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Generative Models for Crystalline Materials

Understanding structure-property relationships in materials is fundamental in condensed matter physics and materials science. Over the past few years, machine learning (ML) has emerged as a powerful tool for advancing this understanding and accelerating materials discovery. Early ML approaches primarily focused on constructing and screening large material spaces to identify promising candidates for various applications. More recently, research efforts have increasingly shifted toward generating crystal structures using end-to-end generative models. This review analyzes the current state of generative modeling for crystal structure prediction and de novo generation. It examines crystal representations, outlines the generative models used to design crystal structures, and evaluates their respective strengths and limitations. Furthermore, the review highlights experimental considerations for evaluating generated structures and provides recommendations for suitable existing software tools. Emerging topics, such as modeling disorder and defects, integration in advanced characterization, incorporating synthetic feasibility constraints, and model explainability are explored. Ultimately, this work aims to inform both experimental scientists looking to adapt suitable ML models to their specific circumstances and ML specialists seeking to understand the unique challenges related to inverse materials design and discovery.

Metni, Houssam [Karlsruhe Inst. of Technology (KIT

CO 2 storage site characterization using ensemble-based approaches with deep generative models

Estimating spatially distributed properties such as permeability from available sparse measurements is a great challenge in efficient subsurface CO 2 storage operations. In this paper, a deep generative model that can accurately capture complex subsurface structure is tested with an ensemble-based inversion method for accurate and accelerated characterization of CO 2 storage sites. We chose Wasserstein Generative Adversarial Network with Gradient Penalty (WGAN-GP) for its realistic reservoir property representation and Ensemble Smoother with Multiple Data Assimilation (ES-MDA) for its robust data fitting and uncertainty quantification capability. WGAN-GP are trained to generate high-dimensional permeability fields from a low-dimensional latent space and ES-MDA then updates the latent variables by assimilating available measurements. Several subsurface site characterization examples including Gaussian, channelized, and fractured reservoirs are used to evaluate the accuracy and computational efficiency of the proposed method and the main features of the unknown permeability fields are characterized accurately with reliable uncertainty quantification. Furthermore, the estimation performance is compared with a widely-used variational, i.e., optimization-based, inversion approach, and the proposed approach outperforms the variational inversion method in several benchmark cases. We explain such superior performance by visualizing the objective function in the latent space: because of nonlinear and aggressive dimension reduction via generative modeling, the objective function surface becomes extremely complex while the ensemble approximation can smooth out the multi-modal surface during the minimization. This suggests that the ensemble-based approach works well over the variational approach when combined with deep generative models at the cost of forward model runs unless convergence-ensuring modifications are implemented in the variational inversion.

42 ENGINEERING

Structural constraint integration in a generative model for the discovery of quantum materials

Billions of organic molecules have been computationally generated, yet functional inorganic materials remain scarce due to limited data and structural complexity. Here, in this work, we introduce Structural Constraint Integration in a GENerative model (SCIGEN), a framework that enforces geometric constraints, such as honeycomb and kagome lattices, within diffusion-based generative models to discover stable quantum materials candidates. SCIGEN enables conditional sampling from the original distribution, preserving output validity while guiding structural motifs. This approach generates ten million inorganic compounds with Archimedean and Lieb lattices, over 10% of which pass multistage stability screening. High-throughput density functional theory calculations on 26,000 candidates shows over 95% convergence and 53% structural stability. A graph neural network classifier detects magnetic ordering in 41% of relaxed structures. Furthermore, we synthesize and characterize two predicted materials, TiPd 0.22 Bi 0.88 and Ti 0.5 Pd 1.5 Sb, which display paramagnetic and diamagnetic behaviour, respectively. Our results indicate that SCIGEN provides a scalable path for generating quantum materials guided by lattice geometry.

36 MATERIALS SCIENCE

A novel conditional generative model for efficient ensemble forecasts of state variables in large-scale geological carbon storage

Integrating monitoring data to efficiently update reservoir pressure and CO 2 plume distribution forecasts presents a significant challenge in geological carbon storage (GCS) applications. Inverse modeling techniques are commonly used to fuse observational data and refine reservoir model parameters, thereby improving state variable forecasts. However, these techniques often rely on linear or Gaussian assumptions, which can limit their effectiveness in accurately predicting state variables. Moreover, simulating large-scale three-dimensional (3D) GCS problems is computationally expensive, making iterative runs in inverse problems prohibitive. To address these challenges, we propose a conditional generative model utilizing the score-based diffusion method for real-time 3D pressure and saturation field distribution predictions. Our approach involves solving the score function with a mini-batch-based Monte Carlo estimator to generate labeled data. This data is subsequently employed to train a fully connected neural network, enabling it to learn the conditional sample generator within a supervised learning framework. This method enables the rapid generation of a large ensemble of predictions, facilitating comprehensive uncertainty quantification of state variables. Here we applied our method to forecast the dynamic 3D distributions of pressure and saturation fields over a 30-year injection period. The statistical assessment with low root mean square error (RMSE) values demonstrates that our method can accurately predict the spatiotemporal distributions of both pressure and saturation fields. Moreover, the developed conditional generative model shows high computational efficiency by generating 100 ensemble forecasts of 3D state variables in less than 10 min. The consistency between ensemble averages and ground truth values further illustrates the model’s capability to capture state variable dynamics during the CO 2 plume injection process. Notably, the ground truth values fall within the ensemble forecasts, indicating that our uncertainty quantification effectively captures variability and potential noise in the observations. Thus, the developed conditional generative model proves to be a more efficient, accurate, and practical tool for GCS applications, facilitating timely risk analysis and informed decision-making.

58 GEOSCIENCES

Automated model generation for reliability analysis programs

Semi-Markov models (a generalization of Markov models) can be used to calculate the reliability of virtually any fault-tolerant system. However, the process of delineating all of the states and transitions in the model of a complex system can be devastatingly tedious and error-prone. The ASSIST program allows the user to describe the semi-Markov model in a high-level language. Instead of specifying the individual states of the model, the user specifies the rules governing the behavior of the system, and these are used by ASSIST to automatically generate the model. A small number of statements in the abstract language can be used to describe a very large, complex model. Because no assumptions are made about the system being modeled, the ASSIST program can be used to generate models describing the behavior of any type of system. The ASSIST program and its input language are described and illustrated by examples.

Johnson, Sally C.

Gaussian-process generative model for the QCD equation of state

We develop a generative model for the nuclear matter equation of state at zero net baryon density using the Gaussian process regression method. We impose first-principles theoretical constraints from lattice quantum chromodynamics and hadron resonance gas at high- and low-temperature regions, respectively. By allowing the trained Gaussian process regression model to vary freely near the phase transition region, we generate random smooth crossover equations of state with different speeds of sound that do not rely on specific parametrizations. Here, we explore a collection of experimental observable dependencies on the generated equations of state, which paves the groundwork for future Bayesian inference studies to use experimental measurements from relativistic heavy-ion collisions to constrain the nuclear matter equation of state.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Leveraging Natural Language Processing and Generative Models in Molecular Chemistry: Property Prediction and Novel Compound Generation

The accurate prediction of molecular properties is important for the rational design and the advancement of green chemistry and sustainable materials research. However, the predictive power of traditional computational chemistry methods is limited due to computational restrictions. Here, in this study, we examine an alternative approach to the accurate prediction of properties of organic compounds: natural language processing (NLP)-based molecular embedding. Using viscosity, partition coefficient (log P), and enthalpy of vaporization as test properties through a survey of comprehensive datasets comprising 5695 data points for viscosity, 25 870 data points for log P, and 2296 data points for enthalpy of vaporization. These are important properties for the design of greener, safer, and sustainable chemical processes. Models were trained using NLP methods such as Mol2vec and fine-tuned ChemBERTa, and results were compared with traditional input featurization techniques such as Morgan fingerprints and quantum chemistry derived sigma profiles and DFT features. Among the various machine learning models, Mol2vec demonstrated superior predictive capabilities, achieving the highest correlation coefficient (R 2 = 0.945) and lowest RMSE (0.106 mPa s) for viscosity, as well as high accuracy for log P and enthalpy of vaporization predictions. These findings establish the Mol2vec featurization technique, graph-convolutional neural networks (GCNN), and fine-tuned ChemBERTa model as powerful tools for predictive modeling of organic compounds properties, offering a significant improvement over previously used featurization techniques and opening up strategies for very-high-throughput computational screening. Finally, we integrated ML models with hybrid language-model-based generative adversarial networks (LM-GAN) to generate novel molecular sequences with desirable properties for different research applications. The ability to computationally design solvents with lower viscosity, lower log P, and lower enthalpy of vaporization offers a data-driven route to accelerating the discovery of sustainable alternatives to traditionally toxic solvents.

ChemBERTa

Learning turbulent flows with generative models for super resolution and sparse flow reconstruction

Neural operators are promising surrogates for dynamical systems but when trained with standard L 2 losses they tend to oversmooth fine-scale turbulent structures. Here, we show that combining operator learning with generative modeling overcomes this limitation. We consider three practical turbulent-flow challenges where conventional neural operators fail: spatio-temporal super-resolution, forecasting, and sparse flow reconstruction. For Schlieren jet super-resolution, an adversarially trained neural operator (adv-NO) reduces the energy-spectrum error by 15 × while preserving sharp gradients at neural operator-like inference cost. For 3D homogeneous isotropic turbulence, adv-NO trained on only 160 timesteps from a single trajectory forecasts accurately for five eddy-turnover times and offers 114 × wall-clock speed-up at inference than the baseline diffusion-based forecasters, enabling near-real-time rollouts. For reconstructing cylinder wake flows from highly sparse Particle Tracking Velocimetry-like inputs, a conditional generative model infers full 3D velocity and pressure fields with correct phase alignment and statistics. These advances enable accurate reconstruction and forecasting at low compute cost, bringing near-real-time analysis and control within reach in experimental and computational fluid mechanics.

Fluid dynamics

Combining Generative Modeling and Advanced Control for Building Scenario Generation

Buildings make up a large portion of energy consumption in the U.S. today. Understanding their energy consumption patterns can improve their efficiency, but requires detailed models that rely on incomplete or unknown information. Previous work has shown that artificial intelligence (AI) can be used to predict missing information and even suggest upgrades to improve building efficiency. However, building upgrades may require undesirable upfront costs. Oppositely, advanced control could improve building efficiency with negligible upfront cost. To explore the tradeoffs between these two approaches, in this work we propose a workflow to compute optimal temperature setpoint schedules to minimize energy consumption and operational cost. Results show that modifying the temperature setpoints in a building using model predictive control (MPC) can effectively reduce its energy consumption and operational cost. This optimal operation cannot fully meet a desired goal. However, we show that by considering MPC in addition to component upgrades, a desired goal can be met with significantly less upfront costs.

24 POWER TRANSMISSION AND DISTRIBUTION

Development and Implementation of a New AI-Based Tool to Support Fast Reactor Software Model Generation and Validation

This report summarizes FY26 work to develop Maggie, an artificial intelligence-based assistant designed to support software model generation and validation activities for fast reactor analysis codes. The project established a modular, code-agnostic software architecture that separates reusable agent capabilities from code-specific knowledge and tools, with initial implementation focused on the FRP-supported fast reactor safety analysis code SAS4A/SASSYS1 (SAS). A curated SAS-specific knowledge base was assembled from the code manual, training materials, historical analysis reports, and representative input files, and was integrated through retrieval-augmented generation to ground Maggie’s responses in authoritative sources. Maggie was deployed on the internal Argonne network, where it demonstrated practical user-facing capability as a chatbot for answering natural language questions about SAS and retrieving relevant technical information. Demonstration cases also showed that Maggie can generate useful snippets of SAS input for selected modeling tasks, while highlighting current limitations in reliability and consistency for more complex input generation tasks. Overall, the FY26 effort established the technical foundation for an AI-assisted capability intended to improve the efficiency, consistency, and accessibility of fast reactor software model development at Argonne and, with further improvements, to support eventual use by the broader fast reactor community, including industry users of FRP-supported analysis tools.

Thomas, Rachel [Argonne National Laboratory (ANL),

Deep Generative Models in Energy System Applications: Review, Challenges, and Future Directions

In recent years, with the advent of mature machine learning products like ChatGPT, Stable Diffusion, and Sora, the world has witnessed tremendous changes driven by the rapid development of generative artificial intelligence (GAI). Beyond applications in text, speech, image, and video creation, deep generative models (DGMs) underpinning these cutting-edge technologies have also been employed by domain researchers to address scientific and engineering challenges. This paper aims to fill a gap in the research community by providing a systematic review of how DGMs have been utilized in energy system applications. After introducing four most popular DGMs, we review and categorize 196 research articles into five focus areas: data generation, forecasting, situational awareness, modeling, and optimal decision-making. Through this classification, we uncover trends in how DGMs are employed for each type of problem, highlighting GAI techniques that contribute to breakthroughs over traditional methods. We discuss limitations in existing literature, engineering challenges, and propose future directions, all tailored to the unique nature of problems in energy system engineering. Our goal is to offer insights for energy system domain researchers, providing a comprehensive view of existing studies and potential future opportunities.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI

Metal oxide candidates for thermochemical water splitting obtained with a generative diffusion model

Generative diffusion models (DMs) for inorganic crystalline materials are being actively investigated for their potential to expand the chemical and structural design spaces for known functional materials. Generative candidates are particularly useful for applications where few functional, let alone commercially viable, materials currently exist, such as metal oxides for thermochemical water-splitting, which have strict requirements for defect thermodynamics and host stability. Here, we critically examine generated metal oxides from the M ATTER G EN DM conditioned on select chemical systems for thermochemical water splitting applications. Perhaps most notably, we find that M ATTER G EN predicts a novel, thermodynamically stable, quinary metal oxide, Ba 2 SrInFeO 6 , although this compound represents an ordered and layered substitution within the same A 3 B 2 O 6 structural prototype as its two ternary end members. Detailed density functional theory calculations and spin configuration sampling for this material and its possible decomposition products—beyond what existed in M ATTER G EN training data—are required to quantitatively validate hull energy predictions and conclusions of stability. Furthermore, the material exhibits oxygen defect formation energies appropriate for thermochemical water splitting, warranting targeted investigation in an experimental validation campaign, along with other future M ATTER G EN candidates in this application space.

36 MATERIALS SCIENCE

VFR Trajectory Forecasting using Deep Generative Model for Autonomous Airspace Operations

To enable the airspace integration of autonomous operations, such as uncrewed aircraft conducting cargo deliveries, there is a need to forecast the positions of the surrounding traffic with which they may interact. This paper focuses on forecasting Visual Flight Rules traffic, a significant source of uncertainty and risk in the airspace, especially around small regional airports, due to the unplanned and often untracked nature of such flights. A deep generative model is developed, trained on historical traffic data at example towered and non-towered airports, and used to predict flight trajectories. Experimental results are presented comparing the performance of variational autoencoder and classical machine learning forecasting when applied to both the towered and non-towered airports over varying time horizons. The results show the advantages of the variational autoencoder in producing accurate probabilistic forecasts over varying time horizons.

uncrewed aircraft

VFR Trajectory Forecasting using Deep Generative Model for Autonomous Airspace Operations

To enable the airspace integration of autonomous operations, such as uncrewed aircraft conducting cargo deliveries, there is a need to forecast the positions of the surrounding traffic with which they may interact. This paper focuses on forecasting Visual Flight Rules traffic, a significant source of uncertainty and risk in the airspace, especially around small regional airports, due to the unplanned and often untracked nature of such flights. A deep generative model is developed, trained on historical traffic data at example towered and non-towered airports, and used to predict flight trajectories. Experimental results are presented comparing the performance of variational autoencoder and classical machine learning forecasting when applied to both the towered and non-towered airports over varying time horizons. The results show the advantages of the variational autoencoder in producing accurate probabilistic forecasts over varying time horizons.

uncrewed aircraft

Spherical harmonic analysis of a model-generated climatology

Monthly mean fields of 850 mb temperature (T850), 500 mb geopotential height (G500) and sea level pressure (SLP) were generated in the course of a five-year climate simulation run with a global general circulation model. Both the model-generated climatology and an observed climatology were subjected to spherical harmonic analysis, with separate analyses of the globe and the Northern Hemisphere. Comparison of the dominant harmonics of the two climatologies indicates that more than 95% of the area-weighted spatial variance of G500 and more than 90% of that of T850 are explained by fewer than three components, and that the model adequately simulates these large-scale characteristics. On the other hand, as many as 25 harmonics are needed to explain 95% of the observed variance of SLP, and the model simulation of this field is much less satisfactory. The model climatology is also evaluated in terms of the annual cycles of the dominant harmonics.

Christidis, Z. D.

Supplementary notes on sea surface temperature anomalies and model-generated meteorological histories

In seasonal computations, the Mintz-Arakawa two-level model is found to be sensitive to a minor alteration in the computational program. Effects of the program change on monthly mean sea level pressure fields are small in the first month, but large in the second and third months, although the meteorological histories generated by both the original and modified programs are equally credible. The inherited effects of a transient (one month) sea surface temperature (SST) anomaly on the computed monthly mean sea level pressure fields over a period of a season are about as large in absolute magnitude as those generated in the model by a persistent (seasonal) SST anomaly. The effects of a transient SST anomaly in the North Pacific Ocean on monthly and seasonal temperature and precipitation in the eastern United States may be large enough to produce a change of one or two class intervals in these predicted weather elements. The model-generated precipitation in the equatorial region is also found to be sensitive to the sea surface temperature field in the North Pacific.

Spar, J.