no guarantee that these models satisfy governing physical conservation laws. In this article, we propose a reduced state dynamics approach, referred to as ECLEIRS, that embeds exact conservation in the solution and flux representation by utilizing a space-time divergence-free neural network formulation. We compare ECLEIRS with other reduced state dynamics approaches, those that do not enforce any physical constraints and those with physics-informed loss functions, for three shock-propagation problems: 1-D advection, 1-D Burgers and 2-D Euler equations. In conclusion, the numerical experiments conducted in this study demonstrate that ECLEIRS provides the most accurate prediction of dynamics for unseen parameters even in the presence of highly sparse and noisy data.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

GeN-ROM—An OpenFOAM®-based multiphysics reduced-order modeling framework for the analysis of Molten Salt Reactors

This work presents a projection-based multiphysics Model Order Reduction (MOR) framework for the analysis of nuclear systems and its application to parametric simulations of Molten Salt Reactors (MSR). The framework, named GeN-ROM, is developed using OpenFOAM® and employs a Proper Orthogonal Decomposition aided Reduced-Basis technique (POD-RB). It can be used to reduce steady-state and transient multiphysics problems involving parametric fluid dynamics, heat exchange, and neutronics phenomena. For the treatment of structural elements in the hydraulic systems, a porous medium approach has been adopted. The reduction process is data-driven and snapshot information is extracted via POD to learn the solution manifold and to build global spatial basis functions. At the data collection phase, GeN-ROM makes use of the solvers available in GeN-Foam, a similarly OpenFOAM®-based multiphysics framework developed for the analysis of nuclear reactors. The global bases are used both to approximate the solution fields and to project the full-order equations onto lower-dimensional subspaces, thus considerably reducing the number of unknowns in a numerical system. This reduction leads to significant computational speedups, which is ideal for multi-query applications such as uncertainty quantification or design optimization. The developed tool has been tested using a 2D multiphysics model of the Molten Salt Fast Reactor (MSFR) with steady-state and transient scenarios, with speedups on the order of 10 – 10 5 .

22 GENERAL STUDIES OF NUCLEAR REACTORS↗