Uranium nitride-fueled triso fuel particles

Abstract

Computer system determines a particle design for a multilayer nuclear fuel particle. A first particle design includes a first set of values for a plurality of design variables corresponding to the multilayer nuclear fuel particle. Using the first set of values as inputs, the computer system (i) causes execution of a thermal-mechanical model and obtains a first predicted outcome; (ii) causes execution of a neutronics model and obtains a second predicted outcome; (iii) determines an aggregate residual for the first particle design based on the first and second predicted outcomes, and (iv) identifies a second particle design for the multilayer nuclear fuel particle. The second particle design includes a second set of values corresponding to the plurality of design variables. The computer system uses the second set of values and repeats steps (i) through (iv) identifying an updated particle design, to obtain an optimized particle design for the multilayer particle.

Description

Patent 102085-5039-WOURANIUM NITRIDE-FUELED TRISO FUEL PARTICLES TECHNICAL FIELD

[0001] The present disclosure relates generally to the design of nuclear fuels and more specifically to systems and methods that utilize machine learning to quickly produce viable designs for multi-layered fissionable fuel particles.BACKGROUND

[0002] In the discussion that follows, reference is made to certain structures and / or methods. However, the following references should not be construed as an admission that these structures and / or methods constitute prior art. The Applicant expressly reserves the right to demonstrate that such structures and / or methods do not qualify as prior art against the present invention.

[0003] A nuclear reactor uses nuclear fuel to sustain a nuclear chain reaction. A TRi- structural ISOtropic (TRISO) fuel particle (or TRISO particle) is a type of nuclear fuel that can handle the higher operating temperatures of advanced nuclear reactors, i.e., above 1170 K. Typically, a TRISO particle comprises a kernel that is made of a radioactive material (e.g., uranium), encapsulated by layers of carbon and ceramic-based materials that act as a containment system to prevent the release of radioactive fission products under all reactor conditions. TRISO particles are then packed into pellets or billiard-sized spherical fuel form for use in high temperature gas or molten salt-cooled reactors.SUMMARY

[0004] TRISO particles must be designed and fabricated to not only meet the operating requirements, but remain intact over the range of operating conditions that can be encountered both during normal reactor operation and during accidents. For example, a TRISO particle must meet neutronics requirements that sustain criticality7(fission reactions), which is also dependent on fuel and moderator properties. Additionally, it must also be resistant to the factors that impact fuel performance, such as neutron irradiation, corrosion, oxidation, and high temperatures. The containment system should not melt or crack under the stresses of energy flux and cycling.DB1 / 154135139.1Patent 102085-5039-WO

[0005] The properties of TRISO particles are affected by various parameters, making the optimization of their design challenging. It can take days or weeks to find a valid combination of values for design variables (e.g., such as number of layers, thickness of a respective layer, material for a respective layer) of a particle. After that, thermal and stress simulations and neutronics calculations must be run. Historically, attempts to speed up this process has taken the form of: (i) adding computing power and / or using supercomputers; (ii) accelerating the computations, such as using a GPU computing development; and / or (iii) utilizing top end software, which treats inefficiencies in workflow and format compatibility, and may deploy an alternative but non-validated solver. However, the processes are still very slow, and often it can take weeks or months to determine that a proposed particle design does not satisfy all of the requirements.

[0006] Accordingly, there is a need for improved methods and systems that enable optimized TRISO particle designs to be determined efficiently. Additionally, there remains a need to develop and qualify TRISO particles in which the dimension and compositions of the layers have been tailored to specific applications and reactor designs.

[0007] Some embodiments of the present disclosure utilize an artificial intelligence (Al) algorithm that combines data science, multi-physics and engineering expertise to accelerate the design and optimization of TRISO particle technologies. The algorithm finds an optimal particle design space within user specified constraints, which provides: (i) rapid, automated assessment of conceptual particle designs; (ii) identifies a valid parameter space and optimal parameters that satisfy neutronic, thermal-mechanical, and thermal-hydraulics requirements; and (iii) synthesizes and analyzes results to facilitate decision making.

[0008] In accordance with some embodiments, a method executes at a computer system having one or more processors and memory. The method includes determining a first particle design for a multilayer nuclear fuel particle. The first particle design includes a first set of values for a plurality of design variables corresponding to the multilayer nuclear fuel particle. Each respective value in the first set of values corresponds to a respective one of the design variables. The method includes, using the first set of values corresponding to the plurality of design variables as inputs: (i) causing execution of a thermal-mechanical model and obtaining, as output from the thermal-mechanical model, a first predicted outcome that is based at least in part on the first particle design; (ii) causing execution of a neutronics model and obtaining.DB1 / 154135139.1Patent 102085-5039-WO as output from the neutronics model, a second predicted outcome based at least in part on the first particle design; (iii) determining an aggregate residual for the first particle design based on the first predicted outcome and the second predicted outcome; and (iv) in accordance with the determined aggregate residual value, identifying a second particle design for the multilayer nuclear fuel particle, the second particle design including a second set of values corresponding to the plurality of design variables. The method includes using the second set of values corresponding to the plurality of design variables as inputs, repeating the steps of (i) causing execution of the thermal-mechanical model, (ii) causing execution of the neutronics model, (iii) determining the aggregate residual value for the second particle design, and (iv) identifying an updated particle design, to obtain an optimized particle design for the multilayer particle.

[0009] In some embodiments, obtaining the optimized particle design for the multilayer particle includes executing a plurality of iterations. Each iteration of the plurality of iterations (1) identifies a respective updated particle design having a respective updated set of values, corresponding to the plurality of design variables, based on a respective prior iteration of the plurality of iterations, and (2) uses the respective updated particle design to perform the steps of (i) causing execution of the thermal -mechanical model, (ii) causing execution of the neutronics model, (iii) determining the aggregate residual value, and (iv) identifying the updated set of values corresponding to the plurality of design variables for a subsequent iteration of the plurality of iterations. In some embodiments, the method includes, after executing the plurality of iterations, receiving user selection of the optimized particle design for the multilayer nuclear fuel particle. The optimized particle design has a corresponding set of values for the plurality of design variables.

[0010] In accordance with some embodiments of the present disclosure, a computer system comprises one or more processors and memory'. Typically, the computer system includes a single computer or workstation, or plurality of computers, each having one or more CPU and / or GPU processors and memory. The memory stores memory storing instructions that, when executed by the one or more processors, cause the computer system to perform any of the methods disclosed herein.

[0011] In accordance with some embodiments of the present disclosure, a non- transitory computer readable storage medium stores computer-executable instructions. TheDB1 / 154135139.1Patent 102085-5039-WO computer-executable instructions, when executed by one or more processors of a computer system, cause the computer system to perform any of the methods disclosed herein.

[0012] Note that the various embodiments described above can be combined with any other embodiments described herein. The features and advantages described in the specification are not all inclusive and, in particular, many additional features and advantages will be apparent to one of ordinary skill in the art in view of the drawings, specification, and claims. Moreover, it should be noted that the language used in the specification has been principally selected for readability and instructional purposes and may not have been selected to delineate or circumscribe the inventive subject matter.BRIEF DESCRIPTION OF THE DRAWINGS

[0013] For a better understanding of the disclosed systems and methods, as well as additional systems and methods, reference should be made to the Description of Implementations below, in conjunction with the following drawings in which like reference numerals refer to corresponding parts throughout the figures.

[0014] Figure 1 A illustrates a cross-sectional view of a TRISO particle in accordance with some embodiments.

[0015] Figure IB illustrates exemplary values for respective metrics of the TRISO particles in accordance with some embodiments.

[0016] Figure 1C shows a scanning electron microscope (SEM) image of uranium nitride kernels.

[0017] Figure 2 provides a high-level overview of a process for designing a nuclear fuel particle, in accordance with some embodiments.

[0018] Figure 3 illustrates a block diagram of a computer system in accordance with some embodiments.

[0019] Figures 4A to 4E illustrate a flowchart diagram for a method of designing nuclear fuel particles, in accordance with some embodiments.DB1 / 154135139.1Patent 102085-5039-WO

[0020] Figures 5A to 5C collectively illustrate experimental data showing the effect of the inner pyrocarbon (IPyC) layer on particle failure, nominal thicknesses of respective layers of a TRISO particle, and their respective varied ranges during a particle optimization process.

[0021] Figures 6A and 6B illustrate thermal physical properties, mechanical properties, and phenomena (e.g., swelling, growth / creep, and a failure mode) of respective layers of a TRISO particle that are input into BISON for thermal-mechanical analysis, in accordance with some embodiments.

[0022] Figure 7 contains views A to D that collectively illustrate the major components and methodology used to determine the failure probability of a population of TRISO particles, in accordance with some embodiments.

[0023] Figures 8A and 8B are plots showing residual values as a function of the two primary criteria for the TRISO particle design, in accordance with some embodiments,

[0024] Figures 9A and 9B are plots showing changes in the aggregate residual values over the course of the particle optimization process, in accordance with some embodiments.

[0025] Reference will now be made to implementations, examples of which are illustrated in the accompanying drawings. In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention. However, it will be apparent to one of ordinary skill in the art that the present invention may be practiced without requiring some of these specific details.DESCRIPTION OF IMPLEMENTATIONS

[0026] Figure 1A illustrates a cross-sectional view of a TRISO particle 100 in accordance with some embodiments. The TRISO particle includes a fuel kernel 102. a carbon buffer layer 1 4 (e.g.. graphite carbon layer or low-density carbon layer), an inner pyrolytic carbon (IPyC) layer 106, a silicon carbide (SiC) layer 108, and an outer pyrolytic carbon (OPyC) layer 110. During fabrication, the carbon buffer layer 104, the IPyC layer 106, the SiC layer 108, and the OPyC layer 110 are deposited on top of the fuel kernel 102 sequentially in this specific order.

[0027] V arious layers have specific functions in the TRISO particle 100. For example, the carbon buffer layer 104 provides space for fission gas and carbon monoxide accumulationDB1 / 154135139.1Patent 102085-5039-WO and accommodates fission recoils and in some embodiments, the carbon buffer layer 104 comprises ~ 50% dense pyrolytic carbon graphite. The IPyC layer 106 contributes to fission gas retention, provides a conducive surface for silicon carbide deposition, and protects the fuel kernel 102 during SiC deposition. The SiC layer 108 is the main structural layer and is also the primary coating layer for retaining non-gaseous fission products. The OPyC layer 110 contributes to fission gas retention, protects the SiC layer during handling, and provides a surface for bonding to the fuel matrix.

[0028] Figure IB illustrates a table 120 that includes exemplary values for the kernel diameter and thicknesses of the carbon buffer layer, IPyC layer, SiC layer, and OPyC layer for a TRISO particle having a UN or UCO kernel, in accordance with some embodiments.

[0029] According to some embodiments of the present disclosure, the fuel kernel 102 of the TRISO particle 100 compnses high-assay, low-enriched (~ 20% uranium-235) uranium carbo-nitride (UCN) or uranium nitride (UN) fuel. The thicknesses of each of the four layers (i.e., the carbon buffer layer 104, the IPyC layer 106, the SiC layer 108, and the OPyC layer 110) has been determined using an Al algorithm (e.g., core reactor suite 328) so that the TRISO particle 100 performs optimally under operating conditions expected in a high-temperature gas- cooled nuclear reactor. The particle design process is described in further detail with respect to Figures 2, 3, and 4.

[0030] The technical advantages of UN and / or UCN over UCO in the TRISO particle 100 include:(i) Compared to traditional uranium oxy-carbide (UCO) fuel, the material make-up of UN and / or UCN allows for an increased number of uranium atoms per unit volume. This feature enables the design of physically smaller nuclear cores, which in turn reduces the total reactor manufacturing cost.(ii) UN and / or UCN have higher thermal conductivities than UCO. This feature enables increased nuclear core and nuclear fuel design freedom and allows the UN / UCN fuel to operate at higher temperatures than UCO, which introduces energy conversion efficiencies to the operation of a given nuclear reactor design.(iii) UN / UCN TRISO fuel particles will perform better at high uranium burnup values.UC / UCN swells less than UCO and produces less fission gases and markedly lessDB1 / 154135139.1Patent 102085-5039-WO fission released oxygen than UCO fuel. These characteristics reduce the likelihood of TRISO particle failure during operation. Better performance at high burnup also allows the UN and / or UCN fuel to operate for longer periods of time before end of life, which introduces efficiencies and cost savings into the operation and capital cost of a given nuclear reactor design.

[0031] Figure 1C shows a scanning electron microscope (SEM) image of uranium nitride kernels.

[0032] Figure 2 provides a high-level overview of an iterative process 200 for designing a nuclear fuel particle, in accordance with some embodiments. An Al algorithm (e.g., core reactor suite 328, Figure 3) that combines data science, multi-physics and engineering expertise receives (201) user specification of a total number of iterations to be executed. The algorithm identifies (202) an initial particle design (e.g., by sampling a particle design space 334). The algorithm passes the initial particle design to a thermal-mechanical analysis engine 344 and a neutronics engine 345.

[0033] The thermal-mechanical analysis engine 344 (e.g.. BISON) performs 2D thermal mechanical stress analysis and calculates a first predicted outcome (e.g., a probability of failure) for the initial particle design. The neutronics engine 345 executes a neutronics model (e.g., Monte Carlo M-Transport (MCNP)) to determine a second predicted outcome (e.g., the core beginning-of-life (BOL) k-effective value) based on the initial particle design. The algorithm obtains (204), the first and second predicted outcomes from the thermal-mechanical analysis engine 344 and the neutronics engine 345. In some embodiments, the algorithm passes the initial particle design to a thermal hydraulics engine 344 (e.g., Mixcoati™) and obtains, as output from the thermal hydraulics engine 344, a third predicted outcome that is based at least in part on the initial particle design. The algonthm determines (206) an aggregate residual value for the initial particle design based on the predicted outcomes and determines (208) an updated particle design based on the aggregate residual value (e.g., by re-sampling a particle design space 334).

[0034] The algorithm determines (210) whether the total number of iterations (specified in step 201) has been reached. In accordance with a determination that the total number of iterations has been reached (212), the algorithm terminates (214) the process 200.DBl / 154135139.1Patent 102085-5039-WO and receives user selection of an optimized particle design (e.g., the optimized particle design is one that has the minimum aggregate residual value amongst all the iterations, or has an aggregate residual value that is around a range of minimal residual values). In accordance with a determination that the total number of iterations has not been reached (216), the algorithm uses (218) the updated particle design as input and repeats steps 206 and 208 to determine another updated particle design, and repeats the process until the total number of iterations has been reached.

[0035] Figure 3 is a block diagram illustrating a computer system 300 in accordance with some embodiments. Various examples of the computer system 300 include high- performance clusters (HPC) of servers, supercomputers, desktop computers, cloud servers, and other computing devices. The computer system 300 typically includes one or more processing units / cores (CPUs) 302 for executing modules, programs, and / or instructions stored in the memory7314 and thereby performing processing operations; one or more network or other communications interfaces 304; memory 314: and one or more communication buses 312 for interconnecting these components. The communication buses 312 may include circuitry that interconnects and controls communications between system components.

[0036] The computer system 300 may include a user interface 306 comprising a display device 308 and one or more input devices or mechanisms 310. In some implementations, the input device / mechanism includes a keyboard. In some implementations, the input device / mechanism includes a “soft” keyboard, which is displayed as needed on the display device 208, enabling a user to “press keys” that appear on the display 308. In some implementations, the display 308 and input device / mechanism 310 comprise a touch screen display (also called a touch sensitive display).

[0037] In some implementations, the memory 314 includes high-speed random access memory, such as DRAM. SRAM, DDR RAM or other random access solid state memory devices. In some implementations, the memory 314 includes non-volatile memory, such as one or more magnetic disk storage devices, optical disk storage devices, flash memory devices, or other non-volatile solid state storage devices. In some implementations, the memory' 314 includes one or more storage devices remotely located from the CPU(s) 302. The memory’ 314, or alternatively the non-volatile memory device(s) within the memory 314, comprises a non-DB1 / 154135139.1Patent 102085-5039-WO transitory computer readable storage medium. In some implementations, the memory 314, or the computer-readable storage medium of the memory 314, stores the following programs, modules, and data structures, or a subset thereof:• an operating system 316, which includes procedures for handling various basic system services and for performing hardware dependent tasks;• a communications module 318, which is used for connecting the computer system 300 to other computers and devices via the one or more communication network interfaces 304 (wired or wireless) and one or more communication networks, such as the Internet, other wide area networks, local area networks, metropolitan area networks, and so on;• a web browser 320 (or other application capable of displaying web pages), which enables a user to communicate over a network with remote computers or devices;• an input user interface 322, which allows a user to specify allowed values 338 (or ranges of allowed values) for the design variables 336. In some embodiments, a user can also specify target (threshold) values for constraints in the design variables;• an output user interface 324, which provides graphical analytics 326 about the designs constructed;• a core reactor suite 328 (e g., COre Reactor Toolset for Engineering Simulation, or CORTESTM), which is an Al-based algorithm that combines data science, multi-physics and engineering expertise to accelerate the design and optimization of nuclear fuel particles. The core reactor suite 328 manages many variables and aids a user in the exploration of the reactor fuel design. The core reactor suite 328 adjusts thermal, neutronic, and structural components simultaneously. This integrated approach enhances the overall design, increases design margins, and allows for the quick adjustment of model uncertainties. In some embodiments, the core reactor suite 328 uses an evolutionary algorithm (e.g., differential evolution or Latin hypercube). In some embodiments, the core reactor suite 328 generates (or stores) a penalty function 329. In some embodiments, the core reactor suiteDB1 / 154135139.1Patent 102085-5039-WO 328 comprises an output engine 330, which determines and outputs a respective aggregate residual value 332 (e.g., a penalty) for a corresponding particle design;• a particle design space 334. In some embodiments, the core reactor suite 328 includes a sampling algorithm that samples a particle design space 344 to obtain a set of values corresponding to a set of design variables for a particle design (e.g., a value 338-1 corresponding to design variable 1 336-1. and a value 338-2 corresponding to design variable 1 336-2, for a first particle design). The design variables 336 can include: kernel layer diameter, kernel material (e.g., UN or UCO or UCN), kernel density, kernel layer thickness, carbon buffer layer thickness, IPyC layer thickness, SiC layer thickness, and / or OPyC layer thickness;• a data sample selector 340. In some embodiments, for a respective particle design, the data sample selector 340 selects one value 338 for each design variable 336 in the particle design space 334. In some embodiments, the data sample selector 340 forms a Latin hypercube. In some embodiments, the Latin hypercube is formed iteratively to reduce the multivariate correlation between the values 338 for the design variables 336;• a thermal hydraulics engine 342, which determines various properties, such as a limiting fuel temperature, the heat flux profile, heat transport, pressure drop, and melting. In some embodiments, this uses Mixcoati™, a Finite Element method (FEM), a Finite Difference Method (FDM), or Finite Volume Method (FVM). In some embodiments, this uses an ANSYS model or a high-fidelity multi-physics simulation suite (e.g., from a government laboratory), such as the MOOSE framework from Idaho National Laboratory;• a thermal-mechanical analysis engine 344. which performs 2D thermal mechanical stress analysis and calculates a probability of failure for a particle design. In some embodiments, the thermal-mechanical analysis engine 344 uses BISON, a finite element, thermo-mechanics code with material models and other customizations to analyze nuclear fuel. The thermal-mechanical analysis engine 344 receives an input file that describes thermal and mechanical material models, boundary conditions, and initial conditions. In some embodiments, effects of swelling, growth / creep, and / or failure mode (e.g., pressure vessel failure, particleDB1 / 154135139.1Patent 102085-5039-WO asphericity, and / or cracking (e.g., in the IPyC layer)) are incorporated into the model. In some embodiments, the thermal-mechanical analysis engine 344 includes a stochastic tool that considers statistical effects on failure probability of small variations in the thicknesses of the TRISO particle layers;• a neutronics engine 345, which calculates various properties such as a beginning of life (BOL) k-effective value, fission criticality, range, moderation, fluence, and sustainability. In some embodiments, the neutronics engine 345 uses Monte Carlo N-Particle simulation (MCNP), SCALE (a modeling and simulation suite for nuclear safety analysis maintained by Oak Ridge National Laboratory), and / or Open MC (a community-developed Monte Carlo neutron and photon transport simulation code);• a machine learning engine 346, which builds machine learning models 348 based on the samples and the computed metrics for each of the samples. In some implementations, the machine learning engine 346 builds a random forest of decision trees. In some implementations, the machine learning engine 346 builds a neural network. In some implementations, the machine learning engine 346 uses Gaussian processes to build the machine learning models 348; and• zero or more databases or data sources 350 (e.g., a first data source 350-1 and a second data source 350-2). In some implementations, the data sources are stored as spreadsheet files, CSV files, XML files, flat files, HDF files, or SQL databases. The databases may be stored in a format that is relational or non-relational.

[0038] Each of the above identified executable modules, applications, or sets of procedures may be stored in one or more of the previously mentioned memory devices, and corresponds to a set of instructions for performing a function described above. The above identified modules or programs (i. e.. sets of instructions) need not be implemented as separate software programs, procedures, or modules, and thus various subsets of these modules may be combined or otherwise re-arranged in various implementations. In some implementations, the memory 314 stores a subset of the modules and data structures identified above. Furthermore, the memory 314 may store additional modules or data structures not described above.DB1 / 154135139.1Patent 102085-5039-WO

[0039] Although Figure 3 shows a computer system 300, Figure 3 is intended more as a functional description of the various features that may be present rather than as a structural schematic of the implementations described herein. In practice, and as recognized by those of ordinary skill in the art, items shown separately could be combined and some items could be separated.

[0040] Figures 4A to 4E illustrate a flowchart diagram for a method 400 of designing nuclear particles (e.g., TRISO particle 100), in accordance with some embodiments. In some embodiments, the method 400 is performed at a computer system (e.g., computer system 300) with one or more processors (e.g., CPU(s) 302) and memory (e.g., memory 314).

[0041] The computer system determines (402) a first particle design for a multilayer nuclear fuel particle (e.g., TRISO particle 100). The first particle design includes a first set of values (e.g., values 338) for a plurality of design variables corresponding to the multilayer nuclear fuel particle. Each respective value in the first set of values corresponds to a respective one of the design variables.

[0042] In some embodiments, the plurality of design variables includes (404) at least two of: a thickness of an IPyC layer (e.g., IPyC layer 106) corresponding to the multilayer nuclear fuel particle; a thickness of a SiC layer (e.g., SiC layer 108) corresponding to the multilayer nuclear fuel particle; and a thickness of an OPyC layer (e.g., OPyC 110) corresponding to the multilayer nuclear fuel particle. In some embodiments, the plurality of design variables includes a thickness of a buffer layer (e.g., carbon buffer layer 104).

[0043] In some embodiments, the plurality of design variables includes (406) a fuel kernel diameter, and a fuel kernel density. In some embodiments, the plurality of design variables further includes a total number of layers in the particle, a material composition of the kernel (e.g., UN or UCO or UCN), and / or a density of the kernel.

[0044] In some embodiments, the fuel kernel comprises (408) uranium nitride (UN). In some embodiments, the fuel kernel comprises uranium carbo-nitride (UCN). In some embodiments, the fuel kernel comprises oxy-carbide (UCO) fuel.

[0045] In some embodiments, the plurality of design variables includes a design variable with a constant value (e.g., a value that is fixed and not varied during the particle design iterations). For example, Figure 5A illustrates that the kernel thickness (e.g., diameter)DB1 / 154135139.1Patent 102085-5039-WO and buffer layer thickness are not varied during the particle design. Figure 5A also includes nominal values for the IPyC layer, SiC layer, and OPvC layer, and their respective varied ranges that are specified in the core reactor suite 328 algorithm.

[0046] Figures 5B and 5C are graphs showing, on the y-axes, UN-TRISO layer thicknesses selected by the core reactor suite 328 (e.g., CORTES™) for modeling using the thermal-mechanical analysis engine 344 (e.g.. BISON code suite), and on the x-axes, the calculated TRISO particle failure probability (represented by SiC overall failure probability) associated with each respective set of TRISO layer thicknesses that are selected. Figure 5C is a zoomed in version of Figure 5B. and plots the IPyC, SiC, and OPyC layer thicknesses, whereas Figure 5B displays only the IPyC layer thickness. The UN-TRISO layer thickness values on the y-axis in Figure 5C are applicable to each of the layers associated with the displayed data, e.g., IPyC, SiC, and OPyC layer thicknesses. Collectively, these figures show that there is a direct correlation between the thickness of the IPyC layer and the probability' of TRISO particle failure. A thinner IPyC layer correlates with a lower TRISO particle failure probability. Figure 5C also shows that there appears to be no correlation between the thicknesses of the SiC and OPyC layers and the TRISO particle failure rate.

[0047] In some embodiments, the computer system determines (410) the first particle design for the multilayer nuclear fuel particle by sampling, using a trained machine learning model (e.g., machine learning models 348), a particle design space (e.g., particle design space 334). The computer system determines, via the trained machine learning model, the first particle design in accordance with the sampling.

[0048] For example, in some embodiments, the trained machine learning model is a random forest of decision trees or a neural network for Bayesian optimization. In some embodiments, the trained machine learning model uses any type of known or to be known ensemble learning method for classification, regression and other task that operates by¬ constructing a multitude of decision trees at training time and outputting the class that is the mode of the classes (classification) or mean prediction (regression) of the individual trees.

[0049] In some embodiments, the trained machine learning model is (412) configured to sample the particle deign space via a sampling algorithm.DB1 / 154135139.1Patent 102085-5039-WO

[0050] In some embodiments, the sampling algorithm is (414) an evolutionary algorithm selected from the group consisting of: a genetic algorithm, a coupled simulated anneal algorithm, and a differential evolutionary algorithm.

[0051] In some embodiments, the sampling algorithm is (4165) a Latin hypercube sampling algorithm. For example, in some embodiments, the Latin hypercube is formed iteratively to reduce a multivariate correlation between the set of values for the design variables.

[0052] Referring now to Figure 4B, the computer system, using (418) the first set of values corresponding to the plurality of design variables as inputs, (i) causes (420) execution of athermal-mechanical model (e.g., thermal-mechanical analysis engine 344) and obtains, as output from the thermal-mechanical model, a first predicted outcome that is based at least in part on the first particle design. In some embodiments, the first predicted outcome is further based on respective thermal physical properties of one or more respective materials of the multilayer nuclear fuel particle, such as a density, thermal conductivity, thermal expansion, and / or heat capacity of a respective material.

[0053] An example of a thermal-mechanical model is BISON, a finite element-based thermo-mechanics code with material models and other customizations to analyze nuclear fuel such as TRISO fuel particles. The table in Figure 6A illustrates the major thermal physical and irradiation-based properties and phenomenal models (e g., swelling, growth / creep, and a failure mode), associated with each material, that affects the stresses realized on the particle. The image in Figure 6B provides a visual representation of an aspherical particle. TRISO particle asphericity contributes to stresses within the modeled TRISO particle and are accounted for when modeling the statistical failure probabilities of a population of TRISO particles because there is a statistical likelihood that some aspherical geometries are present.

[0054] In some embodiments, the first predicted outcome is (422) a probability of failure for a first population of particles due to one or more failure modes (e.g., the probability of failure is computed as a ratio of the number of failed particles to the total number of particles in the first population). The first population of particles is generated by the thermal-mechanical analysis engine 344 according to the first particle design.DB1 / 154135139.1Patent 102085-5039-WO

[0055] In some embodiments, the one or more failure modes are (424) selected from the group consisting of: a change in shape (e.g., as phen city, due to particle deformation, or a change in particle shape from a substantially spherical shape to a non-spherical / aspherical shape, or change in diameter, length of a major axis, or a minor axis of the particle) of the particles beyond a first predetermined threshold; cracking of the particles; (e.g., in the IPyC layer); and failure of a pressure vessel.

[0056] During the particle optimization process, all TRISO particle aspherical failure models were implemented using an aspect ratio of 1.04, calculated by dividing the largest diameter of the aspherical TRISO particle by the smallest diameter of the aspherical TRISO particle. The aspect ratio can change or evolve as a function of modeling; it is set by a modeler prior to running the model. A nominal TRISO particle has an aspect ratio of 1.00 (meaning that it is a spherical particle). The type of asphericity that was modeled can be visualized as a portion of the TRISO particle that is flat, rather than curved, as illustrated in the Figure 6B. Increasing the aspect ratio increases the surface area of the flat portion of the TRISO particle, which in turn increases the stress in the SiC TRISO layer relative to the same TRISO particle design with a smaller aspect ratio, due to pressure accumulation.

[0057] As used herein, the term '‘pressure vessel” refers to the SiC layer 108 within a TRISO particle. Similar to a nuclear reactor’s pressure vessel, which is designed to contain the reactor core, the TRISO pressure vessel is a term used to define the SiC layer 108, as it is designed to resist pressure buildup from fission gases released from the kernel (e.g.. fuel kernel 102) during operation and to contain fission products and prevent release of these fission products or source term (e.g. radioactive material).

[0058] In some embodiments, the first population of particles is generated (426) by stochastic modeling. As one example, in some embodiments, the first population of particles generated by stochastic modeling includes a respective particle having a corresponding set of values that differs from the first set of values by a margin that does not exceed a predefined threshold percentage (e.g., the corresponding set of values is within ± 2%, ± 3%, ± 5%, ± 10%, ± 15% of the first set of values). As another example, in some embodiments, the first population of particles generated by stochastic modeling includes a respective particle having a corresponding set of values that differs from the first set of values by a margin that does not exceed a predefined number of standard deviations and / or distribution of the first particleDB1 / 154135139.1Patent 102085-5039-WO design, e g., within 3, 4, or 5 standard deviations. The thermal-mechanical model considers statistical effects on failure probability of variations in the thicknesses of the particle layers.

[0059] Figure 7 collectively illustrates the major components and methodology used to determine the failure probability of a population of TRISO particles, in accordance w ith some embodiments. The failure probability is determined by using a combination of stress analysis on the particle layer(s), failure modes analysis, and stochastic analysis (see panel A in Figure 7). In some embodiments, the failure probability of the particles is determined using Weibull analysis, which takes into account the particle manufacturing process and particle failure modes. For each nominal TRISO particle architecture / design, BISON runs a two-dimensional (2D) asphericity and pressure vessel failure model as well as a 2D IPyC cracking and pressure vessel failure model. This is illustrated as models 702 in panel B of Figure 7. For particles with localized flaws, such as asphericity and cracking in the IPyC layer, adjustments of the maximum stress and effective mean strengths of the affected TRISO layers are made during modeling.

[0060] In some embodiments, during TRISO particle modeling using BISON, the core reactor suite 328 uses a quadrature-smolyak-sparse grid sampling scheme, in which each TRISO particle that is analyzed is a realization of a set of statistically sampled parameters from the distributions of as-fabricated particle characteristics (e.g., dimensions) that can be found within a population of TRISO particles. The sparse grid sampling scheme can significantly reduce the number of quadrature points for the number of parameters considered in TRISO particle failure analysis, compared to other sampling schemes. The scatter plot 704 shown in panel C of Figure 7, which is extracted from Jiang et. al., “Efficient high-fidelity TRISO statistical failure analysis using Bison: Applications to AGR-2 irradiation testing”, Journal of Nuclear Materials (2022), show s a visual representation of quadrature point locations in a sparse grid when quadrature order Nq = 5.

[0061] The failure probability determination also includes an assessment process, which compares the calculated mean strength and the stress concentration realized on the layer of interest at a given fluence and temperature and outputs a failure probability for each failure mode (i.e., pressure vessel failure, asphericity failure, IPyC-cracking failure), as depicted in table 706 (see panel D in Figure 7). The failure probabilities for all three failure modes areDB1 / 154135139.1Patent 102085-5039-WO then integrated to generate an overall TRISO particle failure probability (i.e., SiC overall failure in the table 706) for a population of TRISO particles.

[0062] With continued reference to Figure 4B, the computer system, using the first set of values corresponding to the plurality' of design variables as inputs, (ii) causes (428) execution of a neutronics model (e.g., neutronics engine 345) (e.g., a model that performs Monte-Carlo simulations) and obtains, as output from the neutronics model, a second predicted outcome based at least in part on the first particle design.

[0063] In some embodiments, the computer system causes the thermal -mechanical model and the neutronics model to be executed simultaneously. In some embodiments, the computer system causes the thermal-mechanical model and the neutronics model to be executed sequentially.

[0064] In some embodiments, the second predicted outcome is (430) a beginning-of- life (BOL) effective neutron multiplication factor (k-effective). The BOL k-effective describes whether the nuclear chain reaction will sustain itself. If BOL k-effective is greater than one, the chain reaction is supercritical and the neutron population will grow exponentially

[0065] In some embodiments, the computer system, using the first set of values corresponding to the plurality7of design variables as inputs, causes (432) execution of a thermal hydraulics model (e.g., thermal hydraulics engine 342) and obtains, as output from the thermal hydraulics model, a third predicted outcome based at least in part on the first particle design.

[0066] In some embodiments, the third predicted outcome is (434) a limiting fuel temperature (e.g., a steady-state operating temperature limit) (e.g., ~ 1500 K).

[0067] Referring now to Figure 4C.. in some embodiments, the computer system generates (436) a penalty function (e.g., penalty function 329, or a residual equation). The penalty function includes a first term associated with the first predicted outcome and a second term associated with the second predicted outcome.DB1 / 154135139.1Patent 102085-5039-WO

[0068] In some embodiments, a large form of the penalty function can be expressed as: Residual = kef f upper bound residual + TH residual + U23 mass residual + core length over diameter residual+ total reactor radius residual + total reactor height residual + input weights residual + TRISO failure probability residual Equation 1 - Large form of penalty function (residual equation)

[0069] In some embodiments, for purposes of particle optimization, a simple form of the penalty function is used:Residual = kef f upper bound residual + TH residual + U 235 mass residual + TRI SO failure probability residualEquation 2 - Simple form of penalty function (residual equation) where:keff upper bound residual = constraint_weight_neutronics * max(0., keff_err )Equation 3 - keff upper bound residual termTH residual = constraint _weight_TH * [2.* TH["max_melt_residual"] + 2.* TH ["max _grad_residual”] + residual_dP ]Equation 4 - TH residual termU235 mass residual= max (0., (u23 _target — core_geometry.u235) / u235_target ) * obj_u235_weightEquation 5 - U235 mass residual termandTRISO proability failure residual= triso_failure_probability * probability_scaling Equation 6 - TRISO probability failure residual term

[0070] The keff upper bound residual value in Equations 1, 2. and 3 is a positive value (i.e., more than 0) only if the keff_error is positive, meaning that the actual k-effectiveDB1 / 154135139.1Patent 102085-5039-WO determined for a particular set of design variables is lower than the k-effective goal. The keff_error increases wi th lower k-effective values. Thus, the sets of design variables with lower k-effective values have worse k-effective residual values.

[0071] The TH residual term in equations 1, 2, and 4 is a combination of how far the limiting temperature for the particular set of design variables is from the melting temperature of the limiting material, how large the temperature gradient is through the fuel, and how far the pressure drop is from the goal input.

[0072] The U235 mass residual term in Equations 1, 2, and 5 is more than 0 if the U235 mass is below the input goal for U235, in which case the residual increases the further away the U235 is from the target goal.

[0073] In Equations 1, 2, and 6, the TRISO failure probability residual term is the TRISO failure probability calculated by BISON, scaled up by the user’s choice.

[0074] All of the residual components listed (keff, TH, U235 mass, and TRISO failure probability) are able to be affected by a scaling factor or weight of constraint given. The scaling factor / weight is controlled by a user and is determined by varying and experimenting with the effects of different constraints on the particle optimization data, and determining what constraints best balance the optimization, such that all these factors were taken into consideration an appropriate amount.

[0075] In some embodiments, the penalty function includes (438) a third term associated with the third predicted outcome.

[0076] In some embodiments, the computer system assigns (440) respective weights to the first term and the second term.

[0077] In some embodiments, the computer system assigns (442) a weight to the third term.

[0078] In some embodiments, the penalty function is a scalar function. In some embodiments, the penalty function is a weighted polynomial. In some embodiments, each of the first residual value and the second residual value has a non-negative value (i.e., each of the residual values is at least zero).DB1 / 154135139.1Patent 102085-5039-WO

[0079] In some embodiments, the penalty function includes a first term corresponding to a first task of reaching a predefined minimum BOL k-effective (e.g., keff upper bound residual term in Equations 1, 2, and 3), a second term corresponding to a second task of satisfying (e.g., not exceeding) a limiting fuel temperature (e.g.. TH residual term in Equations 1, 2, and 4), a third term corresponding to a third task of reaching a minimum uranium-235 mass (e.g., U235 mass residual term in Equations 1, 2, and 5), and a fourth term corresponding to a fourth task of minimizing a failure probability of the first population of particles (e.g., TRISO probability failure residual term in Equations 1, 2, and 6).

[0080] The computer system, using the first set of values corresponding to the plurality of design variables as inputs, (iii) determines (444) an aggregate residual value (e.g., residual values 322) for the first particle design based on the first predicted outcome and the second predicted outcome. According to some embodiments of the present disclosure, residual values are synonymous with “penalty values.” A residual value is imposed when a design constraint is violated. A particle with a larger aggregate residual value is one whose design is less optimal. By contrast, a more optimal particle design is one whose aggregate residual value is smaller (e.g., because fewer and / or less severe constraints have been violated).

[0081] In some embodiments, the computer system applies (446) the penalty function to determine the aggregate residual value.

[0082] In some embodiments, the aggregate residual value comprises (448) an aggregate (e.g., sum, weighted sum, average, or weighted average) of a plurality of residual values, including a first residual value associated with the first predicted outcome. The first residual value is a positive value and is positively correlated with the first predicted outcome. For example, in some embodiments, the first predicted outcome is a probability of particle failure and the first residual value corresponds to the probability value. In this example, the more likely that the particles will fail, the larger the first residual value (e.g., penalty). The first residual value is a positive value, meaning that there is no lower threshold to when the penalty function starts penalizing.

[0083] In some instances, an aggregate residual value includes a component that scales with severity. In some embodiments, the aggregate residual value comprises (450) an aggregate of a plurality of residual values, including a second residual value associated with the second predicted outcome. The second residual value is a non-negative value (i.e., zero orDB1 / 154135139.1Patent 102085-5039-WO more) that varies according to (e.g., proportionally, is positively correlated with) an amount by which the second predicted outcome differs from a target constraint value corresponding to the second predicted outcome.

[0084] For example, in some embodiments, the second predicted outcome is a calculated k-effective based on the first particle design and the target constraint value is a lower limit (bound) of k-effective value. If the first particle design has a computed BOL k-effective that is below the lower bound of k-effective value, the second residual value will scale according to the deviation between the computed value and the value of the lower limit. On the other hand, if the first particle design has a computed BOL k-effective that satisfies (e.g., meets or exceeds) the lower bound of k-effective value, the second cost is zero.

[0085] In some instances, an aggregate residual value includes a binary component. In some embodiments, the aggregate residual value comprises (452) an aggregate of a plurality of residual values including a third residual value. The third residual value has (e.g., consists of) two (and only two) possible values (e.g., zero or a positive value). For example, in some embodiments, the third predicted outcome concerns whether or not the temperature limit of a material is reached. If the temperature limit of a material is not reached, the third residual value has a value of zero (i.e., no penalty), whereas if the temperature limited of a material is reached or exceeded, the third residual value is a pre-determined positive value.

[0086] With continued reference to Figure 4D, in some embodiments, the computer system, (iv) in accordance with the determined aggregate residual value, identifies (454) a second particle design for the multilayer nuclear fuel particle (e.g., by re-sampling the particle design space 334). The second particle design includes a second set of values corresponding to the plurality of design variables. Each respective value in the second set of values corresponds to a respective one of the design variables.

[0087] In some embodiments, the computer system identifies the second particle design by re-sampling (456), using the trained machine learning model, the particle design space and identifying, by the trained machine learning model, the second particle design in accordance with the re-sampling.DB1 / 154135139.1Patent 102085-5039-WO

[0088] In some instances, identifying, by the trained machine learning model, the second particle design is further in accordance with a determination (458), by the trained machine learning model, that the updated particle design satisfies a set of one or more criteria.

[0089] In some embodiments, the set of one or more criteria includes (460) one or more of: (i) a first criterion that a predicted aggregate residual value for the second particle design (e.g.. as predicted by the core reaction suite algorithm 328 and / or by the trained machine learning model 348) is lower (e.g., smaller) than the determined aggregate residual value for the first particle design; and (ii) a second criterion that a respective value in the second set of values, corresponding to a respective design variable in the plurality of design variables, falls within a respective range of values defined in the particle design space. Because the goal is to minimize the aggregate residual value (e.g., minimize Equations 1 or 2), the core reaction suite algorithm 328 and / or the trained machine learning model 348 will select values in the particle design space that produce lower residual values. However, in some instances, the aggregate residual value does not get lower. Accordingly, the core reaction suite algorithm 328 and / or the trained machine learning model 348 learns parameters (e.g., values, range of values) that will lead to smaller residual values and moves in that direction over the life of the optimization.

[0090] In some embodiments (and as described above), the core reaction suite algorithm 328 and / or by the trained machine learning model 348 uses an evolutionary algorithm to sample the particle design space. The solutions generated by the core reaction suite algorithm 328 and / or the trained machine learning model 348 ensures that the optimization does not get “stuck” in just one smaller portion of the design space, but that the entire design space overall is considered.

[0091] The computer system, using the second set of values corresponding to the plurality of design variables as inputs, repeats (462) the steps of (i) causing execution of the thermal-mechanical model, (ii) causing execution of the neutronics model, (iii) determining the aggregate residual value for the second particle design, and (iv) identifying an updated particle design, to obtain an optimized particle design for the multilayer particle.

[0092] Referring now to Figure 4E, in some embodiments, the computer system obtains the optimized particle design for the multilayer particle by executing (464) a plurality of iterations. Each iteration of the plurality of iterations (1) identifies a respective updated particle design having a respective updated set of values, corresponding to the plurality of designDB1 / 154135139.1Patent 102085-5039-WO variables, based on a respective prior iteration of the plurality of iterations, and (2) uses the respective updated particle design to perform the steps of (i) causing execution of the thermalmechanical model, (ii) causing execution of the neutronics model, (iii) determining the aggregate residual value, and (iv) identifying the updated set of values corresponding to the plurality of design variables for a subsequent iteration of the plurality of iterations.

[0093] Figures 8A and 8B are plots showing residual values as a function of the two primary criteria for the TRISO particle design, which are (i) failure probability (FP) of the TRISO particles and (ii) how close to the k-effective goal the particle design is, at different levels of detail. Figure 8A, which is a zoomed-out plot, shows that there are some cases with very high residuals. During the iterative process, the core reactor suite 328 (e.g., CORTES™) very quickly moved away from particle designs that generated such high residual values. Figure 8B shows the trend at a more granular level of detail than in Figure 8A. Figure 8B shows the TRISO failure probability has the biggest effect on the residual in the particular case being plotted.

[0094] Figures 9A and 9B are plots showing changes in the aggregate residual values over the course of the particle optimization process, at different levels of detail. Figure 9B is zoomed in on the y-axis to show only the lower residual cases, which make up most of the optimization process.

[0095] In some embodiments, executing the plurality of iterations generates (466) a plurality of respective aggregate residual values corresponding to a plurality of updated particle designs. The optimized particle design is a respective updated particle design, of the plurality of updated particle designs, having a corresponding aggregate residual value that is within a predefined margin (e.g., within ±1%, ±2%, ±3%, or ±5%) of the smallest aggregate residual value, of the plurality of respective aggregate residual values. In some embodiments, the optimal particle design is selected based on the particle design having a minimum residual value, or around a range (e.g., within ±1%, ±2%, ±3%, or ±5%) of minimum residual values.

[0096] In some embodiments, the plurality of iterations is (468) at least 100 iterations.

[0097] In some embodiments, the plurality of iterations is (470) at least 250 iterations.

[0098] In some embodiments, the plurality of iterations is (472) at least 500 iterations.DB1 / 154135139.1Patent 102085-5039-WO

[0099] In some embodiments, for each iteration of the plurality of iterations, the computer system causes (474) execution of the thermal hydraulics model (e.g., thermal hydraulics engine 342) using the respective updated particle design to obtain a respective third predicted outcome.

[0100] In some embodiments, after executing the plurality of iterations, the computer system receives (476) user selection of the optimized particle design for the multilayer nuclear fuel particle. The optimized particle design has a corresponding set of values for the plurality of design variables. For example, in some circumstances, the optimized particle design selected by the user is a particle design that has the minimum aggregate residual value amongst the plurality of iterations. In some situations, the optimized particle design selected by the user is a particle design that has an aggregate residual value that is around a range of minimal residual values (e.g., there is a design space envelope around the optimized particle design, such that particle designs that are within the envelope yield similar performance results).

[0101] In some embodiments, after a user selects the optimized particle design, additional tests are performed to verify that the selected particle design would perform as intended. Depending on the critical-to-quality and fuel performance requirements, a set of tests designed to describe the fission product release may be assessed. These requirements are dependent on further nuclear reactor design maturation in conjunction with regulatory requirements; nonetheless, all of them involve the tracking of phenomena affecting fission product release or the source term, including (and not limited to) fission product diffusion through and release from the TRISO particle, TRISO particle failure due to chemical attack of the SiC TRISO layer by fission products, and manufacturing specification limits (e.g., due to aspect ratio, densities, or thickness).

[0102] Although some of various drawings illustrate a number of logical stages in a particular order, stages that are not order dependent may be reordered and other stages may be combined or broken out. While some reordering or other groupings are specifically mentioned, others will be obvious to those of ordinary skill in the art, so the ordering and groupings presented herein are not an exhaustive list of alternatives. Moreover, it should be recognized that the stages could be implemented in hardware, firmware, software or any combination thereof.DB1 / 154135139.1Patent 102085-5039-WO

[0103] It will also be understood that, although the terms first, second, etc. are, in some instances, used herein to describe various elements, these elements should not be limited by these terms. These terms are only used to distinguish one element from another. For example, a first particle design could be termed a second segmentation value, and, similarly, a second particle design could be termed a first particle design, without departing from the scope of the various described implementations. The first particle design and the second particle design are both particle designs, but they are not the same type of particle design.

[0104] The terminology7used in the description of the various described implementations herein is for the purpose of describing particular implementations only and is not intended to be limiting. As used in the description of the various described implementations and the appended claims, the singular forms '‘a”, “an” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will also be understood that the term “and / or” as used herein refers to and encompasses any and all possible combinations of one or more of the associated listed items. It will be further understood that the terms “includes,” “including,” “comprises,” and / or “comprising,” when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and / or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof.

[0105] As used herein, the term “if’ is, optionally, construed to mean “when” or “upon” or “in response to determining” or “in response to detecting” or “in accordance with a determination that,” depending on the context. Similarly, the phrase “if it is determined” or “if [a stated condition or event] is detected” is, optionally, construed to mean “upon determining” or “in response to determining” or “upon detecting [the stated condition or event]” or “in response to detecting [the stated condition or event]” or “in accordance with a determination that [a stated condition or event] is detected.” depending on the context.

[0106] The foregoing description, for purpose of explanation, has been described with reference to specific implementations. However, the illustrative discussions above are not intended to be exhaustive or to limit the scope of the claims to the precise forms disclosed. Many modifications and variations are possible in view of the above teachings. The implementations were chosen in order to best explain the principles underlying the claims andDB1 / 154135139.1Patent 102085-5039-WO their practical applications, to thereby enable others skilled in the art to best use the implementations with various modifications as are suited to the particular uses contemplated.DBl / 154135139.1

Claims

Patent 102085-5039-WO CLAIMSWhat is claimed is:

1. A method of designing nuclear fuel particles, comprising:at a computer system with one or more processors and memory:determining a first particle design for a multilayer nuclear fuel particle, the first particle design including a first set of values for a plurality of design variables corresponding to the multilayer nuclear fuel particle, wherein each respective value in the first set of values corresponds to a respective one of the design variables;using the first set of values corresponding to the plurality of design variables as inputs:(i) causing execution of a thermal-mechanical model and obtaining, as output from the thermal-mechanical model, a first predicted outcome that is based at least in part on the first particle design;,(ii) causing execution of a neutronics model and obtaining, as output from the neutronics model, a second predicted outcome based at least in part on the first particle design.(iii) determining an aggregate residual value for the first particle design based on the first predicted outcome and the second predicted outcome, and(iv) in accordance with the determined aggregate residual value, identifying a second particle design for the multilayer nuclear fuel particle, the second particle design including a second set of values corresponding to the plurality of design variables; andusing the second set of values corresponding to the plurality of design variables as inputs, repeating the steps of (i) causing execution of the thermal-mechanical model, (ii) causing execution of the neutronics model, (iii) determining the aggregate residual value for the second particle design, and (iv) identifying an updated particle design, to obtain an optimized particle design for the multilayer particle.DB1 / 154135139.1Patent 102085-5039-WO 2. The method of claim 1, wherein obtaining the optimized particle design for the multilayer particle includes:executing a plurality of iterations, wherein each iteration of the plurality' of iterations (1) identifies a respective updated particle design having a respective updated set of values, corresponding to the plurality of design variables, based on a respective prior iteration of the plurality of iterations, and (2) uses the respective updated particle design to perform the steps of (i) causing execution of the thermal-mechanical model, (ii) causing execution of the neutronics model, (lii) determining the aggregate residual value, and (iv) identifying the updated set of values corresponding to the plurality of design variables for a subsequent iteration of the plurality' of iterations, andwherein the method further comprises:after executing the plurality’ of iterations, receiving user selection of the optimized particle design for the multilayer nuclear fuel particle, the optimized particle design having a corresponding set of values for the plurality' of design variables.

3. The method of claim 2, wherein:executing the plurality of iterations generates a plurality7of respective aggregate residual values corresponding to a plurality’ of updated particle designs, andthe optimized particle design is a respective updated particle design, of the plurality’ of updated particle designs, having a corresponding aggregate residual value that is within a predefined margin of the smallest aggregate residual value of the plurality of respective aggregate residual values.

4. The method of claim 2 or claim 3, wherein the plurality of iterations is at least 100 iterations.

5. The method of claim 2 or claim 3, wherein the plurality of iterations is at least 250 iterations.

6. The method of claim 2 or claim 3, wherein the plurality’ of iterations is at least 500 iterations.DB1 / 154135139.1Patent 102085-5039-WO 7. The method of any of claims 1-6, wherein the plurality of design variables includes:a thickness of an inner pyrolytic carbon (IPyC) layer corresponding to the multilayer nuclear fuel particle,a thickness of a silicon carbide layer corresponding to the multilayer nuclear fuel particle, anda thickness of an inner pyrolytic carbon (OPyC) layer corresponding to the multilayer nuclear fuel particle.

8. The method of any of claims 1-7, wherein the plurality' of design variables includes a fuel kernel diameter and a fuel kernel density of the multilayer nuclear fuel particle.

9. The method of claim 8, wherein the fuel kernel comprises uranium nitride.

10. The method of any of claims 1-9, wherein the first predicted outcome is a probability of failure for a first population of particles due to one or more failure modes, wherein the first population of particles is generated by the thermal-mechanical model according to the first particle design.

11. The method of claim 10, wherein the one or more failure modes are selected from the group consisting of:a change in shape of the particles beyond a first predetermined threshold, cracking of the particles, andfailure of a pressure vessel.

12. The method of claim 10 or claim 11, wherein the first population of particles is generated by stochastic modeling.

13. The method of any of claims 1-12, wherein the second predicted outcome is a beginning- of-life effective neutron multiplication factor (BOL keff).DB1 / 154135139.1Patent 102085-5039-WO 14. The method of any of claims 1-13, further comprising:using the first set of values corresponding to the plurality of design variables as inputs:causing execution of a thermal hydraulics model and obtaining, as output from the thermal hydraulics model, a third predicted outcome based at least in part on the first particle design.

15. The method of claim 14, wherein the third predicted outcome is a limiting fuel temperature.

16. The method of claim 14 or claim 1 , wherein obtaining the optimized particle design for the multilayer particle includes executing a plurality of iterations, wherein each iteration of the plurality of iterations identifies a respective updated particle design having a respective updated set of values, corresponding to the plurality of design variables, based on a respective prior iteration of the plurality of iterations, andwherein the method further comprises:for each iteration of the plurality of iterations, causing execution of the thermal hydraulics model using the respective updated particle design to obtain a respective third predicted outcome.

17. The method of any of claims 1-16, further comprising:prior to determining the aggregate residual value of the first particle design, generating a penalty function, the penalty function including a first term associated with the first predicted outcome and a second term associated with the second predicted outcome. wherein determining the aggregate residual value for the first particle design includes applying the penalty function to determine the aggregate residual value.

18. The method of claim 17, further comprising assigning respective weights to the first term and the second term.DB1 / 154135139.1Patent 102085-5039-WO 19. The method of any of claims 1-18, wherein:the aggregate residual value comprises an aggregate of a plurality of residual values, including a first residual value associated with the first predicted outcome, andthe first residual value is a positive value and is positively correlated with the first predicted outcome.

20. The method of any of claims 1-19, wherein:the aggregate residual value comprises an aggregate of a plurality of residual values, including a second residual value associated with the second predicted outcome, andthe second residual value is a non-negative value that varies according to an amount by which the second predicted outcome differs from a target constraint value corresponding to the second predicted outcome.

21. The method of any of claims 1-20, wherein:the aggregate residual value comprises an aggregate of a plurality of residual values, including a third residual value, andthe third residual value has two possible values.

22. The method of any of claims 1-21, wherein determining the first particle design for the multilayer nuclear fuel particle includes:sampling, using a trained machine learning model, a particle design space, and determining, by the trained machine learning model, the first particle design in accordance with the sampling.

23. The method of claim 22, wherein the trained machine learning model is configured to sample the particle deign space via a sampling algorithm.

24. The method of claim 23, wherein the sampling algorithm is an evolutionary algorithm selected from the group consisting of: a genetic algorithm, a coupled simulated anneal algorithm, and a differential evolutionary algorithm.

25. The method of claim 23 or claim 24, wherein the sampling algorithm is a Latin hypercube sampling algorithm.DB1 / 154135139.1Patent 102085-5039-WO 26. The method of any of claims 22-25, wherein identifying the second particle design for the multilayer nuclear fuel particle in accordance with the determined aggregate residual value includes:re-sampling, using the trained machine learning model, the particle design space, and identifying, by the trained machine learning model, the second particle design in accordance with the re-sampling.

27. The method of claim 26, wherein identifying, by the trained machine learning model, the second particle design is further in accordance with a determination, by the trained machine learning model, that the updated particle design satisfies a set of one or more criteria.

28. The method of claim 26 or claim 27, wherein the set of one or more criteria includes one or more of:a first criterion that a predicted aggregate residual value for the second particle design is lower than the determined aggregate residual value for the first particle design, anda second criterion that a respective value in the second set of values, corresponding to a respective design variable in the plurality of design variables, falls within a respective range of values defined in the particle design space.

29. A computer system, comprising:one or more processors; andmemory storing instructions that, when executed by the one or more processors, cause the computer system to perform the method of any of claims 1-28.

30. A non-transitory computer-readable storage medium having stored thereon program code instructions that, when executed by a processor, cause the processor to perform the method of any of claims 1-28.

31. The method of claim 3, wherein the plurality of iterations is at least 100 iterations, wherein the plurality of design variables includes:a thickness of an inner pyrolytic carbon (IPyC) layer corresponding to the multilayer nuclear fuel particle.DB1 / 154135139.1Patent 102085-5039-WO a thickness of a silicon carbide layer corresponding to the multilayer nuclear fuel particle, anda thickness of an inner pyrolytic carbon (OPyC) layer corresponding to the multilayer nuclear fuel particle.wherein the plurality of design variables includes a fuel kernel diameter and a fuel kernel density of the multilayer nuclear fuel particle,wherein the first predicted outcome is a probability of failure for a first population of particles due to one or more failure modes, wherein the first population of particles is generated by the thermal -mechanical model according to the first particle design.wherein the one or more failure modes are selected from the group consisting of: a change in shape of the particles beyond a first predetermined threshold, cracking of the particles, andfailure of a pressure vessel.wherein the second predicted outcome is a beginning-of-life effective neutron multiplication factor (BOL keff), andwherein the third predicted outcome is a limiting fuel temperature.

32. The method of claim 31, further comprising:using the first set of values corresponding to the plurality of design variables as inputs:causing execution of a thermal hydraulics model and obtaining, as output from the thermal hydraulics model, a third predicted outcome based at least in part on the first particle design.

33. The method of claim 32, wherein obtaining the optimized particle design for the multilayer particle includes executing a lurality of iterations, wherein each iteration of the plurality of iterations identifies a respective updated particle design having a respective updated set of values, corresponding to the plurality of design variables, based on a respective prior iteration of the plurality of iterations, andwherein the method further comprises:for each iteration of the plurality of iterations, causing execution of the thermal hydraulics model using the respective updated particle design to obtain a respective third predicted outcome.DB1 / 154135139.1Patent 102085-5039-WO 34. The method of claim 33, further comprising:prior to determining the aggregate residual value of the first particle design, generating a penalty function, the penalty function including a first term associated with the first predicted outcome and a second term associated with the second predicted outcome, wherein determining the aggregate residual value for the first particle design includes applying the penalty function to determine the aggregate residual value.

35. The method of claim 34, further comprising assigning respective weights to the first term and the second term.

36. The method of any of claims 35, wherein the aggregate residual value comprises an aggregate of a plurality’ of residual values, including:a first residual value associated with the first predicted outcome, a second residual value associated with the second predicted outcome, and a third residual valuewherein the first residual value is a positive value and is positively correlated with the first predicted outcome,wherein the second residual value is a non-negative value that varies according to an amount by which the second predicted outcome differs from a target constraint value corresponding to the second predicted outcome, andwherein the third residual value has two possible values.

37. The method of claim 36, wherein determining the first particle design for the multilayer nuclear fuel particle includes:sampling, using a trained machine learning model, a particle design space, and determining, by the trained machine learning model, the first particle design in accordance with the sampling,wherein identifying the second particle design for the multilayer nuclear fuel particle in accordance with the determined aggregate residual value includes:re-sampling, using the trained machine learning model, the particle design space, andidentifying, by the trained machine learning model, the second particle design in accordance with the re-sampling,DB1 / 154135139.1Patent 102085-5039-WO wherein identifying, by the trained machine learning model, the second particle design is further in accordance with a determination, by the trained machine learning model, that the updated particle design satisfies a set of one or more criteria, andwherein the set of one or more criteria includes one or more of:a first criterion that a predicted aggregate residual value for the second particle design is lower than the determined aggregate residual value for the first particle design;a second criterion that a respective value in the second set of values, corresponding to a respective design variable in the plurality of design variables, falls within a respective range of values defined in the particle design space.

38. The method of claim 37, wherein the first population of particles is generated by stochastic modeling.

39. The method of claim 38, wherein the fuel kernel comprises uranium nitride.DB1 / 154135139.1

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