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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Exact solution of the frustrated Potts model with next-nearest-neighbor interactions in one dimension via AI bootstrapping

The one-dimensional (1D) 𝐽 1 −𝐽 2 𝑞-state Potts model is solved exactly for arbitrary 𝑞 by analytically block-diagonalizing the original 𝑞 2 ×𝑞 2 transfer matrix into a simple 2 × 2 maximally symmetric subspace, based on using OpenAI's reasoning model o3-mini-high to exactly solve the 𝑞 = 3 case. Furthermore, by matching relevant subspaces, we map the Potts model onto a simpler effective 1D 𝑞-state Potts model, where 𝐽 2 acts as the nearest-neighbor interaction and 𝐽 1 as an effective magnetic field, nontrivially generalizing a 56-year-old theorem previously limited to the simplest case (𝑞 = 2, the Ising model). Our exact results provide insights to phenomena such as atomic or electronic order stacking in layered materials and the emergence of dome-shaped phases in complex phase diagrams. In conclusion, this work is anticipated to fuel both research in 1D frustrated magnets for recently discovered finite-temperature application potentials and the fast moving topic area of AI in science.

1-dimensional spin chains↗
DOE OSTI2024

Lattice realizations of topological defects in the critical (1+1)-d three-state Potts model

Topological/perfectly-transmissive defects play a fundamental role in the analysis of the symmetries of two dimensional conformal field theories (CFTs). In the present work, spin chain regularizations for these defects are proposed and analyzed in the case of the three-state Potts CFT. In particular, lattice versions for all the primitive defects are presented, with the remaining defects obtained from the fusion of the primitive ones. The defects are obtained by introducing modified interactions around two given sites of an otherwise homogeneous spin chain with periodic boundary condition. The various primitive defects are topological on the lattice except for one, which is topological only in the scaling limit. The lattice models are analyzed using a combination of exact diagonalization and density matrix renormalization group techniques. Low-lying energy spectra for different defect Hamiltonians as well as entanglement entropy of blocks located symmetrically around the defects are computed. The latter provides a convenient way to compute the g-function which characterizes various defects. Finally, the eigenvalues of the line operators in the “crossed channel” and fusion of different defect lines are also analyzed. The results are all in agreement with expectations from conformal field theory.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Surrogate modeling of Cellular-Potts agent-based models as a segmentation task using the U-Net neural network architecture

The Cellular-Potts model is a powerful and ubiquitous framework for developing computational models for simulating complex multicellular biological systems. Cellular-Potts models (CPMs) are often computationally expensive due to the explicit modeling of interactions among large numbers of individual model agents and diffusive fields described by partial differential equations (PDEs). In this work, we develop a convolutional neural network (CNN) surrogate model using a U-Net architecture that accounts for periodic boundary conditions. We use this model to accelerate the evaluation of a mechanistic CPM previously used to investigate in vitro vasculogenesis. The surrogate model was trained to predict 100 computational steps ahead (Monte-Carlo steps, MCS), accelerating simulation evaluations by a factor of 562 times compared to single-core CPM code execution on CPU. Over short timescales of up to 3 recursive evaluations, or 300 MCS, our model captures the emergent behaviors demonstrated by the original Cellular-Potts model such as vessel sprouting, extension and anastomosis, and contraction of vascular lacunae. This approach demonstrates the potential for deep learning to serve as a step toward efficient surrogate models for CPM simulations, enabling faster evaluation of computationally expensive CPM simulations of biological processes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

An Integrated Simulation of Multiple-Pass U-10Mo Alloy Hot Rolling and Static Recrystallization

To achieve a desired microstructure and minimize the thickness variation in rolled foils, researchers must understand the effects of foil fabrication process variables on microstructure evolution. We developed an integrated simulation of deformation and recrystallization that employs the finite element method (FEM) and the kinetic Monte Carlo (KMC) Potts model, respectively, to investigate microstructure evolution during multiple-pass hot rolling and heat treatment in polycrystalline U-10Mo fuel. Scanning electron microscopy and electron backscatter diffraction images of microstructures were directly used as input in FEM calculation of deformation, and the calculated strains were used to determine the driving force of nucleation and growth of recrystallized grains in the Potts model. Grain structures predicted by the Potts model were used to update the grain structure and material properties for FEM. Simulation alternated between FEM and the Potts model to simulate grain structure evolution during multiple rolling and heat treatments. The initial model parameters were determined by benchmarking the recrystallization kinetics against experimental data. Then, the model was applied to predict the grain structure evolution. Results showed that our model can capture the coupling between deformation and recrystallization and can quantitatively reproduce the observed U-10Mo recrystallization and grain growth kinetics. The simulation results demonstrated that the developed model can predict U-10Mo grain structures as a function of initial microstructure and foil fabrication parameters.

36 MATERIALS SCIENCE↗
DOE OSTI2023

A new efficient grain growth model using a random Gaussian-sampled mode filter

This paper presents the use of a Gaussian neighborhood mode filter for predicting grain growth in a manner similar to the solutions obtained by a Monte Carlo Potts model. This flexible grain growth model can quickly utilize modern, computationally optimized data science strategies on graphics processing units to simulate grain growth up to 100 times faster than the state-of-the-art, publicly available Monte Carlo Potts model. We show that, given the correct neighborhood, the mode filter can replicate normal grain growth in two or three dimensions. In addition, the paper briefly demonstrates the ability to model limited anisotropic in grain boundary energy and mobility. Anisotropic grain boundary energy is modeled by defining a weighted mode filter operation. Anisotropic grain boundary mobility is modeled by scaling and orienting the Gaussian neighborhood in a particular direction.

Anisotropy↗
DOE OSTI2024

Classical analog of quantum models in synthetic dimensions

We introduce a classical analog of quantum matter in ultracold molecule-synthetic or Rydberg atom-synthetic dimensions, by extending the Potts model to include interactions J 1 between atoms adjacent in both real and synthetic space and studying its finite-temperature properties. For intermediate values of J 1 , the resulting phases and phase diagrams are similar to those of the clock and Villain models, in which three phases emerge. There exists a sheet phase analogous to that found in quantum synthetic dimension models between the high-temperature disordered phase and the low-temperature ferromagnetic phase. Furthermore, we also employ machine learning to uncover nontrivial features of the phase diagram using the learning by confusion approach, which is able to discern several successive phase transitions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

A triple junction energy study using an inclination-dependent anisotropic Monte Carlo Potts grain growth model

This work presents a Monte Carlo Potts grain growth model in which the grain boundary (GB) energies depend on the GB inclination. The inclination is calculated using a linear smoothing approach developed by the authors. In bicrystal simulations with a shrinking grain, the grain changes shape to prefer low energy GB inclinations. However, in polycrystal simulations the preferred inclinations depend on the approach used to assign the triple junction (TJ) energies. Approaches that produce unimodal TJ energy distributions result in the expected behavior of preferring low energy GB inclinations. However, approaches that produce bimodal TJ energy distributions result in medium energy or even high energy inclinations being preferred. Overall, this study underscores the importance of TJs in anisotropic grain growth.

Grain boundary inclination↗
DOE OSTI2023

Strain-tuned quantum criticality in electronic Potts-nematic systems

Motivated by recent observations of threefold rotational symmetry breaking in twisted moiré systems, cold-atom optical lattices, quantum Hall systems, and triangular antiferromagnets, we phenomenologically investigate the strain-temperature phase diagram of the electronic 3-state Potts-nematic order. While in the absence of strain the quantum Potts-nematic transition is first-order, quantum critical points (QCP) emerge when uniaxial strain is applied, whose nature depends on whether the strain is compressive or tensile. In one case, the nematic amplitude jumps between two non-zero values while the nematic director remains pinned, leading to a symmetry-preserving metanematic transition that terminates at a quantum critical end-point. For the other type of strain, the nematic director unlocks from the strain direction and spontaneously breaks an in-plane twofold rotational symmetry, which in twisted moiré superlattices triggers an electric polarization. Such a piezoelectric transition changes from first to second-order upon increasing strain, resulting in a quantum tricritical point. Using a Hertz-Millis approach, we show that these QCPs share interesting similarities with the widely studied Ising-nematic QCP. The existence of three minima in the nematic action also leaves fingerprints in the strain-nematic hysteresis curves, which display multiple loops. At non-zero temperatures, because the upper critical dimension of the 3-state Potts model is smaller than three, the Potts-nematic transition is expected to remain first-order in 3D, but to change to second-order in 2D. As a result, the 2D strain-temperature phase diagram displays two first-order transition wings bounded by lines of critical end-points or tricritical points, reminiscent of the phase diagram of metallic ferromagnets. Furthermore, we discuss how our results can be used to unambiguously identify spontaneous Potts-nematic order.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Microstructure-process relationships in monolithic U-10Mo fuel foil single-pass rolling: A parametric simulation study

In this work, a previously validated coupling of Kinetic Monte Carlo (KMC) Potts Model and finite element method (FEM) simulations was implemented to investigate the effects of microstructural features in as-cast and homogenized monolithic U-10Mo foils on the emergent microstructure after rolling and reheating. Parameters that could potentially affect recrystallization behavior of the rolled U-10Mo foils were considered: grain size distribution, uranium carbide (UC) size distribution, UC volume fraction, spatial distribution of UC, and rolling reduction magnitude. Grain structure and the magnitude of rolling reduction have the strongest influence on recrystallization kinetics and the fabricated grain size distribution. The UC distribution had only a weak effect on the recrystallization kinetics and final microstructures. While particle-stimulated nucleation (PSN) occurred in simulation more frequently as grain size increased, its incidence did not appear to considerably affect the recrystallization kinetics or grain size distribution.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2025

Generative diffusion model surrogates for mechanistic agent-based biological models

Mechanistic, multicellular, agent-based models are commonly used to investigate tissue, organ, and organism-scale biology at single-cell resolution. The Cellular-Potts Model (CPM) is a powerful and popular framework for developing and interrogating these models. CPMs become computationally expensive at large space- and time- scales making application and investigation of developed models difficult. Surrogate models may allow for the accelerated evaluation of CPMs of complex biological systems. However, the stochastic nature of these models means each set of parameters may give rise to different model configurations, complicating surrogate model development. In this work, we leverage denoising diffusion probabilistic models (DDPMs) to train a generative AI surrogate of a CPM used to investigate in vitro vasculogenesis. We describe the use of an image classifier to learn the characteristics that define unique areas of a 2-dimensional parameter space. We then apply this classifier to aid in surrogate model selection and verification. Our CPM model surrogate generates model configurations 20,000 timesteps ahead of a reference configuration and demonstrates approximately a 22x reduction in computational time as compared to native code execution. Our work represents a step towards the implementation of DDPMs to develop digital twins of stochastic biological systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Constrained curve fitting for semi-parametric models with radial basis function networks

Common to many analysis pipelines in lattice gauge theory and the broader scientific discipline is the need to fit a semi-parametric model to data. We propose a fit method that utilizes a radial basis function network to approximate the non-parametric component of such models. The approximate parametric model is fit to data using the basin hopping global optimization algorithm. Parameter constraints are enforced through Gaussian priors. The viability of our method is tested by examining its use in a finite-size scaling analysis of the $q$-state Potts model and $p$-state clock model with $q=2,3$ and $p=4,\infty$.

Peterson, Curtis T.↗
DOE OSTI2025

Improving microstructures segmentation via pretraining with synthetic data

Image analysis of material microstructures through microscopy is an integral capability in the field of materials science. The topological and chemical information obtained through microscopy allow us to draw vital connections between material microstructures, properties, and processing. While scanning electron microscopy (SEM) is able to yield a considerable wealth of information interpretable by the intuition of experts, there has been considerable interest in using machine learning, convolutional neural networks (CNNs) in particular, for such image analysis task. Training CNNs for an image analysis task requires a large annotated dataset. However, in many materials science applications, obtaining a large annotated dataset is cost and labor intensive. In this work, we study the use of synthetic data to enlarge the available annotated experimental data of uranium oxide. We utilize a modified Potts model to simulate uranium oxide particles with morphologies similar to those observed experimentally. We then leverage an image-to-image translation model to synthesize the simulated particles as if they are acquired with SEM. Through this process, we obtain pairs of particle images and their corresponding SEM representations, which corresponds to pairs of annotations and images. Unlike previous works, we leverage synthetic data for pretraining a CNN model prior, and finetune that model further with experimental data. We experimentally demonstrate that using synthetic data as incremental learning process benefits the overall performance compared to training a model on combined synthetic and experimental data.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Frustrated magnetic cycloidal structure and emergent Potts nematicity in CaMn 2 P 2

We report neutron-diffraction results on single-crystal CaMn 2 P 2 containing corrugated Mn honeycomb layers, and we determine its ground-state magnetic structure. The diffraction patterns consist of prominent (1/6,1/6, L ) reciprocal-lattice unit (r.l.u.; L = integer) magnetic Bragg reflections, whose temperature-dependent intensities are consistent with a first-order antiferromagnetic phase transition at the Néel temperature T N = 70 (1) K. Our analysis of the diffraction patterns reveals an in-plane 6 × 6 magnetic unit cell with ordered spins that in the principal-axis directions rotate by 60°steps between nearest neighbors on each sublattice that forms the honeycomb structure, consistent with the P A c magnetic space group. We find that a few other magnetic subgroup symmetries (P A 2 /c, P C 2/m, P S 1, P C 2, P C m, P S 1) of the paramagnetic $P\bar{3}m11'$ crystal symmetry are consistent with the observed diffraction pattern. We relate our findings to frustrated J 1 -J 2 -J 3 Heisenberg honeycomb antiferromagnets with single-ion anisotropy and the emergence of Potts nematicity.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Half-ice, half-fire-driven ultranarrow phase crossover in one-dimensional decorated 𝑞-state Potts ferrimagnets: An AI-co-led exploration

OpenAI’s reasoning model o3-mini-high was used to carry out an exact analytic study of one-dimensional ferrimagnetic site- and bond-decorated 𝑞-state Potts models. We demonstrate that the finite-temperature ultranarrow phase crossover (UNPC), driven by a hidden “half-ice, half-fire” state recently discovered in the 𝑞=2 case (Ising model), persists for 𝑞>2. Moreover, we identify unique features for 𝑞>2, including the dome structure in the field-temperature phase diagram, and for large 𝑞 a secondary high-temperature UNPC to the fully disordered paramagnetic state. As the UNPC quickly approaches a genuine transition by enhancing 𝐽, the interaction between the backbone spins, two distinct behaviors emerge: In the site-decorated Potts model, 𝑇 0 is independent of 𝐽 and thus remains unchanged (Type-I UNPC), and in the bond-decorated Potts model with 𝑞>2, 𝑇 0 depends on 𝐽 and quickly shifts toward a finite temperature as 𝐽 increases (Type-II UNPC). These results establish a versatile framework for engineering controlled fast state-flipping switches in low-dimensional systems. Our nine-dan artificial intelligence (AI)-contribution framework assigns AI the meritorious status of AI-co-led discovery in this work.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Anisotropic physics-regularized interpretable machine learning of microstructure evolution

Anisotropic Physics-Regularized Interpretable Machine Learning Microstructure Evolution (APRIMME) is a general-purpose machine learning solution for grain growth simulations. In prior work, PRIMME employed a deep neural network to predict site-specific migration as a function of its neighboring sites to model normal, isotropic, grain growth behavior. This work aims to extend this method by incorporating grain boundary misorientation-based grain growth behavior. APRIMME is trained on anisotropic simulations created using the Monte Carlo-Potts (MCP) model. Furthermore, the results of this work are compared statistically using grain radius, number of sides per grain, mean neighborhood misorientations, and the standard deviation of triple junction dihedral angles, and are found to match in most cases. The exceptions are small and seem to be related to two causes: (1) the deterministic model of APRIMME is learning from the stochastic simulations of MCP, which seems to accentuate triple junction behaviors; and, (2) a bias against very small grains is made evident in a quicker decrease in grains than expected at the beginning of an APRIMME simulation. APRIMME is also evaluated for its general ability to capture anisotropic grain growth behavior by first investigating different test case initial conditions, including a circle grain, three grain, and hexagonal grain microstructures.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Beyond curvature-driven grain growth: Insights from fully anisotropic Monte Carlo Potts simulations

Grain boundary (GB) motion away from the center of curvature, termed anti-curvature behavior, has recently been observed in 3D experiments but is not predicted by classical grain growth theory. In this study, we investigate this behavior using a novel, fully anisotropic Monte Carlo Potts (MCP) model that incorporates both misorientation and inclination dependencies of GB energy. We perform 3D grain growth simulations with isotropic and anisotropic GB energies to explore the relationship between GB velocity and curvature. Contrary to the classical relation that velocity is a product of reduced mobility and mean curvature, we observe no consistent correlation between velocity and mean curvature for individual GBs, even under isotropic conditions, though there is correlation between the average velocity and curvature for some cases. The 3D simulations exhibit frequent anti-curvature motion regardless of GB energy anisotropy including with isotropic GBs, though larger curvatures occur with anisotropic GB energy functions that promote low-energy GBs. In 2D simulations, anti-curvature behavior only occurs with the anisotropic functions that favor low-energy GBs. This difference between 2D and 3D results suggests that anti-curvature behavior results in part from the increased freedom of motion intrinsic in 3D GB networks. Furthermore, our results support recent experimental observations that demonstrate that simple curvature-driven models are insufficient for describing GB migration in polycrystals.

Anti-curvature↗
DOE OSTI2023

Three-state Potts nematic order in stacked frustrated spin models with SO(3) symmetry

Here, we propose stacked two-dimensional lattice designs of frustrated and SO(3) symmetric spin models consisting of antiferromagnetic (AF) triangular and ferromagnetic (FM) sixfold symmetric sublattices that realize emergent $\mathbb{Z}_{3}$ Potts nematic order. Considering bilinear-biquadratic spin interactions, our models describe an SO(3)-symmetric triangular lattice AF subject to a fluctuating magnetization arising from the FM coupled sublattice. We focus on the classical AFM-FM windmill model and map out the zero- and finite-temperature phase diagram using Monte Carlo simulations and analytical calculations. We discover a state with composite Potts nematic order above the ferrimagnetic three-sublattice up-up-down ground state and relate it to Potts phases in SO(3)-broken Heisenberg and Ising AFMs in external magnetic fields. Finally, we show that the biquadratic exchange in our model is automatically induced by thermal and quantum fluctuations in the purely bilinear Heisenberg model, easing the requirements for realizing these lattice designs experimentally.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Artificial Magnetic Tripod Ice

We study the collective behavior of interacting arrays of nanomagnetic tripods. These objects have six discrete moment states, in contrast to the usual two states of an Ising-like moment. Our experimental data demonstrate that triangular lattice arrays form a “tripod ice” that exhibits charge ordering among the effective vertex magnetic charges, in direct analogy to artificial kagome spin ice. The results indicate that the interacting tripods have effective moments that act as emergent local variables, with strong connections to the well-studied Potts and clock models. In addition, the tripod moments display a tendency toward a nearest neighbor alignment in our thermalized samples that separates this system from kagome spin ice. In conclusion, our results open a path toward the study of the collective behavior of nonbinary moments that is unavailable in other physical systems.

36 MATERIALS SCIENCE↗