Approaching 18 years of existence, MOOSE-the Multiphysics Object-Oriented Simulation Environment-is being developed at a higher pace than ever before. With significant support from four research institutions across the globe, and dozens of new contributors, the capabilities of the framework are being expanded to meet modeling challenges in a wide variety of fields from nuclear system design, to geomechanics, to material science. This includes new development in equation discretization techniques, solver methods, meshing capabilities, application deployment, and user interface improvements. Applications built on MOOSE benefit from all these improvements.

The development of MOOSE has kept accelerating since the last release, with over 2,100 pull requests merged over the last 30 months that involved nearly fifty contributors across close to a dozen institutions internationally. The growth in MOOSE's capabilities and downstream applications is reflected in the growth of the community. User support provided on the GitHub discussions forum has steadily increased to nearly 50 daily interactions. New simulation projects, notably to model advanced nuclear reactor and fusion devices, are driving a significant expansion of the capabilities. This paper reports on these developments, with several major released features, new physics modules, and key improvements to the user experience and simulation workflow.

Stochastic simulations are ubiquitous across scientific disciplines. The Multiphysics Object-Oriented Simulation Environment (MOOSE) includes an optional module – stochastic tools – for implementing stochastic simulations. It implements an efficient and scalable scheme for performing stochastic analysis in memory. It can be used for building meta models to reduce the computational expense of multiphysics problems as well as perform analyses requiring up to millions of stochastic simulations. To illustrate, we have provided an example that trains a proper orthogonal decomposition reduced-basis model. The impact of the module is detailed by explaining how it is being used for failure analysis in nuclear fuel and reducing the computational burden via dynamic meta model training. The module is unique in that it provides the ability to use a single framework for simulations and stochastic analysis, especially for memory intensive problems and intrusive meta modeling methods.

Statistical nuclear fuel failure analysis is critical for the design and development of advanced reactor technologies. Although Monte Carlo Sampling (MCS) is a standard method of statistical failure analysis for fuels, the low failure probabilities of some advanced fuel forms and the correspondingly large number of required model evaluations limit its application to low-fidelity (e.g., 1-D) fuel models. In this paper, we present four other statistical methods for fuel failure analysis in Bison, considering tri-structural isotropic (TRISO)-coated particle fuel as a case study. The statistical methods considered are Latin hypercube sampling (LHS), adaptive importance sampling (AIS), subset simulation (SS), and the Weibull theory. Using these methods, we analyzed both 1-D and 2-D representations of TRISO models to compute failure probabilities and the distributions of fuel properties that result in failures. The results of these methods compare well across all TRISO models considered. Overall, SS and the Weibull theory were deemed the most efficient, and can be applied to both 1-D and 2-D TRISO models to compute failure probabilities. Moreover, since SS also characterizes the distribution of parameters that cause TRISO failures, and can consider failure modes not described by the Weibull criterion, it may be preferred over the other methods. Finally, a discussion on the efficacy of different statistical methods of assessing nuclear fuel safety is provided.

As the nuclear industry moves toward construction of microreactors and next-generation reactors, these efforts pose new challenges. A digital-twin tool will reduce costs and risk through integration of the disparate systems used in the design, construction, and operation of these reactors. Recent investments at Idaho National Laboratory (INL) in open-source digital engineering and multiphysics framework development provide a foundation from which to create and evaluate a digital twin for nuclear reactors. This digital-twin tool will use the Single Primary Heat Pipe Extraction and Removal Emulator (SPHERE) and Microreactor AGile Non-nuclear Experimental Testbed (MAGNET) as case studies to develop a digital twin with both single and 37 heat pipe test articles. The digital twin will provide the capabilities of remote monitoring and unattended operation (autonomous control) of these systems.A digital twin is a digital replica of an operating asset that can display data received from live sensors, update a physics model for the asset with the received data, compute predictive results of operational status with artificial intelligence (AI) to aid in optimizing asset use, and apply asset control accordingly. This twin will be developed through integration of the open-source technologies Deep Lynx (a data-warehouse technology) and the Multiphysics Object-Oriented Simulation Environment (MOOSE), physical-asset sensors, and physical-asset controls. Specifically, the general AI will successfully predict the events described as MAGNET heat pipe article test cases (such as heat pipe failure) using integrated data from the MAGNET sensors and physics-based models, including developed meta models. The integration of open-source INL software and AI assets with sensor data from a test bed will lead to a repeatable framework and guide for the creation of future digital twins. The team will also perform AI model training and experimentation to determine what models and features are most important to enable intelligent, autonomous control as well as to evaluate and determine best practices for digital-twin cybersecurity.

While multifidelity modeling provides a cost-effective way to conduct uncertainty quantification with computationally expensive models, much greater efficiency can be achieved by adaptively deciding the number of required high-fidelity (HF) simulations, depending on the type and complexity of the problem and the desired accuracy in the results. We propose a framework for active learning with multifidelity modeling emphasizing the efficient estimation of rare events. Our framework works by fusing a low-fidelity (LF) prediction with an HF-inferred correction, filtering the corrected LF prediction to decide whether to call the high-fidelity model, and for enhanced subsequent accuracy, adapting the correction for the LF prediction after every HF model call. The framework does not make any assumptions as to the LF model type or its correlations with the HF model. In addition, for improved robustness when estimating smaller failure probabilities, we propose using dynamic active learning functions that decide when to call the HF model. We demonstrate our framework using several academic case studies and two finite element (FE) model case studies: estimating Navier-Stokes velocities using the Stokes approximation and estimating stresses in a transversely isotropic model subjected to displacements via a coarsely meshed isotropic model. Across these case studies, not only did the proposed framework estimate the failure probabilities accurately, but compared with either Monte Carlo or a standard variance reduction method, it also required only a small fraction of the calls to the HF model.

Abstract The Multiphysics Object Oriented Simulation Environment (MOOSE) is an open-source, finite element framework for solving highly coupled sets of nonlinear equations. The development of the framework and applications occurs concurrently using an agile, continuous-integration software package. Included in the framework is an in-code, extensible documentation system. Using these two tools in union with the repository management tools GitHub and GitLab, a software quality plan was created and followed such that MOOSE and a MOOSE-based application (BISON) have been shown to meet the American Society of Mechanical Engineers’ Nuclear Quality Assurance-1 standard. The approach relies heavily on automation for both testing and documentation. The resulting effort demonstrates that a rigorous software quality plan may be implemented that incurs a minimal impact on day-to-day development of the software, satisfying the stringent guidelines necessary to operate the software in a safety function within a nuclear facility.

Efficient solution via Newton's method of nonlinear systems of equations requires an accurate representation of the Jacobian, corresponding to the derivatives of the component residual equations with respect to the degrees of freedom. In practice these systems of equations often arise from spatial discretization of partial differential equations used to model physical phenomena. These equations may involve domain motion or material equations that are complex functions of the systems' degrees of freedom. Computing the Jacobian by hand in these situations is arduous and prone to error. Finite difference approximations of the Jacobian or its action are prone to truncation error, especially in multiphysics settings. Symbolic differentiation packages may be used, but often result in an excessive number of terms in realistic model scenarios. An alternative to symbolic and numerical differentiation is automatic differentiation (AD), which propagates derivatives with every elementary operation of a computer program, corresponding to continual application of the chain rule. Automatic differentiation offers the guarantee of an exact Jacobian at a relatively small overhead cost. In this work, we outline the adoption of AD in the Multiphysics Object Oriented Simulation Environment (MOOSE) via the MetaPhysicL package. We describe the application of MOOSE's AD capability to several sets of physics that were previously infeasible to model via hand-coded or Jacobian-free simulation techniques, including arbitrary Lagrangian-Eulerian and level-set simulations of laser melt pools, phase-field simulations with free energies provided through neural networks, and metallic nuclear fuel simulations that require inner Newton loop calculation of nonlinear material properties.

Application packaging and distribution are the final steps for delivering software to end-users; both are frequently neglected when creating scientific software. Commercial businesses rely on electronic distribution systems that have rendered disk drives obsolete. Still, national laboratories continue to rely heavily on removable media to distribute and limit access to controlled appli- cations. With increasing concerns of unauthorized copying of sensitive applications, a modern distribution system that utilizes cryptographically secure communication and authentication pro- tocols has been developed. This new distribution system will secure the chain of custody for nuclear software while simultaneously simplifying access to these tools. This report summarizes four primary advancements made toward the secure distribution of Nu- clear Energy Advanced Modeling and Simulation (NEAMS)-developed, Multiphysics Object Ori- ented Simulation Environment (MOOSE)-based applications: application installation, package distribution, automated package building, and distribution of documentation. NEAMS is currently developing more than ten separate applications based on the open-source MOOSE Framework. Distribution of these applications has primarily been accomplished by dis- tributing source code, with end-users compiling the applications themselves. This work created a mechanism where MOOSE applications can be installed in a similar way to any other software. This allows both administrators and end-users simplified access to runnable executables. With this new installation capability, it was then possible to rethink distribution. A new, secure ca- pability for delivering MOOSE-based applications over the internet has been created. This system requires unique cryptographic tokens for authentication, greatly securing the custody chain for software. Once granted access, installation of any NEAMS code can be accomplished with these terminal commands: conda install ncrc ncrc install ncrc-bison After these two commands (and authenticating) the BISON application will be securely down- loaded from Idaho National Laboratory (INL)’s servers, installed, and ready to use. To enable this new distribution capability to be successful, the open-source Continuous Integra- tion, Verification, Enhancement, and Testing (CIVET) Continuous Integration (CI) capability was augmented to add Continous Delivery (CD). CD enables the automated building and packaging of MOOSE-based applications as they are modified by development teams, ensuring that our cus- tomers can obtain up-to-date versions of the software at any time. The need for instruction on how to use these applications was addressed through modifications to the MOOSE documentation system. The MooseDocs capability, which enables robust docu- mentation of MOOSE-based applications, has been extended to allow both for the installation of documentation and the packaging of documentation with installed applications. Together, these enhancements form the core of a new, secure distribution mechanism for nuclear simulation tools. In concert with the Nuclear Computational Resource Center (NCRC), NEAMS- developed applications will now be straightforward to obtain securely.

Because of its widespread use in multiple advanced reactor concepts, the ability to accurately simulate tri-structural isotropic (TRISO) fuel performance is essential for ensuring the safe operation of these reactors. To that end, the BISON fuel performance code has undergone significant recent development to expand its TRISO particle fuel performance modeling capabilities. This includes the development of material models, such as elastic, creep, swelling, thermal expansion, thermal conductivity, and fission gas release models. The capability to perform statistical failure analysis on large sets of samples has also been developed, utilizing a Monte Carlo scheme to execute fast-running 1-D spherically symmetric models. Stress adjustments are made in those 1-D models to account for multi-dimensional failure phenomena. Stress correlation functions are extracted from multi-dimensional failure simulation results, such as from a particle with cracked inner pyrolytic carbon (IPyC) and an aspherical particle. This paper provides a detailed description of the models used by BISON for TRISO fuel, along with a set of problems that test these models by (favorably) comparing them both with another code and experimental data. These include simulations of the Advanced Gas Reactor (AGR)-2 and AGR-5/6/7 experiments, with predictions for fuel performance parameters, failure probability, and fission product transport.

The multigroup neutron transport equation is crucial for studying the motion of neutrons and their interaction with materials. Numerical simulation of the multigroup neutron transport equation is computationally challenging because the equation is defined on a high-dimensional phase space, the computational spatial domain is complex, and the materials are heterogeneous. A scalable parallel solver is required to address such a challenge. In this paper, we study a highly parallel Newton-Krylov-Schwarz (NKS) method consisting of a Newton-based eigenvalue solver, a Krylov subspace method, and a novel multilevel Schwarz preconditioner. The multilevel method is one of the most popular preconditioners for accelerating neutron transport calculations, but the construction of coarse spaces can be expensive and often unscalable when a large number of processors is used. We propose a novel matrix coarsening algorithm in which a multilevel hierarchy is constructed using a single-component matrix instead of the full matrix of the neutron transport equation. This new coarsening algorithm is referred to as "subspace-based coarsening." Above 8,000 processors, we show a 13x enhancement in multilevel preconditioner setup time when using the subspace-based coarsening method. A partition-based balancing strategy is studied to enhance the parallel efficiency of the NKS algorithm by equalizing the work for each processor. A hierarchical mesh partitioning algorithm is employed to generate a large number of submeshes while minimizing off-node communication. We demonstrate that the proposed algorithm is scalable with more than 10,000 processors for a realistic application on three-dimensional unstructured meshes with a few billion degrees of freedom. Neutron transport calculations using the improved NKS algorithm are twice as fast as those based on the unmodified NKS solver when over 8,000 processors are employed.

With the recent development of advanced numerical algorithms, software design, and low-cost high-performance computer hardware, reliance on coupled multiphysics to predict the behavior of complex physical systems is beginning to become standard practice. This is especially true in nuclear energy applications where strong nonlinear interdependencies exist between reactor physics, radiation transport, multi-scale nuclear fuels performance, thermal fluids, etc. Resolving these nonlinear dependencies requires choices in multiphysics software approaches. Two main multiphysics modeling and simulation approaches have emerged. The first is based upon "code coupling" where disparate physics codes of different software design, code languages, and spatial and temporal integration schemes are coupled together with relatively complex data passing interfaces. The second multiphysics software approach is to employ a "cohesive" framework where all physics applications are developed with a common software design, i.e., data structures, syntax, input format, integrated spatial and temporal discretization schemes, etc. Here we present the Multiphysics Object-Oriented Simulation Environment (MOOSE) development and runtime framework and describe the framework's cohesive modeling and simulation multiphysics approach. Then, a "cohesive-like" extension of the MOOSE framework is presented where MOOSE-based physics software applications are efficiently coupled to non-MOOSE (external) physics codes to form multiphysics applications using MOOSE's unique interface capabilities. Finally, several examples of MOOSE's cohesive and cohesive-like multiphysics applications will be demonstrated. These multiphysics demonstrations will incorporate both MOOSE-based applications and external codes, including Nek5000, RELAP-7, TRACE, BISON, and Pronghorn.

Seismic analysis and risk assessment of safety-critical infrastructure like hospitals, nuclear power plants, dams, and facilities handling radioactive materials involve computationally intensive numerical models and coupled multiphysics scenarios. They are also performed in a strict regulatory environment that requires high software quality assurance standards, and in the case of safety-related nuclear facilities, a conformance to the American Society of Mechanical Engineers Nuclear Quality Assurance (NQA-1) standard. This paper introduces the open-source finite-element software, MASTODON (Multi-hazard Analysis of Stochastic Time-Domain Phenomena), which implements state-of-the-art seismic analysis and risk assessment tools in a quality-controlled environment. MASTODON is built on MOOSE (Multi-physics Object-Oriented Simulation Environment), which is a highly parallelizable, NQA-1 conforming, coupled multiphysics, finite-element framework developed at Idaho National Laboratory. MASTODON is capable of fault rupture and source-to-site wave propagation using the domain reduction method, nonlinear site response, and soil-structure interaction analysis, implicit and explicit time integration, automated stochastic simulations, and seismic probabilistic risk assessment. When coupled with other MOOSE applications, MASTODON can also solve strongly and weakly coupled multiphysics problems. This paper presents a summary of the capabilities of MASTODON and some demonstrative examples.

Microreactors are small mobile transportable nuclear reactors with thermal power less than 20 MWt that are designed to meet the needs of remote areas, military installations, emergency operations, and disaster relief zones. These reactor are concepts that are intended to be factory-manufacturable, easily transportable, and will allow for semi- or full-autonomous operation. To assist with development of microreactors, modeling and experimentation need to be performed with verification and validation to gain confidence in the models and tools. The objective of this study is apply advanced modeling and simulation capabilities being developed by the DOE Office of Nuclear Energy Nuclear Energy Advanced Modeling and Simulation (NEAMS) program to perform integrated modeling and simulation capability for multiphysics simulation of the microreactor concepts. This activity will provide an opportunity to exercise the codes to provide both gain experience and to provide feedback to the developers.