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At least 343 records · Page 19

Dynamic flux surrogate-based partitioned methods for interface problems

Loosely coupled partitioned methods for multiphysics problems treat each subproblem as a separate entity and advance them independently in time. In so doing these methods enable code reuse, increase concurrency and provide a convenient framework for plug-and-play multiphysics simulations. However, mathematically loosely coupled schemes are equivalent to a single step of an iterative solution method, which can compromise their accuracy and stability. We present a new data-driven partitioned method for coupled parametric PDEs that can improve upon the accuracy of traditional loosely coupled methods without incurring a performance penalty. To that end, we replace conventional field transfers across the interface by a surrogate for the dynamics of the interface flux exchanged between the subdomains. To develop this surrogate we apply dynamic mode decomposition to a non-standard staggered-in-time state, comprising the interface flux and small solution patches near the interface. The new approach shifts the main computational burden to an offline training phase, whereas application of the surrogate in the online phase amounts to a single matrix–vector multiplication. In conclusion, we provide stability analysis of the surrogate-based partitioned scheme and include numerical results that demonstrate its potential.

Dynamic mode decomposition (DMD)↗

Griffin Software Development Plan

Griffin is a MOOSE-based reactor physics application for advanced reactor multiphysics modeling and simulation. The application is developed in a consistent multiphysics environment with strong software quality assurance. Griffin inherited most of the capabilities of MAMMOTH/Rattlesnake and is adopting the capabilities from PROTEUS that are needed in the code. The toolset includes a variety of deterministic radiation transport solvers for fixed source, k-eigenvalue, ad-joint, and subcritical multiplication, as well as transient solvers for point-kinetics, improved quasi-static, and spatial dynamics. The code contains the cross-section preparation capabilities applicable to fast and thermal reactors, including TRISO-fueled reactors. Core management capabilities include core performance, fuel depletion and shuffling, equilibrium core calculation, pebble-bed reactor run-in and equilibrium core, molten-salt reactor delayed neutron precursor drift, and control rod and drum movement with cusping correction. This software development plan presents the current and future capabilities and features in Griffin for the design and analysis of non-light-water reactor systems in steady-state and transient conditions.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Multiphysics Simulations of MSRE with NEAMS Thermal Hydraulics Tools

This report documents the benchmarks being developed and simulations performed using tools and codes developed under the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program, utilizing MSRE experimental data. In FY23, three main work scopes were investigated under the NEAMS MSR work package at ANL. The first scope investigated the Griffin-SAM coupling model for simulating the pump startup transient experiment of MSRE. The analyses start with a simple model (single-channel, single-lattice), gradually adding more details (multi-channel, full-core) into the model. The results show that the reactivity loss curve is very sensitive to the axial boundary conditions and the radial core discretization. The simple model can predict a similar reactivity trend as that of the more sophisticated model, which is likely due to error cancellation. Accurately modeling the axial boundary condition may further improve the reactivity trend but would require significant efforts to generate the mesh of the MSRE inlet and upper plenum. The core channel radial discretization for the Griffin-SAM coupled model also depends on the flow distribution. Given the complex geometry in the inlet plenum, the flow distribution needed to be calculated from CFD analysis, which was performed using the NekRS code. This analysis employed a MSRE CAD model developed by Copenhagen Atomics. The CAD model was disassembled to keep the inlet plenum region only, which was subsequently cleaned and modified so that the mesh generated is under the memory limit. The results are merged to a few radial regions to show that the flow rate is highest in the central region. This would be useful for future improvement of the Griffin-SAM coupling model of the MSRE core. The last task investigated is tritium transport modeling using the standalone SAM code. This task aimed to initiate the effort to demonstrate and validate the tritium transport model implemented in SAM. The preliminary investigation employed an MSRE model consisting of the primary loop. Three tritium transport pathways were examined including the retention in the graphite, the permeation through the HX tube wall, and the removal from the off-gas system. The results compare well with the MSRE data, but improvements are still needed on the initial conditions (i.e., the present state may not have reached equilibrium), the boundary conditions, the off-gas system modeling, and a better numerical strategy to reach the equilibrium state.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Three-dimensional cooperative inversion of airborne magnetic and gravity gradient data using deep-learning techniques

Using multiple geophysical methods has become a prevailing approach in numerous geophysical applications to investigate subsurface structures and parameters. These multimethod-based exploration strategies have the potential to greatly diminish uncertainties and ambiguities encountered during geophysical data analysis and interpretation. One of the applications is the cooperative inversion of airborne magnetic and gravity gradient data for the interpretation of data obtained in mineral, oil and gas, and geothermal explorations. In this paper, a unified cooperative inversion framework is designed by combining the standard separate inversions with a deep neural network (DNN), which serves as the link between different types of data. A well-trained DNN takes the separately inverted susceptibility and density models as the inputs and provides improved models that will be used as the initial models of deterministic inversions. A two-round iteration strategy is adopted to guarantee the reasonability of the recovered models and overall efficiency of the inversion. In addition, this deep-learning (DL)-based framework demonstrates excellent generalization abilities when tested on models that are entirely distinct from the training data sets. The framework can easily incorporate multiphysics without necessitating any structural changes to the network. Synthetic experiments validate that our DL-based method outperforms conventional separate inversions and cross-gradient-based joint inversion in view of the accuracy of the recovered models and inversion efficiency. Successful application to field data further verifies the effectiveness of our DL-based method.

Geochemistry & Geophysics↗

Thermal Hydraulics Validation Activities in the ART-GCR Campaign

The Advanced Reactor Technologies - Gas Cooled Reactor Campaign (ART-GCR) is part of the United States Department of Energy - Office of Nuclear Energy's Advanced Reactor Technologies program aimed at developing a High Temperature Gas-cooled Reactor (HTGR) which will offer enhancements in safety and efficiency. The Design, Methods, and Validation arm of the ART-GCR program provides experience and advanced tools for HTGR design and analysis. The Methods and Validation arm is developing data to validate predictions of decay heat removal through an extensive experimental campaign the Natural Convection Shutdown Heat Removal Test Facility at Argonne National Laboratory. In-core thermal hydraulics validation is being facilitated through the OECD/NEA's Thermal Hydraulic Code Validation Benchmark for High Temperature Gas-Cooled Reactors using HTTF Data. That benchmark contains code-to-code and code-to-data comparisons for 3 sets of HTGR thermal hydraulics phenomena. This ongoing benchmark activity has 16 participants from 9 countries developing leading insights into HTGR thermal hydraulics code validation. The ART-GCR campaign is also working on the development of state-of-the-art MOOSE-based models of the High Temperature Engineering Test Reactor (HTTR). Through the OECD/NEA's HTTR Loss of Forced Cooling (LOFC) program, the ART-GCR campaign is developing a multiphysics transient code validation benchmark based on 3 HTTR experiments that will provide an opportunity for international collaboration on multiphysics code validation.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

Interface Problem Formulation Improvements with Application to Nuclear Fuel Performance Analysis

The U.S. Department of Energy’s Nuclear Energy Advanced Modeling and Simulation Program aims to develop predictive capabilities by applying computational methods to the analysis and design of advanced reactor and fuel cycle systems. This program has been providing engineering scale support for the development of BISON, a high-fidelity and high-resolution fuel performance tool. This report documents new developments and robustness improvements in mechanical and thermal (gap heat transfer) contact formulations. The improvements range from the migration of industrial level (“assessment”) nuclear fuel model setups to the usage of mortar formulations, the addition of frictional contact to one-dimensional layered representations of fuel and cladding components, and the addition of the Petrov-Galerkin approach to dual mortar, which improves performance on curved, relatively coarse meshes. In addition, the Lagrange-multiplier enforcement of mechanical mortar contact constraints has been extended to two additional types of enforcement: penalty and augmented Lagrange-Uzawa. We show that the latter approach yields the same interface results as dual mortar in the Multiphysics Object-Oriented Simulation Environment, with the advantage of not worsening the condition number of the system matrix—thereby enabling the use of some general implementations of iterative preconditioners, at the expense of additional system evaluations (i.e., augmentations).

42 ENGINEERING↗

Smoothed particle hydrodynamics modeling and analysis of oxide reduction process for uranium oxides

A common kinetic feature for oxide reduction chemical/electrochemical processes is oxygen transport via a porous metallic layer, which has been considered as a rate-determining step for reducing uranium oxides to metallic uranium. Accounting this kinetic behavior must involve the resolution of the moving reactive interface between shrinking oxide and expanding metal phases. This study presents a numerical model using smoothed particles hydrodynamics (SPH) to effectively deal with the evolution of the shrinking core reaction interface and oxygen transport via mass transfer of lithium oxide (Li 2 O) species in multiple mass transfer domains. We successfully validated the proposed model against a theoretical derivation for the oxide reduction process handling a shrinking oxide core with molten salt and metal ash medium on a simple planar geometry. Armed with successful validation results, the model examined a realistic reactant geometry to extend the arguments beyond the one-dimensional analyses, allowing the proposed model to apply to general application scenarios with multi-dimensional geometry. Here, this study demonstrated that the proposed model could simulate and evaluate an arbitrary reaction basket design without iterative experimental trials, which is prohibitive for a scaled high-temperature molten salt study in an inert environment. The construct potentially provides not only deep insights on multiphysics behaviors governing the process dynamics but also a robust framework for evaluating and screening candidate basket designs in the most cost-effective manner.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Progress Towards NQA-1 for Cardinal in FY25

Cardinal is a wrapping of the GPU-oriented spectral element Computational Fluid Dynamics (CFD) code NekRS and the Monte Carlo particle transport code OpenMC within the Multiphysics Object-Oriented Simulation Environment (MOOSE). Cardinal provides high-resolution thermal-hydraulics and/or radiation transport feedback to MOOSE multiphysics simulations. Multiphysics feedback is implemented in a geometry-agnostic manner which eliminates the need for rigid one-to-one mappings. A generic data transfer implementation also allows NekRS and OpenMC to couple to any MOOSE application, enabling a broad set of multiphysics capabilities. Cardinal simulations can also leverage combinations of MPI, OpenMP, and GPU resources. Cardinal continuous development and improvement efforts have led to the software being considered as a high-fidelity design and licensing tool for key areas of nuclear reactor relevant physics, including neutron transport, fluid flow, heat transfer, and mechanical processes. The fast development and expansion of the software from a pure R&D framework towards its application in the nuclear industry and regulation require a focus on developing, enhancing,and maintaining Cardinal’s software quality through strict adherence to a Software Quality Assurance (SQA) framework and SQA program. To facilitate compliance with SQA standards, the Cardinal SQA Program was initiated during Fiscal Year 2023 (FY23). During the development of the Cardinal SQA Program, multiple gaps have been identified. These gaps are primarily related to model verification and code pedigree as they relate to the use of Cardinal as an analysis tool. These gaps were captured in a report published in 2023. A second report highlighted the progress made during Fiscal Year 2024 (FY24) and described Argonne’s effort to document and integrate software verification within Cardinal’s software development process. This report documents the progress made towards NQA-1 for Cardinal in the Fiscal Year 2025 (FY25). All cases in the expanded Continuous Integration (CI) suite of NekRS are included in this report which test the solvers and modules available in NekRS exhaustively. The NekRS tests are integrated with the Cardinal CI suite and made available in publicly accessible Github documentation. Following the CI practice permits integrating of source code changes frequently and ensuring that the integrated codebase clears the verification testing for the software. Also in this report is a brief overview of the development of the Cardinal Software Quality Assurance Plan (SQAP) that was done in FY25, though it should be noted that the rest of the documentation for the SQA program needs to be developed in a future step of this task.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Hydraulic Modeling of Induced and Propagated Fractures: Analysis of Flow and Pressure Data From Hydromechanical Experiments in the COSC-1 Deep Borehole in Crystalline Rock Near Åre, Sweden

To characterize the coupled hydromechanical behavior of rock fractures, the step-rate injection method for fracture in-situ properties (SIMFIP) was conducted with a specialized downhole probe developed by Guglielmi et.al. In June 2019, a field campaign was carried out near Åre, Sweden, where the SIMFIP probe was applied in the Collisional Orogeny in the Scandinavian Caledonides-1 scientific borehole to understand the dynamics of injection-induced fracture initiation, fracture opening, and shearing due to water injection-withdrawal in a borehole interval isolated by two packers. Three intervals were investigated at ~500 m depth: (a) an unfractured section (intact rock), (b) a section with non-conductive fractures, and (c) a section with hydraulically conductive fractures. Pressure, injection flow rate, and borehole wall displacement were simultaneously measured during the tests. In the present study, the geometry of the induced fracture and deformation of existing fractures at different time stages of the tests are determined based on a hydrologic model by using the measured pressure and flow data during each time stage of the experiment. A numerical model for the fluid flow within the fracture and the packed-off borehole interval is implemented within COMSOL Multiphysics. By matching model simulations with observed data for all three sections, estimates of the induced and propagated fractures' radius and aperture at successive time stages have been obtained in each case. We could also determine the non-linear relationship between fracture aperture and pressure for values above fracture opening pressures. The model results provide insights for the understanding of pressure-induced fracture initiation and propagation in crystalline rock.

58 GEOSCIENCES↗

Software Quality Assurance for the MOOSE-Based Open-Source Multiphysics Code Cardinal - An Expanded CI Testing Suite

Cardinal is a wrapping of the GPU-oriented spectral element Computational Fluid Dynamics (CFD) code NekRS and the Monte Carlo particle transport code OpenMC within the Multiphysics Object-Oriented Simulation Environment (MOOSE). Cardinal provides high-resolution thermal-hydraulics and/or radiation transport feedback to MOOSE multiphysics simulations. Multiphysics feedback is implemented in a geometry-agnostic manner which eliminates the need for rigid one-to-one mappings. A generic data transfer implementation also allows NekRS and OpenMC to couple to any MOOSE application, enabling a broad set of multiphysics capabilities. Cardinal simulations can also leverage combinations of MPI, OpenMP, and GPU resources. Cardinal continuous development and improvement efforts have led to the software being considered as a high-fidelity design and licensing tool for key areas of nuclear reactor relevant physics, including neutron transport, fluid flow, heat transfer, and mechanical processes. The fast development and expansion of the software from a pure R&D framework towards its application in the nuclear industry and regulation require a focus on developing, enhancing and, maintaining Cardinal’s software quality through strict adherence to a Software Quality Assurance (SQA) framework and SQA program. To facilitate compliance with SQA standards, the Cardinal SQA Program has been initiated during Fiscal Year 2023 (FY23). During the development of the Cardinal SQA Program, multiple gaps have been identified. These gaps are primarily related to model verification and code pedigree as they relate to the use of Cardinal as a safety analysis tool. These gaps have been captured in a report published in 2023. A second report highlighted the progress made during Fiscal Year 2024 (FY24) and described Argonne’s effort to document and integrate software verification within Cardinal’s software development process. This report documents a snapshot of the verification test cases currently available for Cardinal and NekRS in their assimilation into a Continuous Integration (CI) platform. Following the CI practice permits the integrating of source code changes frequently and ensuring that the integrated codebase clears the verification testing for the software. It should be noted that the SQA program itself, including the program plans, procedures, configuration management, and testing strategies, need to be developed in a future step of this task.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Accelerating Nuclear Fuels and Materials Qualification by Multi-Level Irradiation Experiment Campaign

The advanced reactor technologies feature fuels, coolants, and materials that promise safer operating conditions under normal and accident scenarios. However, the nuclear fuels and materials qualifications require several decades (for example, new reactor fuel qualification from conceptualization requires about 20 years). Therefore, accelerating nuclear fuels and materials qualification is essential, and it can be achieved by combining high through-put materials irradiation and testing, advanced post-irradiation examinations, and Multiphysics modeling. This paper addressed the associated challenges in accelerating nuclear fuels and material qualification for new and advanced reactor designs, which differ based on fuel, coolant, operating conditions, and structural materials. These challenges vary for radiation level, operating conditions (e.g., temperature and pressure), and coolant type (e.g., corrosion environment). In addition, the challenges and limitations in modeling tools, experimental facilities, and licensing guidelines are also discussed, and a general solution path forward is recommended.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Presentation: Accelerating Nuclear Fuels and Materials Qualification by Multi-Level Irradiation Experiment Campaign

The advanced reactor technologies feature fuels, coolants, and materials that promise safer operating conditions under normal and accident scenarios. However, the nuclear fuels and materials qualifications require several decades (for example, new reactor fuel qualification from conceptualization requires about 20 years). Therefore, accelerating nuclear fuels and materials qualification is essential, and it can be achieved by combining high through-put materials irradiation and testing, advanced post-irradiation examinations, and Multiphysics modeling. This paper addressed the associated challenges in accelerating nuclear fuels and material qualification for new and advanced reactor designs, which differ based on fuel, coolant, operating conditions, and structural materials. These challenges vary for radiation level, operating conditions (e.g., temperature and pressure), and coolant type (e.g., corrosion environment). In addition, the challenges and limitations in modeling tools, experimental facilities, and licensing guidelines are also discussed, and a general solution path forward is recommended.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Virtual Engineering of Low-Temperature Conversion

In this work, we present the development of an overarching software framework and supporting multiphysics models to simulate the end-to-end process of biomass conversion. This virtual engineering (VE) software is designed with the goal of accelerating research and development and reducing risk for market-relevant biomass conversion processes. We currently support multiple models, computing paradigms, and fidelities representing the steps of feedstock pretreatment, enzymatic hydrolysis, and bioconversion. Although this VE approach was developed to support a biomass workflow, we have designed each component in a way that allows us to easily support new domains, unit models, and feedstocks. We begin by presenting the user-facing aspects of the VE software and highlight how simulated elements are defined and linked by VE functions. We then present an overview of the high-fidelity computational fluid dynamics (CFD) models developed to support our target domain before segueing into our efforts to develop accurate and fast surrogate models, capturing the salient outcomes from the CFD simulations in a significantly less computationally demanding manner. We then present how VE calculations interface with a commercial techno-economic analysis software, Aspen Plus. We conclude by presenting VE case studies that leverage these methods and discuss how our methods can be extended to support a wide variety of accelerated biofuel commercialization pathways in the future.

biofuel↗

Assessment of CASL VERA for BWR analysis and application to accident tolerant SiC/SiC channel box

Application of the Virtual Environment for Reactor Applications (VERA) to BWR analysis is assessed in this paper by comparing results to those calculated using other widely-used modeling tools, namely the U.S. Nuclear Regulatory Commission’s PARCS/PATHS and the Serpent Monte Carlo particle transport code. Additionally, VERA is used to calculate 3-D temperature and fast neutron flux distributions in silicon carbide (SiC) fiber-reinforced, SiC matrix composite (SiC/SiC) BWR channel boxes, which are being studied as an Accident Tolerant Fuel core structural material concept. We found that the code-to-code comparisons were favorable, and the SiC/SiC channel box evaluation demonstrates the many advanced modeling features VERA provides while also highlighting the non-uniformity in fast neutron flux distributions that can play a role in potential SiC/SiC channel box deformation. Traditional BWR analysis tools do not have the calculation fidelity necessary for coupled assessment of flux and temperature gradients in a SiC/SiC channel box. VERA is a state-of-the-art modeling environment that was developed to increase the safety and economic competitiveness of nuclear power through improved modeling accuracy. While VERA has already been deployed in the nuclear industry for PWR applications, the current study is a vital initial step in the extensive development, validation, and verification that VERA must go through to be useful for BWR applications.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Design and Analysis of a Mutual Inductance Level Sensor for Liquid Metals

Here, this article describes the design and analysis of an electromagnetic level sensor for use in high-temperature liquid metal systems. The mutual inductance level sensor (MILS) described in this work was fabricated using two single-conductor mineral insulated cables wrapped in a bifilar fashion around a stainless steel tube core and was housed in an isolating thimble that preserved the pressure boundary of the test vessel. Two sensor variations were fabricated that differ only in active length, 1016 and 1778 mm. Experimental data were collected using the 1016-mm sensor (MILS-MKII-040) that demonstrated a sensitivity of 9.2 μ V/mm in a room temperature testing stand that used solid aluminum as a surrogate for liquid metal. Experimental data were collected using the 1778-mm sensor (MILS-MKII-070) that demonstrated a sensitivity of 6.9 μ V/mm in the high-temperature (300 ° C) liquid sodium environment at the mechanisms engineering test loop (METL) of Argonne National Laboratory. The sensor performance was found to be repeatable over the course of several months, with roughly ±1% deviation from nominal output. Finite element models were developed in COMSOL Multiphysics that fully describe each test setup, and the models were validated using experimental data. The validated COMSOL models were used to perform an array of analyses that examined the performance of the sensor in differing environments. Maximizing the coil diameter inside the isolating thimble was found to maximize the signal and sensitivity of the sensor. An optimal operating frequency was found near 1000 Hz using both experimental data and COMSOL. The influence of a metallic thimble surrounding the sensor and a metallic sensor core was quantified and found to be negligible at the optimal operating frequency. The sensitivity of the sensor was quantified when monitoring the level of additional liquid metals. These include lead, lead-bismuth eutectic (LBE), sodium-potassium alloy (NaK), and lithium (in addition to sodium). The sensitivities were quantified using liquid metal properties at 350 ° C and 650 ° C. The geometry of the test stand model, all material properties used in the model, and the results are presented in a manner that allows the reader can replicate the model and perform additional analyses.

COMSOL↗

Electron Target Cooling Analyses of the KIPT ADS Using MCNP and Ansys Fluent

This study presents multiphysics analyses of the electron target cooling system of the accelerator-driven system (ADS) of the Kharkiv Institute of Physics and Technology (KIPT) using MCNP and Fluent computer programs. MCNP has been used to transport electrons, gammas, and neutrons, and to calculate the energy deposition in the target materials. The MCNP mesh-tally data have been imported into Fluent by a C subroutine that has been compiled and linked to Fluent as a user-defined function.The KIPT ADS is located in Ukraine and was in operation until February 2022. The Fluent model is based on the computer-aided design files from the manufacturing process of the target assembly. Here, the Fluent results for the reference case match very well the literature results obtained by STAR-CCM+ during the design phase. Other cases that differ from the reference one have been analyzed; in these cases, it is assumed a malfunction of the electron accelerator or of the water cooling system. The target cooling system operates normally for all the analyzed cases except when the inlet water mass flow rate is decreased. The transient analysis showed that the target cooling system can operate for 180 s with full power when the inlet water mass flow rate is decreased down by 75%.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Modeling Isotope Separation in Electrochemical Lithium Deposition

Naturally occurring Li consists of two stable isotopes, 6 Li with an abundance of about 7.5%, and 7 Li making up the remainder with 92.5%. The development of a 6 Li enrichment technique, in terms of technical reliability and environmental safety to reach 6 Li future requirements, represents a key step in the roadmap for nuclear fusion energy supply worldwide. This paper uses finite element analysis-based models to simulate electrochemical Li isotope separation, which is an attractive method in terms of simplicity, safety, and scalability. In the model, we quantitatively analyze how different electrochemical factors including thermodynamics, charge-transfer kinetics, and diffusivities affect the separation process (separation factor), together with cell parameters, such as cell length and current density. The maximum separation factor of 1.128 could be obtained with the cell under the optimal thermodynamic, kinetic, and diffusive conditions, which is among the highest separation factors ever reported. Furthermore, these results will assist in designing the actual isotope separation setup with large separation factor and appropriate timing for sample collection.

07 ISOTOPE AND RADIATION SOURCES↗

Non-intrusive reduced order modeling of natural convection in porous media using convolutional autoencoders: Comparison with linear subspace techniques

Natural convection in porous media is a highly nonlinear multiphysical problem relevant to many engineering applications (e.g., the process of CO 2 sequestration). Here, we extend and present a non-intrusive reduced order model of natural convection in porous media employing deep convolutional autoencoders for the compression and reconstruction and either radial basis function (RBF) interpolation or artificial neural networks (ANNs) for mapping parameters of partial differential equations (PDEs) on the corresponding nonlinear manifolds. To benchmark our approach, we also describe linear compression and reconstruction processes relying on proper orthogonal decomposition (POD) and ANNs. Further, we present comprehensive comparisons among different models through three benchmark problems. The reduced order models, linear and nonlinear approaches, are much faster than the finite element model, obtaining a maximum speed-up of 7 × 10 6 because our framework is not bound by the Courant–Friedrichs–Lewy condition; hence, it could deliver quantities of interest at any given time contrary to the finite element model. Our model’s accuracy still lies within a relative error of 7% in the worst-case scenario. We illustrate that, in specific settings, the nonlinear approach outperforms its linear counterpart and vice versa. We hypothesize that a visual comparison between principal component analysis (PCA) and t-Distributed Stochastic Neighbor Embedding (t-SNE) could indicate which method will perform better prior to employing any specific compression strategy.

97 MATHEMATICS AND COMPUTING↗