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Chapter 4: Physically informed deep learning networks for simulating microstructure evolution of 3D polycrystals

As discussed in the previous chapter, high energy diffraction microscopy (HEDM) is used to study the micromechanical evolution of a material during in situ loading. HEDM experiments have been used to verify crystal plasticity (CP) simulations [119, 91, 90, 120], for experimental planning, material design, and to further analyze experimental results. However, Fast Fourier transform-based CP (CP-FFT) or finite element-based CP (CP-FE) methods are often too slow to be used in real-time during an experiment. CP-FFT is faster than CP-FE simulations due to the absence of meshing, but can still take hours to simulate the response of a single volume depending on the size and number of strain steps [127]. Reducing computation time would create a larger exploration space in planning and design, and enable faster analysis of experimental results and real-time feedback during an experiment. This research expands upon previous works to develop a workflow for predicting the full-field evolution of a 3D polycrystal. The workflow is simplified from previous works to predict only orientation and elastic strain tensors (from which stress tensors are calculated). The network is physically informed through loss functions and network architecture for a more robust model. The orientation predictions are informed about the cubic crystal symmetry of the material by incorporating disorientation and misorientation information into the network architecture and loss. The Von Mises stress is used to enforce the correct stress-strain trends in the strain tensor predictions. Additional total strain steps from the elastic and elastoplastic region are included to better capture the stress-strain evolution at smaller total strain steps. Material and hardening parameters are additional inputs into the networks to further inform the network and to study the network’s ability to predict different materials other than those used for training.

36 MATERIALS SCIENCE↗

The ionomer as an oxygen evolution reaction promoter: piperidinium’s impact on mechanistic pathways on NiO, IrO 2 , and Fe–NiO

The commercial viability of anion exchange membrane (AEM) electrolysis requires optimization of various stack components, with specific catalyst-ionomer combinations often yielding higher current densities, lowered Tafel slopes, and improved mass activity. In this joint theoretical-experimental study, theoretical calculations detail the impact of Versogen’s piperidinium functional group on the complex, kinetically limiting oxygen evolution reaction, finding that the functional group can act as a promoter of specific steps (O*/O 2 * formation; H 2 O/O 2 desorption with reaction enthalpies ranging between 0.2–0.6 eV at higher coverages of O x H y intermediates) on NiO and NiFeO x catalysts. In particular, Fe sites on the NiFeO x catalyst facilitate concerted mechanisms of O*/O 2 * formation and H 2 O desorption with a low enthalpy of 0.5 eV; O 2 desorption alone requires only 0.3 eV. In contrast, Versogen-IrO 2 results in stronger Ir–O bonds, where the enthalpies for bond breaking (Ir–OH 2 and Ir–O 2 ) are considerably higher (1.4 eV and 1.6 eV, respectively). Rotating disk electrode studies utilized commercially available NiO and IrO 2 and synthesized 7.5 wt % Fe in NiFeO x catalysts in combination with Versogen, a common AEM ionomer, and Nafion, an alternative binder. Electrochemical testing validated the impact of these mechanistic changes on ionomer-catalyst combinations, finding that Versogen particularly activates NiO and NiFeO x compared to IrO 2 . Following a 13.5 h hold at 1.8 V, mass activities and Tafel slopes improved to 34 ± 13 A g −1 and 79 ± 2 mV dec −1 (NiO) and 82 ± 4.9 A g −1 and 72 ± 2 mV dec −1 (NiFeO x ). In contrast, Versogen-IrO 2 only reached 17 ± 2.9 A g −1 and 81 ± 3 mV dec −1 . Optimization of the ionomer-catalyst can yield significant increases in performance from initial activity and after an electrochemical conditioning procedure: this enhancement to the mass activity resulted in a 200.9 ± 106.1% improvement for Versogen-NiFeO x and 1284.2 ± 260.5% for Versogen-NiO. In contrast, Nafion-NiFeO x and -NiO offered moderate improvements of 39.1 ± 30.5% and 120.9 ± 59.1%, respectively.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Nonlinear excitation of energetic particle driven geodesic acoustic mode by resonance overlap with Alfvén instability in ASDEX Upgrade

The Alfvén instability nonlinearly excited the energetic-particle-driven geodesic acoustic mode on the ASDEX-Upgrade tokamak, as demonstrated experimentally. The mechanism of the energetic-particle-driven geodesic acoustic mode excitation and the mode nonlinear evolution is not yet fully understood. In the present work, a first-principles simulation using the MEGA code investigated the mode properties in both the linear growth and nonlinear saturated phases. Here we show that the simulation successfully reproduced the excitation and coexistence of these two modes, and agreed with the experimental results well. Conclusive evidence showed that the resonance overlap is the excitation mechanism of the energetic-particle-driven geodesic acoustic mode. In the linear growth phase, energetic particles that satisfied different resonance conditions excited the Alfvén instability, which then caused energetic particle redistribution in phase space. These redistributed energetic particles caused resonance overlap, exciting the energetic-particle-driven geodesic acoustic mode in the nonlinear phase.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Towards the Ultimate Strength of Medium‐Entropy Alloys Through Pulsed Lasers

The tensile strength of metals at extreme strain rates is a key predictor of their performance in ballistic and structural impact applications. An important experimental method to reach these extreme strain rates is the use of high-amplitude, short-duration pulsed lasers. The Jupiter Laser Facility at the Lawrence Livermore National Laboratory enabled probing for the first time the mechanical response of several promising High Entropy Alloys at times on the order of nanoseconds (strain rates of ∼10 7 and ∼10 9 s −1 ). The measured strength is in the range of 6 to 10 GPa, ten times the quasistatic value. The mechanisms of plastic deformation and failure were identified and quantified through analysis and molecular dynamics simulation. The reflected wave amplitudes, obtained by VISAR, were used to determine the tensile (spall) stress. The high tensile strength obtained is due to two factors: the strain-rate dependence of plastic flow and the kinetics of void nucleation, growth, and coalescence. The experimental results are compared with an analytical prediction considering both grain-interior and grain-boundary void initiation. Molecular dynamics simulations, conducted at strain rates of 10 8 and 10 9 s −1 , rationalize the experimental results. In conclusion, they provide valuable information about the process of failure evolution, and reveal that grain boundary separation plays a pivotal role in spalling.

Materials science↗

Flame Chemistry Workshop: a perspective on challenges and strategic actions in combustion experiments and chemical kinetics modeling

Continued progress in the development of predictive models for combustion chemistry—including ignition and flame behavior, species evolution, and combustion system performance—relies on overcoming enduring and emerging challenges in experimental measurements, theoretical formulations, and chemical kinetics mechanism construction. As combustion science continues to coincide with advances in sustainable fuels development, plasma technologies, and automated modeling capabilities, the need for coordinated, community-driven strategies is essential. The Flame Chemistry Workshop (FCWS), held biennially before the International Symposium on Combustion, serves as a dedicated platform to identify, consolidate, and address these challenges in a structured and collaborative manner. This perspective arises from discussions at the 7th FCWS in Milan, Italy (2024), and presents a collective view of the critical barriers currently limiting progress. Across the five technical domains discussed during the 7th FCWS – sustainable fuels combustion, advanced diagnostics for combustion measurements, experiments and modeling in plasma combustion, artificial intelligence and automated methods for theory and mechanisms generation, and chemical kinetic models—a series of persistent and emerging scientific challenges were identified, highlighting the need for deeper integration between three areas: theory, experiments, and modeling. In conclusion, the present article concisely describes present challenges that were identified in each of the technical domains in an effort to streamline and coordinate solutions to accelerate progress in combustion science.

Chemical kinetics↗

Mesoscale modeling of restructuring in high burnup UO 2 fuel

Here, this work aims to simulate the restructuring behavior observed in different regions of high burnup fuel, providing a first-of-its-kind restructuring model for the dark zone and rim region of high-burnup UO 2 fuel. We employed a grand-potential-based phase-field model to concurrently evaluate subgrain formation and the growth of fission gas bubbles within the fuel. An energy-based subgrain formation criterion was introduced to simulate the restructuring process. The effects of different initial conditions and different modeling parameters were systematically studied to capture how each of these parameters influences the characteristics of the restructured fuel. Subgrain formation was observed to begin around existing fission gas bubbles and proceed toward triple junctions, grain boundaries, and grain interiors. Restructuring was demonstrated to be influenced by a combination of initial dislocation densities, burnup rate, subgrain formation rate, and temperature. Under a given subgrain formation rate, the rate of restructuring increases with rising fuel temperature. A restructuring bias was observed within the microstructure, due to the variation in defect accumulation when comparing different grains. Microstructures corresponding to the dark zone and rim region can be obtained by parameterizing the model with the appropriate defect production rate, as determined based on the burnup rate and temperature. Furthermore, bubble size and distribution do not significantly affect the rate of restructuring. The predicted microstructures are consistent with experimental observations of the restructured regions. Finally, we present a correlation demonstrating the evolution of the restructuring volume fraction as a function of local burnup.

UO2↗

Simulation of DIII-D disruption with argon pellet injection and runaway electron beam

Abstract The next generation of large tokamaks, including ITER, will be equipped with a disruption mitigation system (DMS) that can be activated if a disruption is deemed to be imminent. Introducing impurities by pellet (large or shattered) or massive gas injection has been shown to be an effective mitigation mechanism on many tokamaks. The goal of the mitigation is to lessen the thermal and electromagnetic loads from the disruption without generating enough high-energy (runaway) electrons to damage the device. Variations of this mitigation process with impurity injection are presently being tested on many experiments. We have modeled one such impurity injection experiment on DIII-D using the M3D-C1 nonlinear 3D extended MHD code (Jardin et al 2012 Comput. Sci. Discovery 6 014002), The model includes an argon large pellet injection and ablation model, impurity ionization, recombination, and radiation, and runaway electron formation and subsequent evolution, including both Dreicer and avalanche sources. We obtain reasonable agreement with the experimental results for the timescale of the thermal and current quench and for the magnitude of the runaway electron plateau formed during the mitigation. This is the first 3D full MHD simulation with pellets and REs to simulate the disruption process and it also provides a partial validation of the M3D-C1 DMS model.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Effects of dose rate on the microstructure and deuterium retention in γ-LiAlO 2 pellets

This report presents experimental findings obtained from November 2024 to September 2025. Defect accumulation and microstructural evolution during ion irradiation at elevated temperatures are governed by two competing processes: defect production, driven by dose rate, and defect recovery, controlled by defect diffusion, interaction, and annihilation. At a given dose, the resulting microstructural evolution depends on both the dose rate and irradiation temperature. As a continuation of our FY24 tritium science project, which investigated temperature effects at a fixed dose rate, this study focuses on dose-rate effects at a fixed temperature to provide deeper insights into the irradiated microstructure and compositional changes in γ-LiAlO 2 pellets. The study aims to elucidate the impact of dose rate on microstructure, precipitate morphology, deuterium retention, and lithium volatility in γ-LiAlO 2 pellets under sequential 120 keV He + and 80 keV D 2 + ion irradiation. Three dose rates of 7.3×10 4 , 2.9×10 4 and 6.8×10 5 dpa/s were applied to achieve the same total ion fluence of 2×10 17 (He + +D + )/cm 2 at 500 °C, corresponding to a maximum combined dose of 7.55 dpa at ~255 nm. The irradiated pellets were subsequently characterized using scanning transmission electron microscopy (STEM) and time-of-flight secondary ion mass spectrometry (ToF-SIMS). The microstructural response of γ-LiAlO 2 to ion irradiation was found to be strongly dose-rate dependent. At medium and high dose rates, irradiation produced a surface amorphized layer and an underlying crystalline layer containing LiAl 5 O 8 precipitates, with implanted gases accumulating and forming blisters at the crystalline-amorphous interface. It remains to be investigated whether the amorphized layer was produced by He + ion irradiation prior to D 2 + ion irradiation. In contrast, at low dose rates, the material remained crystalline, with cavities, likely gas-filled, distributed around precipitates, within the γ-LiAlO 2 matrix, and along grain boundaries. While precipitate morphology exhibited anisotropy, their size showed little sensitivity to dose rate in the applied range of this study. This result, however, does not rule out the possibility that further reductions in dose rate could influence precipitate size. High dose-rate irradiation enhanced protonium–deuterium isotopic exchange and lithium depletion in the amorphized region. Collectively, the results show that dose rate governs amorphization, gas redistribution, isotopic exchange, and lithium depletion, providing important insights into the mechanisms underlying structural evolution in γ-LiAlO 2 pellets under reactor-relevant irradiation conditions.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Evaluation of Corrosion and Its Impact on the Mechanical Performance of Al–Steel Joints

Aluminum–steel joints are increasingly used in the automotive industry to meet the requirements for energy saving and emission reduction. Among various joining technologies, self-pierce riveting (SPR) and resistance spot welding (RSW) are two well-established technologies for fabricating dissimilar joints with stable and high mechanical performance. However, corrosion will occur in these joints inevitably due to different electrochemical properties, which can degrade the surface quality and the mechanical performance, such as strength. This paper presents a method of understanding the corrosion mechanisms in joining aluminum and steel. For this understanding, a hybrid method combining experimental observations, mechanical properties identification, and analytical approaches was used to assess the evolution of the impact of corrosion on the joining performance, such as traction separation curves. The study was conducted on common combinations used in the vehicles, e.g., a 1.2 mm thickness aluminum alloy (AA 6022) and 2.0 mm thickness hot deep galvanized steel (HDG HSLA 340) joined by SPR and RSW. After the fabrication of these joints, accelerated cyclic corrosion tests of up to 104 cycles were performed, which reproduced the environmental conditions to which a vehicle was exposed. By investigating the microstructural evolution within the joints, the corrosion mechanisms of SPR and RSW joints were revealed, including the initiation and propagation. Moreover, the intrinsic impact of the corrosion on the mechanical performance, including the strength, axial stiffness, and crashworthiness, was analyzed by performing a lap-shear test. It showed that as corrosion proceeds, the fracture modes and mechanical performance are affected significantly.

Chemistry↗

Formation of Carbon–Carbon Interlinkage Bonds under High Pressure

The formation of carbon–carbon interlinkage bonds (CCIBs) via the chemical binding of interlayer carbon atoms of many sp 2 -bonded carbon precursors is an essential step for synthesizing various diamond and diamond-like materials. Although the existence of CCIBs may be reasonably assumed under high-pressure conditions, direct experimental evidence has been scarce. Micro-Raman spectroscopy is here employed to track in situ the evolution of C–C bonds in a pressure range from ambient to 54 GPa. A pressure-induced two-stage (polynomial and linear) shift of the G peak and new generation of the CCIB peak at about 1550 cm –1 are observed in multiple types of layer-structured carbon precursors, including glassy carbon, natural graphite, and carbon nanotubes. In conclusion, the experimental discovery of CCIBs holds significance in comprehending phase transitions of sp 2 -bonded carbon materials and has implications for the advancement of novel carbon structures.

Anode materials↗

Structural evolution of liquid silicates under conditions in Super-Earth interiors

Molten silicates at depth are crucial for planetary evolution, yet their local structure and physical properties under extreme conditions remain elusive due to experimental challenges. In this study, we utilize in situ X-ray diffraction (XRD) at the Matter in Extreme Conditions (MEC) end-station of the Linear Coherent Linac Source (LCLS) at SLAC National Accelerator Laboratory to investigate liquid silicates. Using an ultrabright X-ray source and a high-power optical laser, we probed the local atomic arrangement of shock-compressed liquid (Mg,Fe)SiO 3 with varying Fe content, at pressures from 81(9) to 385(40) GPa. We compared these findings to ab initio molecular dynamics simulations under similar conditions. Results indicate continuous densification of theO-O and Mg-Si networks beyond Earth’s interior pressure range, potentially altering melt properties at extreme conditions. This could have significant implications for early planetary evolution, leading to notable differences in differentiation processes between smaller rocky planets, such as Earth and Venus, and super-Earths, which are exoplanets withmasses nearly three times that of Earth.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Bulk‐Boundary Correspondence of Semimetal Ru 3 Sn 7 and Topological Surface States on Chemically Realistic Terminations

Ru 3 Sn 7 is experimentally demonstrated as an efficient catalyst, with potential utilization of topological surface states for hydrogen evolution reaction. Despite its promising catalytic performance, the topological nature of Ru 3 Sn 7 remains uncertain. Particularly, the bulk-boundary correspondence has not yet been established, hence hindering a rigorous justification of its topologically-protected surface states. In this work, the bulk topology of Ru 3 Sn 7 is detailed using first-principles calculations and the topological quantum chemistry formalism. Ru3Sn7 turns out to be an enforced semimetal possessing symmetry-protected crossings within a set of bands near the Fermi level, which are enforced and prescribed by the violations of symmetry-prescribed compatibility relations. Moreover, the surface states and the associated origin from the same set of entangled bands are identified, thereby establishing the bulk-boundary correspondence. To evaluate the effects of chemical modifications, the response of topological surface states to various surface terminations, stoichiometry, and oxidation is examined. The surface structures are globally optimized, and the phase diagrams for various experimental conditions are built. It is shown that, due to changes in the local chemical environment, the original surface states are significantly altered. Modified surface bands can be observed near the Fermi level on surface terminations that preserve the C 4v symmetry.

36 MATERIALS SCIENCE↗

Self-Learning Kinetic Monte Carlo Simulations of Radiation Damage in Nuclear Fuels

Understanding how irradiation affects the thermo-physical and mechanical properties of nuclear materials, such as thermal conductivity degradation in fuels and embrittlement of structural components, is critical to the safety and efficiency of nuclear reactors. These effects are largely governed by the formation and evolution of atomic-scale point defects and defect clusters. Due to their small sizes, however, these defects are invisible under high-resolution scanning transmission electron microscopy. This project aims to fill this experimental knowledge gap by integrating density functional theory (DFT), machine learning interatomic potential (MLIP), and kinetic Monte Carlo (KMC) techniques to predict longtime evolution of irradiation-induced defects in nuclear fuels.

36 - MATERIALS SCIENCE↗

(Doublon) Benchmarking of Different Inverse Point Kinetics Implementations for an Autocorrected Reactimeter Algorithm

In November 2017, the Transient Reactor Test Facility returned to operation. Since that time, many transient test series have been completed, such as the Transient Heatsink Overpower Response capsule (THOR), the Transient Water Irradiation System for TREAT (TWIST), and Sirius. Each has provided valuable data for materials performance and reactor safety that can be applied in future designs. During each experimental series, detector count rates provided important information on the core behavior during transients. However, a limitation of these data is that variations in the neutron distribution during experiments can cause errors when attempting to infer reactivity evolution from detector signals. Neutron physics codes can be used to compute the flux shape variations. However, this is a poor solution when the experimental data is used for code verification, validation and uncertainty quantification. Indeed, if the output of the code is used both as a reference and to correct what the reference is compared to, the circular dependency limits the quality of the verification, validation and uncertainty quantification approach. To overcome this problem, the autocorrected reactimeter algorithm (ACRA) has been developed. This approach infers a time-dependent reactivity evolution by testing different spatial corrections and selecting the one that minimizes reactivity variations when the core is in a frozen configuration (i.e., when there is no variation in parameters affecting reactivity). However, the scope of this method was limited to transients where there were negligible thermal feedback. Indeed, the core is never in a frozen configuration when the fuel temperature varies during the whole transient. This is our motivation for developing an improved version of the ACRA that does not require frozen configurations. To develop this new algorithm, we need a precise and unbiased implementation of the inverse point kinetic equations (IPKEs) as any error in the reactivity evaluation will be propagated into the choice of the optimal spatial correction. Indeed, the previous reactimeter algorithm would use approximations, such as a negligible flux amplitude derivative, to focus on rapidity. For the numerical validation of ACRA, we aim at absolute error under for reactivity derived from signals similar to the one of this study. In this summary, we test eight different IPKE implementations. Each will process a mockup signal built for this study, similar to those that the future ACRA will process. Each reactivity output will be compared to the reference reactivity that has been used to generate the mockup signal. The implementation minimizing the difference with the reference reactivity will be used in the development of a new ACRA formulation.

73 - NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Electrochemical Control of the Ultrafast Lattice Response of a Layered Semimetal

The unique layer-stacking in two-dimensional (2D) van der Waals materials facilitates the formation of nearly degenerate phases of matter and opens novel routes for the design of low-power, reconfigurable functional materials. Electrochemical ion intercalation between stacked layers offers a promising approach to stabilize bulk metastable phases and to explore the effects of extreme carrier doping and strain. However, in situ characterization methods to study the structural evolution and dynamical functional properties of these intercalated materials remains limited. Here a novel experimental platform is presented capable of simultaneously performing electrochemical lithium-ion intercalation and multimodal ultrafast characterization of the lattice using both electron diffraction and nonlinear optical techniques. Using the layered semimetal WTe 2 as a model system, the interlayer shear phonon mode that modulates stacking between 2Dlayers is probed, showing that small amounts of lithiation enhance the amplitude and lifetime of the phonon, contrary to expectations. This results from the dynamically fluctuating and anharmonic structure between nearly degenerate phases at room temperature, which can be stabilized by electronic carriers accompanying the inserted lithium ions. At high lithiation, the T d ’ structure emerges and quenches the phonon response. This work defines new approaches for using electrochemistry to engineer the dynamic structure of 2D materials.

36 MATERIALS SCIENCE↗

Correlated Ion Transport Governed by Dynamic Local Structure in High Concentration and Localized High Concentration Electrolytes

Understanding the dynamics of cluster formation and network percolation provides the mechanistic link between microscopic solvation structure and transport in concentrated electrolytes, including localized high-concentration electrolytes (LHCEs). Although recent studies have shown LHCEs to form micelle-like aggregates at specific compositions, a quantitative understanding of how solvation structures and transport properties depend on salt–solvent–diluent ratios remains limited. Here, we integrate molecular dynamics with Onsager transport analyses to chart the evolution of solvation microstructure and associated ionic transport in LiFSI/DMC/TTE, achieving good agreement with experimental conductivities across composition. We show that micelle formation arises from a dynamic instability of the cation–anion network, and that network percolation is the primary determinant of conductivity. Two compositional thresholds emerge: A critical network concentration (CNC) and a critical micelle concentration (CMC) that delineate transitions from extended percolating networks to micelle-like clusters and then to fragments. These structural transitions rationalize the nonintuitive conductivity decrease at intermediate dilution despite monotonically decreasing viscosity and provide composition-level design rules for LHCEs.

Mohanakrishnan, Rohith Srinivaas [University of Ca↗

Coupled neutronics, thermochemistry, corrosion modeling and sensitivity analyses for isotopic evolution in molten salt reactors

This study presents a computational methodology for analyzing isotopic evolution and associated uncertainties in molten salt reactors (MSRs), focusing on both fluoride- and chloride-based fuel salts. The primary goal is to enhance the understanding of isotopic behavior in MSRs and provide data to support future experimental efforts. The methodology integrates transport-coupled depletion calculations using OpenMC, equilibrium thermodynamics modeling with Thermochimica, and a corrosion model. Sensitivity analyses are performed to evaluate the impact of power density, air ingress, and humidity content on isotopic evolution in MSR concepts. This study examines representative F- and Cl-based MSR designs, highlighting the dominant influence of power density on isotopic composition, which significantly affects isotope production and depletion rates, accounting for approximately 76% of the observed variance in element concentration. Air ingress and humidity content also affect the redox potential, solubility of heavier elements, and corrosion rates, thereby altering the expected isotopic evolution in the reactor. On average, air ingress accounts for around 17% of the variance in element concentrations, while humidity explains the remaining 7%. These variances differ significantly from element to element, depending on the element’s role in depletion, redox potential evolution, and galvanic corrosion. The findings indicate that power density, air ingress, and humidity content are all critical factors for optimizing reactor design and operational strategies. Furthermore, the study provides expected ranges for key impurities in the fuel salt, which are crucial for guiding future experimental studies and refining MSR designs. Finally, this study demonstrates the importance of modeling depletion coupled with the evolution of redox potential and chemical interactions in MSR fuel salts.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Continuous-variable quantum Boltzmann machine

Here, we propose a continuous-variable quantum Boltzmann machine (CVQBM) using a powerful energy-based neural network. It can be realized experimentally on a continuous-variable (CV) photonic quantum computer. We used a CV quantum imaginary time evolution (QITE) algorithm to prepare the essential thermal state and then designed the CVQBM to proficiently generate continuous probability distributions. We applied our method to both classical and quantum data. Using real-world classical data, such as synthetic-aperture radar (SAR) images, we generated probability distributions. For quantum data, we used the output of CV quantum circuits. We obtained high fidelity and low Kullback–Leibler (KL) divergence showing that our CVQBM learns distributions from given data well and generates data sampling from that distribution efficiently. We also discussed the experimental feasibility of our proposed CVQBM. Our method can be applied to a wide range of real-world problems by choosing an appropriate target distribution (corresponding to, e.g., SAR images, medical images, and risk management in finance). Moreover, our CVQBM is versatile and could be programmed to perform tasks beyond generation, such as anomaly detection.

SAR images↗