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DOE OSTI2025

A resolution independent neural operator

The Deep operator network (DeepONet) is a powerful yet simple neural operator architecture that utilizes two deep neural networks to learn mappings between infinite-dimensional function spaces. This architecture is highly flexible, allowing the evaluation of the solution field at any location within the desired domain. However, it imposes a strict constraint on the input space, requiring all input functions to be discretized at the same locations; this limits its practical applications. Here, in this work, we introduce a general framework for operator learning from input–output data with arbitrary number and locations of sensors. This begins by introducing a resolution-independent DeepONet (RI-DeepONet), enabling it to handle input functions that are arbitrarily, but sufficiently finely, discretized. To this end, we propose two dictionary learning algorithms to adaptively learn a set of appropriate continuous basis functions, parameterized as implicit neural representations (INRs), from correlated signals defined on arbitrary point cloud data. These basis functions are then used to project arbitrary input function data as a point cloud onto an embedding space (i.e., a vector space of finite dimensions) with dimensionality equal to the dictionary size, which can be directly used by DeepONet without any architectural changes. In particular, we utilize sinusoidal representation networks (SIRENs) as trainable INR basis functions. The introduced dictionary learning algorithms are then used in a similar way to learn an appropriate dictionary of basis functions for the output function data, which defines a new neural operator architecture referred to as the R esolution I ndependent N eural O perator (RINO). In the RINO, the operator learning task simplifies to learning a mapping from the coefficients of input basis functions to the coefficients of output basis functions. We demonstrate the robustness and applicability of RINO in handling arbitrarily (but sufficiently richly) sampled input and output functions during both training and inference through several numerical examples.

Deep operator network (DeepONet)↗

DOE OSTI2026

Higher-order LaSDI: Reduced order modeling with multiple time derivatives

Solving complex partial differential equations (PDEs) is essential across scientific disciplines but often requires numerical models that can be prohibitively expensive in time-sensitive applications. Reduced-order models (ROMs) address this challenge by exploiting low-dimensional structure to create fast approximations. The Latent Space Dynamics Identification (LaSDI) framework has demonstrated success in learning ROMs for parameterized PDE families, but remains limited to first-order systems. Here, in this paper, we propose Higher-Order LaSDI (HLaSDI), which extends the LaSDI framework to PDEs with arbitrary order of time derivatives. This generalization significantly expands the applicability of LaSDI-based methods to systems previously outside their scope, including hyperbolic PDEs. We demonstrate HLaSDI’s accuracy and efficiency on several linear and nonlinear benchmark problems.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Co-optimized machine-learned manifold models for large eddy simulation of turbulent combustion

Many modeling approaches in large eddy simulation (LES) of turbulent combustion employ a projection of the thermochemical state onto a low-dimensional manifold within state space to reduce the number of transported variables and hence computational cost. Flamelet-generated manifolds (FGM) is an example of a well-established, physics-based approach, but increasingly, principal component analysis (PCA) is being used as a data-driven method for generating manifold models. For both approaches, the nonlinear relationship between the location on the predefined manifold and the outputs of interest, such as reaction rates, can be tabulated or encoded in a neural network. This work proposes a new approach for manifold modeling that extends these existing approaches. A modified neural network structure simultaneously encodes the definition of the manifold variables, the nonlinear mapping, and the subfilter closure for LES. This allows all three of these aspects of the model to be co-optimized, generating a model from any source of combustion thermochemical state data. The manifold parameterizing variables are constrained to be linear combinations of species, as in FGM and PCA-based models, to aid in interpretability and implementation. For LES, subfilter variances of the manifold variables are also included as inputs. Two types of a priori analysis are performed to evaluate the new approach. In the first, the model is trained on data from one-dimensional premixed flames. In this case, the approach recovers the behavior of flamelet-based manifold approaches, and in fact slightly improves performance by identifying an optimized progress variable. The approach is also applied to data from direct numerical simulations of spherical ignition kernels in isotropic turbulence. For any specified manifold dimensionality, the new approach provides substantially lower prediction errors than a PCA-based model developed from the same data set. Additionally, the LES formulation of the new approach can provide accurate predictions for filtered reaction rates across a variety of filter widths.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

The effect of stress on the migration of He gas bubbles under a thermal gradient in Fe by phase-field modeling

Here a phase-field model is parameterized to study the effect of elastic stresses on the migration of He gas bubbles in Fe under a temperature gradient. Stresses caused by the gas bubble pressure and residual stress in the Fe matrix are considered. The dependence of He bubble migration velocity on the magnitude of the residual stress, average temperature, temperature gradient, and bubble size is measured. In agreement with a theoretical model based on surface diffusion, simulation results demonstrate that He bubbles move towards the high temperature region with velocities in Fe that are orders of magnitude faster than previously reported in UO 2 . It is found that local stresses in the matrix caused by the He bubble have negligible effect on the bubble migration process; however, residual stresses in the Fe matrix, potentially caused by processing or irradiation, can modestly modify bubble kinetics through pressure dependence of the He diffusion coefficients. Compressive residual stress decreases diffusion coefficients for bulk and surface diffusion mechanisms, thus reducing the migration velocity of the gas bubble. In contrast, tensile residual stress increases the diffusion coefficients, resulting in an increase in the gas bubble migration velocity. This pressure dependence is also consistent with a theoretical model. This phase field model lays the foundation for analysis of bubble coalescence-induced fracture in He bubble-containing steels.

36 MATERIALS SCIENCE↗

DOE OSTI2022

CASM — A software package for first-principles based study of multicomponent crystalline solids

CASM is a software package that enables first-principles based studies of crystalline materials. It has been designed to treat coupled chemical, mechanical, vibrational, and magnetic degrees of freedom to determine ground state and finite temperature properties of crystals. The symmetry of the underlying parent crystal structure is used to enumerate perturbations of the parent crystal structure and generate derivative structures which can be input to first-principles calculations in order to explore the ground state energy landscape. CASM algorithmically constructs cluster expansions that fully couple discrete and continuous degrees of freedom, and generates highly efficient code to evaluate the cluster expansion basis functions. Widely used machine learning methods are integrated for fitting expansion coefficients to first-principle calculations. The fully parameterized cluster expansions can be combined with (kinetic) Monte Carlo methods to calculate finite temperature thermodynamic and kinetic properties. CASM Alloy Manager identifies distinct parent crystal structures in an alloy system, creating individual projects for each, and integrating the results. The integrated infrastructure facilitates the linkage between first-principles statistical mechanics predictions with higher length scale computational methods, such as phase field simulations. In conclusion, CASM projects are designed to be easy to share in repositories, to re-use, and to extend to include additional chemical species or types of degrees of freedom.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Mesoscale modeling and semi-analytical approach for the microstructure-aware effective thermal conductivity of porous polygranular materials

Here we established a comprehensive modeling approach for investigating the microstructure-aware effective thermal conductivity ($κ_{eff}$) for porous microstructures containing solid particles and gaseous pores. Our approach combines the mesoscale computational modeling framework and the semi-analytical method, allowing for efficient prediction of $κ_{eff}$ for realistic porous microstructures, while considering complicated microstructural thermal conduction pathways effectively in the prediction. We used the diffuse-interface mesoscale computational model to generate extensive simulated $κ_{eff}$ data for realistic digital representations of microstructures with wide ranges of porosity ($f_p$), thermal conductivity of the gas phase ($κ_g$), and thermal conductivity of the solid phase ($κ_s$). From the simulated data, we identified two property variation regimes for $κ_{eff}$: (1) a slow $κ_{eff}$ increase for $κ_s ~ κ_g$; and (2) a faster $κ_{eff}$ increase for $κ_s \gg κ_g$. To capture the key features of the relationship between the microstructure and $κ_{eff}$, we derived a semi-analytical model by introducing structure and intensification factors. The two new factors incorporate the calibrated effective contribution of the solid volume with $κ_s$ and additional interfacial effects into the prediction of $κ_{eff}$, respectively, allowing for consideration of parallel, serial, and interfacial conduction mechanisms effectively. Using the selected simulation data, we quantified key model parameters within the semi-analytical model and verified that the parameterized model exhibits excellent agreement with simulated $κ_{eff}$ for the entire range of the parameter space.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Cluster expansion by transfer learning for phase stability predictions

Recent progress towards universal machine-learned interatomic potentials holds considerable promise for materials discovery. Yet the accuracy of these potentials for predicting phase stability may still be limited. In contrast, cluster expansions provide accurate phase stability predictions but are computationally demanding to parameterize from first principles, especially for structures of low dimension or with a large number of components, such as interfaces or multimetal catalysts. We overcome this trade-off via transfer learning. Using Bayesian inference, we incorporate prior statistical knowledge from machine-learned and physics-based potentials, enabling us to sample the most informative configurations and to efficiently fit first-principles cluster expansions. Furthermore, this algorithm is tested on Pt:Ni, showing robust convergence of the mixing energies as a function of sample size with reduced statistical fluctuations.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Phase-field modeling of radiation-induced composition redistribution: An application to additively manufactured austenitic Fe–Cr–Ni

Multicomponent alloys undergoing irradiation damage develop radiation-induced composition redistribution at point defect sinks such as grain boundaries (GBs) and dislocations. Such redistribution results in undesired changes to their mechanical behavior and corrosion resistance. Additively manufactured alloys proposed for future nuclear applications are expected to demonstrate a distinct response to irradiation owing to their unique microstructure with as-solidified dislocation density and chemical microsegregation. To capture the composition redistribution in such systems, we develop a mesoscale model with coupled evolution of atomic and point defect components in the presence of dislocation density, dislocation heterogeneity, and thermodynamic interactions at the GB. The model is parameterized for an FCC Fe–Cr–Ni alloy as a representative system for austenitic stainless steels, and simulations are performed in 1D and 2D as a function of irradiation temperature, dose, dislocation density, and grain size. Radiation-induced segregation (RIS) characterized by Cr depletion and Ni enrichment is predicted at both the GB and the dislocation cell wall, with RIS being lower in magnitude but wider at the cell wall. Strongly biased absorption of self-interstitials by dislocations is found to suppress Ni enrichment but slightly enhance Cr depletion under certain conditions. Thermodynamic segregation at the GB is predicted to be narrower and opposite in sign to RIS for both Cr and Ni. Importantly, non-monotonic segregation is found to occur when both thermodynamic and RIS mechanisms are considered, providing a novel physical interpretation of experimental observations. The model is expected to serve as a key tool in accelerated qualification of irradiated materials.

additively manufactured microstructure↗

DOE OSTI2025

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↗

DOE OSTI2020

Optimization-based control using input convex neural networks

Input convex neural networks (ICNNs) are a family of deep learning models where the outputs are constructed to be convex functions of the inputs. By parameterizing system models using ICNNs, optimization-based control problems can be solved as convex optimization problems, leading to improved performance and robustness. This work proposes a novel framework where the control objective function and constraints are modelled using ICNNs. A case study of optimization-based control with output constraints is conducted on a process with input multiplicity and nonminimum phase behavior. The simulation results demonstrate improved economic yield compared with normal neural networks. Additionally, the input convexity formulation is compared with simple regularization techniques, and unique benefits such as improved data efficiency and robustness of the proposed formulation are shown. Finally, by explicitly incorporating prior knowledge about convexity, this framework provides a good balance between the universal approximation power of deep learning and computational feasibility required by control.

42 ENGINEERING↗

DOE OSTI2024

A data-driven multiscale model for reactive wetting simulations

Here, we describe a data-driven, multiscale technique to model reactive wetting of a silver–aluminum alloy on a Kovar™ (Fe-Ni-Co alloy) surface. We employ molecular dynamics simulations to elucidate the dependence of surface tension and wetting angle on the drop’s composition and temperature. A design of computational experiments is used to efficiently generate training data of surface tension and wetting angle from a limited number of molecular dynamics simulations. The simulation results are used to parameterize models of the material’s wetting properties and compute the uncertainty in the models due to limited data. The data-driven models are incorporated into an engineering-scale (continuum) model of a silver–aluminum sessile drop on a Kovar™ substrate. Model predictions of the wetting angle are compared with experiments of pure silver spreading on Kovar™ to quantify the model-form errors introduced by the limited training data versus the simplifications inherent in the molecular dynamics simulations. The paper presents innovations in the determination of “convergence” of noisy MD simulations before they are used to extract the wetting angle and surface tension, and the construction of their models which approximate physio-chemical processes that are left unresolved by the engineering-scale model. Together, these constitute a multiscale approach that integrates molecular-scale information into continuum scale models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

A cross-sectional aeroelastic analysis and structural optimization tool for slender composite structures

A fully open-source available framework for the parametric cross-sectional analysis and design optimization of slender composite structures, such as helicopter or wind turbine blades, is presented. The framework—Structural Optimization and Aeroelastic Analysis (SONATA)—incorporates two structural solvers, the commercial tool VABS, and the novel open-source code ANBA4. SONATA also parameterizes the design inputs, postprocesses and visualizes the results, and generates the structural inputs to a variety of aeroelastic analysis tools. It is linked to the optimization library OpenMDAO. This work presents the methodology and explains the fundamental approaches of SONATA. Structural characteristics were successfully verified for both VABS and ANBA4 using box beam examples from literature, thereby verifying the parametric approach to generating the topology and mesh in a cross section as well as the solver integration. The framework was furthermore exercised by analyzing and evaluating a fully resolved highly flexible wind turbine blade. Computed structural characteristics correlated between VABS and ANBA4, including off-diagonal terms. Stresses, strains, and deformations were recovered from loads derived through coupling with aeroelastic analysis. The framework, therefore, proves effective in accurately analyzing and optimizing slender composite structures on a high-fidelity level that is close to a three-dimensional finite element model.

42 ENGINEERING↗

DOE OSTI2021

Considering coasts: Adapting terrestrial models to characterize coastal wetland ecosystems

The Energy Exascale Earth System Model (E3SM) simulates fully coupled processes and interactions among water, energy, carbon and nutrient cycles. E3SM connects vegetation and soil dynamics through nutrient uptake, plant production, litterfall and decomposition as a function of abiotic parameters (e.g. temperature and moisture). However, E3SM is designed to characterize terrestrial ecosystems and connects land and open ocean systems using a single streamflow transport term, ignoring the complex dynamics of energy, water, carbon, and nutrients in coastal systems. The goals of our project were to: (1) Parameterize a point version of E3SM to capture coastal wetland habitats and (2) Determine marsh community responses to increased temperature and elevated CO 2 . We adapted a version of the E3SM land model, previously configured to represent forested bog hydrology to a coastal ecosystem using datasets from field experiments conducted at the Smithsonian Environmental Research Center's Global Change Research Wetland (GCReW). Tidal forcing in a marsh environment was simulated using a two-column system in which the columns are connected by lateral hydrologic flows. One column simulates interactions between vegetation and soil while a second column simulates variation in water level (both tidal and sea level rise). The updated model captures many aspects of the field experiments, showing that plant community responses to environmental change are non-linear, non-additive and different between plant types. Elevated CO 2 treatments increased C 3 plant biomass more than C 4 (33% vs 17%). Temperature exacerbated CO 2 responses in C 3 plants (0 °C: 26%, 5.1 °C: 56%). We were more successful at characterizing C 3 than C 4 responses and simulating above rather than belowground biomass production. Furthermore, the next steps will include updates to key physiological parameters such as root:shoot carbon allocation and the addition of mechanistic feedbacks between vegetation and biogeochemical processes.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

Reducing impacts of artificial ponding in modeling salt marshes using a conductivity-formulated subgrid model

The landforms of salt marsh systems are rather complex, with meandering channel networks cutting through low-lying, extensive marsh platforms. Some small-scale topographic details are critical to flooding and draining processes but cannot be reflected in the Digital Elevation Model (DEM) due to limited measurement resolution and vegetation bias. Numerical models need a grid with high enough resolution to capture the small-scale connectivity to correctly model the small-scale flow processes, making the model computationally unaffordable. Here, in this study, we derived a subgrid model, which couples two flow components, one is the regular subgrid model for simulating the subgrid-resolved flows, and the other is a conductivity-formulated porous flow model for modeling small-scale gut flows unresolved at the subgrid level. The model validation was performed using an idealized case with a narrow slot that was unresolved in the coupled flow model. Model results were compared with a slot-resolved regular subgrid model where only surface flows are solved and suggested that, with a proper model parameterization, the coupled flow model is capable of reproducing flooding and draining processes similar to the slot-resolved subgrid model of surface flow. The model was applied to simulating flooding and draining processes in a meso-tidal salt marsh. The model results demonstrate that the coupled subgrid model can be used to reduce the impacts of artificial ponding that usually occur in numerical simulations of salt marshes with numerous narrow gullies and creeks.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Toward control co-design of utility-scale wind turbines: Collective vs. individual blade pitch control

A large-eddy simulation framework has been coupled with controller modules to systematically investigate the impacts of collective (CPC) and individual (IPC) pitch control strategies on utility-scale wind turbine energy production and fatigue loads. Wind turbine components were parameterized using an actuator surface model to simulate the rotor blades and the turbine nacelle. The baseline CPC and IPC algorithms, consisting of single-input single-output proportional–integral controllers and two integral controllers, respectively, were incorporated into the numerical framework. A series of simulations were carried out to investigate the relative performance of the two controllers under various turbulent inflow conditions, spanning hub-height velocities of 7 to 14 m/s. The numerical simulation results of this study showed that, in comparison to the CPC, the IPC controller could successfully reduce the damage equivalent loads of utility-scale turbines at regions 2 and 3 of turbine operation by about 3% and 40%, respectively, without any penalty on the power production of the turbine. It was also shown that, despite its minor impact on the turbulence kinetic energy of the wake, the IPC controller did not influence the recovery of the turbine wake.

17 WIND ENERGY↗

DOE OSTI2022

Quantifying transport and electrocatalytic reaction processes in a gastight rotating cylinder electrode reactor via integration of Computational Fluid Dynamics modeling and experiments

Understanding the complexity of the multiple processes of mass, momentum, charge, and heat transport, and how these affect reaction kinetics at the electrode/electrolyte interface is one of the major challenges in the field of energy and catalysis. The rapid and rational scale-up of electrocatalytic systems to industrial scales require a detailed understanding of nonlinear transport-reaction processes, accessible only through the building of multi-physics models that capture with high fidelity the complexity of real-world devices. The gastight rotating cylinder electrode (RCE) reactor is a promising lab-scale tool that can decouple transport from intrinsic kinetics to generate data for first-principle models useful in the design of industrial, electrochemical reactors. Computational Fluid Dynamics (CFD) studies have previously been used to investigate the bulk flow in RCE reactors for simple corrosion and electroplating processes. However, the quantification of changes in local concentration within the viscous layer where catalysis takes place requires capturing the correct flow conditions inside the hydrodynamic boundary layer near the surface of the electrode. Further, this requires simulations with spatial resolution in the nm and μm scale and temporal resolutions between ms and s scales that are similar to the timescales for reactions on the electrode surface. In this study, experimental electrocatalysis is combined with CFD modeling to elucidate and parameterize the hydrodynamics in a gastight RCE reactor. CFD simulations of the electrochemical ferricyanide reduction reaction under mass transport limited conditions are used to evaluate the validity of the CFD model parameters by comparing calculated dimensionless mass transport descriptors to dimensionless correlations obtained experimentally. Justifications for assumptions and details of the simulation methods used in this study are presented to provide a detailed understanding of the effect that each model parameter has on the ability to accurately simulate electrocatalysis in RCE systems. The simulation methodology reported here is a first step towards the development of multi-scale models for the study of transport dependent electrocatalytic processes, such as the electrochemical transformation of CO 2 to fuels and chemicals.

42 ENGINEERING↗

DOE OSTI2024

A deep learning-based Bayesian framework for high-resolution calibration of building energy models

Calibrating building energy models (BEMs), i.e., closing discrepancy between modeling and field measurements, is of significance to support its applications in building sustainability and resilience analysis. However, as being widely used in practice, current Bayesian calibration is mostly performed in low-resolution (annual or monthly), instead of high-resolution (hourly or sub-hourly), which is crucial to support emerging BEM applications, such as building-renewable energy integration (demand response) and smart control. This is attributable to the gaps in current Bayesian calibration process, including (1) difficulty in supporting reliable high-resolution calibration with over-parameterization and multi-solution issues, (2) inadequacy of meta-model to capture temporal building dynamics in high-resolution, and (3) excessive computational burdens of covariance matrix calculation in Bayesian inference. Therefore, to close these gaps, this research proposes a novel deep learning-based Bayesian calibration framework, involving pre-calibration mechanism, Long Short-Term Memory as surrogate models, and simplified covariance matrix calculation, to calibrate BEMs in high temporal resolution (i.e., hourly) with enhanced accuracy and computational efficiency. Finally, the case study demonstrates its effectiveness to match modeling outcomes with measurements and realize CV-RMSE of < 30 % and NMBE of < 6 % in hourly resolution, as well as a significant reduction of calibration time (by > 99 %, from > 600 h to ~ 1.5 h).

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2026

Improving energy efficiency while reducing anthropogenic heat from buildings: how retrofits influence the building stock and urban microclimate in Los Angeles

Anthropogenic heat (AH) from buildings contributes to urban overheating, especially during heat waves, yet building retrofit studies usually evaluate energy savings without assessing impacts on AH. This study quantifies how common building retrofit measures affect both building energy use and AH emissions across the City of Los Angeles. Using a bottom-up urban building energy modeling framework coupled with high-resolution local weather from the Weather Research and Forecasting model with Building Effect Parameterization (WRF-BEP), we evaluate eleven retrofit measures and two multi-measure retrofit packages. HVAC and LED lighting retrofits provide the largest city-wide annual site energy savings, while roof coating is most effective for reducing AH. A package optimized for energy savings reduces summer site energy use by about 32% (2.3 TWh), while a package incorporating AH-focused measures reduces the total AH by over 50% (137 PJ) with minimal difference in energy savings. The AH-aware package produces substantially greater urban cooling, reducing mean near-surface air temperature by up to 0.62 ℃ and peak temperature by up to 3.79 ℃. These results show that retrofit strategies selected only for energy savings may overlook major opportunities for urban heat mitigation. The study provides a framework for integrating AH into building retrofit planning and urban heat resilience policy.

Anthropogenic heat↗