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All sources NASA NTRS DOE OSTI

DOE OSTI2023

Understanding the Formation of Complex Phases: The Case of FeSi 2

One of the fundamental goals of materials science is to understand and predict the formation of complex phases. In this study, FeSi 2 is considered as an illustration of complex phase formation. Although Fe and Si both crystallize with a simple structure, namely, body-centered cubic (bcc A2) and diamond (A4) structures, respectively, it is rather intriguing to note the existence of two complex structures in the Si-rich part of the phase diagram around FeSi 2 : α-FeSi 2 at high temperatures (HT) with a slight iron-deficient structure and β-FeSi2 (also referred to as Fe 3 Si 7 ) at low temperatures (LT). We re-analyze the geometry of these two phases and rely on approximant phases that make the relationship between these two phases simple. To complete the analysis, we also introduce a surrogate of the C16 phase that is observed in FeGe 2 . We clearly identify the relationship that exists between these three approximant phases, corroborated by a ground-state analysis of the Ising model for describing ordering that takes place between the transition metal element and the “vacancies”. This work is further supported by ab initio electronic structure calculations based on density functional theory in order to investigate properties and transformation paths. Finally, extension to other alloys, including an entire class of alloys, is discussed.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Machine learning for surrogate process models of bioproduction pathways

Technoeconomic analysis and life-cycle assessment are critical to guiding and prioritizing bench-scale experiments and to evaluating economic and environmental performance of biofuel or biochemical production processes at scale. Traditionally, commercial process simulation tools have been used to develop detailed models for these purposes. However, developing and running such models can be costly and computationally intensive, which limits the degree to which they can be shared and reproduced in the broader research community. This study evaluates the potential of an automated machine learning approach to develop surrogate models based on conventional process simulation models. The analysis focuses on several high-value biofuels and bioproducts for which pathways of production from biomass feedstocks have been well-established. The results demonstrate that surrogate models can be an accurate and effective tool for approximating the cost, mass and energy balance outputs of more complex process simulations at a fraction of the computational expense.

09 BIOMASS FUELS↗

DOE OSTI2025

Graph Neural Networks for Surrogate Modeling of Offshore Floating Platforms

Floating offshore wind turbines (FOWTs) present an significant opportunity to increase renewable energy generation. However, significant challenges remain before FOWTs can be widely commercialized and deployed. In particular, hydrodynamic loading on the platforms can stress the overall structure, damage the mooring systems, and impact power generation. Studying these loads is difficult and often relies on computationally expensive models or experiments. In this work, we explore the use of graph neural networks (GNNs) to construct flexible, data-driven surrogates for hydrodynamic loads on platforms. We leverage the natural graph-like structure of offshore wind platform designs to enable the GNN model to learn to approximate the loads for different wave conditions and structural designs. We demonstrate potential uses for the surrogate by performing parameter sweeps and ridge analysis on the trained model to identify the impacts of different wave and structural features on the loads.

floating offshore wind turbines↗

DOE OSTI2023

Constraints on OPF Surrogates for Learning Stable Local Volt/Var Controllers

We consider the problem of learning local Volt/Var controllers in distribution grids (DGs). Our approach starts from learning separable surrogates that take both local voltages and reactive powers as arguments and predict the reactive power setpoints that approximate optimal power flow (OPF) solutions. We propose an incremental control algorithm and identify two different sets of slope conditions on the local surrogates such that the network is collectively steered toward desired configurations asymptotically. Our results reveal the trade-offs between each set of conditions, with coupled voltage-power slope constraints allowing an arbitrary shape of surrogate functions but risking limitations on exploiting generation capabilities, and reactive power slope constraints taking full advantage of generation capabilities but constraining the shape of surrogate functions. AC power flow simulations on the IEEE 37-bus feeder illustrate their guaranteed stability properties and respective advantages in two DG scenarios.

asymptotic stability↗

DOE OSTI2022

A Fast Time-Stepping Strategy for Dynamical Systems Equipped with a Surrogate Model

Simulation of complex dynamical systems arising in many applications is computationally challenging due to their size and complexity. Model order reduction, machine learning, and other types of surrogate modeling techniques offer cheaper and simpler ways to describe the dynamics of these systems but are inexact and introduce additional approximation errors. In order to overcome the computational difficulties of the full complex models, on one hand, and the limitations of surrogate models, on the other, this work proposes a new accelerated time-stepping strategy that combines information from both. This approach is based on the multirate infinitesimal general-structure additive Runge--Kutta framework. The inexpensive surrogate model is integrated with a small time step to guide the solution trajectory, and the full model is treated with a large time step to occasionally correct for the surrogate model error and ensure convergence. Here, we provide a theoretical error analysis, and several numerical experiments, to show that this approach can be significantly more efficient than using only the full or only the surrogate model for the integration.

Surrogate models↗

NASA NTRS1998

On Managing the Use of Surrogates in General Nonlinear Optimization and MDO

This paper is concerned with a trust region approximation management framework (AMF) for solving the nonlinear programming problem in general and multidisciplinary optimization problems in particular The intent of the AMF methodology is to facilitate the solution of optimization problems with high-fidelity models. While such models are designed to approximate the physical phenomena they describe to a high degree of accuracy, their use in a repetitive procedure, for example, iterations of an optimization or a search algorithm, make such use prohibitively expensive. An improvement in design with lower-fidelity, cheaper models, however, does not guarantee a corresponding improvement for the higher-fidelity problem. The AMF methodology proposed here is based on a class of multilevel methods for constrained optimization and is designed to manage the use of variable-fidelity approximations or models in a systematic way that assures convergence to critical points of the original high-fidelity problem.

Alexandrov, Natalia M.↗

DOE OSTI2024

Bayesian reduced-order deep learning surrogate model for dynamic systems described by partial differential equations

We propose a reduced-order deep-learning surrogate model for dynamic systems described by time-dependent partial differential equations. This method employs space–time Karhunen–Loève expansions (KLEs) of the state variables and space-dependent KLEs of space-varying parameters to identify the reduced (latent) dimensions. Subsequently, a deep neural network (DNN) is used to map the parameter latent space to the state variable latent space. An approximate Bayesian method is developed for uncertainty quantification (UQ) in the proposed KL-DNN surrogate model. The KL-DNN method is tested for the linear advection–diffusion and nonlinear diffusion equations, and the Bayesian approach for UQ is compared with the deep ensembling (DE) approach, commonly used for quantifying uncertainty in DNN models. It was found that the approximate Bayesian method provides a more informative distribution of the PDE solutions in terms of the coverage of the reference PDE solutions (the percentage of nodes where the reference solution is within the confidence interval predicted by the UQ methods) and log predictive probability. The DE method is found to underestimate uncertainty and introduce bias. For the nonlinear diffusion equation, we compare the KL-DNN method with the Fourier Neural Operator (FNO) method and find that KL-DNN is 10% more accurate and needs less training time than the FNO method.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Fusion RF Modeling Machine Learning (FusionML_RF) v1.0

FusionML_RF consists of multiple codes and trained machine learning (ML) models that perform low-cost output modeling from the Genray-CQL3D. Three machine learning techniques (multilayer perceptron, random forest, and Gaussian process) provide fast surrogate models for lower hybrid current drive (LHCD) simulations. For example, completing a single GENRAY/CQL3D simulation without radial diffusion of fast electrons requires several minutes of wall-clock time. On the other hand, these ML models achieve ~ms of inference time with high accuracy across the input parameter space. This software collection consists of multiple components. (1) codes that use ML methods and precomputed Genray-CQL3D simulation output to build regression models that enable approximate computations of Genray-CLQ3D outputs from arbitrary but physically meaningful input parameters (surrogate modeling); (2) three trained models created by the team, using a database of 16,000+ GENRAY/CQL3D simulations, to study the performance of ML models for surrogate modeling; (3) codes that load the trained models and simulation data, and then compute mean squared error between the models' predictions and the ground truth of simulation output data. This collection is being made available in conjunction with a scientific publication about the work to promote reusability and provide an artifact of the scientific work.

Bai, Zhe↗

DOE OSTI2023

Atomistic simulations and machine learning of solute grain boundary segregation in Mg alloys at finite temperatures

Understanding solute segregation thermodynamics is the first step in investigating grain boundary (GB) properties, such as strong yttrium (Y) effects on grain growth and texture evolution in micro-scale polycrystalline magnesium (Mg) alloys. To estimate the average GB segregation behavior in low-solute-concentration Mg alloys (e.g., 2 at.% Y), a state-of-the-art spectral approach is applied based on a per-site segregation energy spectrum for Y solute atoms at zero K obtained from molecular statistics (MS) simulations of ~10 4 GB sites in Mg symmetric tilt GBs (STGBs). Although selected MS simulation results are consistent with verification by density functional theory (DFT) calculations, estimates of average segregation tendency based on the zero-K energy spectrum deviate from experimental observations. To resolve this problem, thermodynamic integration (TI) methods based on molecular dynamics (MD) simulations are used to determine the per-site segregation free energies of Y at representative GB sites, which show contributions beyond harmonic approximations can be important for certain GB sites at high temperatures. A surrogate model of per-site segregation free energy is constructed from a small set of TI data points using stacking cross-validation regressors and physics-informed descriptors. This model is applied to predict the Y segregation free energy spectra for thousands of GB sites in Mg STGBs with uncertainty quantification. Finally, the average segregation tendency predicted by the spectral approach based on the free energy spectra agrees well (within the uncertainty range) with experimental observations for micro-scale polycrystalline Mg alloys at typical thermomechanical processing temperatures (500 ~ 800 K), where thermodynamic equilibrium states are likely to be achieved due to fast diffusion.

Atomistic simulations↗

NASA NTRS2004

Spaceborne microwave remote sensing of seasonal freeze-thaw processes in theterrestrial high l atitudes : relationships with land-atmosphere CO2 exchange

Landscape transitions between seasonally frozen and thawed conditions occur each year over roughly 50 million square kilometers of Earth's Northern Hemisphere. These relatively abrupt transitions represent the closest analog to a biospheric and hydrologic on/off switch existing in nature, affecting surface meteorological conditions, ecological trace gas dynamics, energy exchange and hydrologic activity profoundly. We utilize time series satellite-borne microwave remote sensing measurements from the Special Sensor Microwave Imager (SSM/I) to examine spatial and temporal variability in seasonal freeze/thaw cycles for the pan-Arctic basin and Alaska. Regional measurements of spring thaw timing are derived using daily brightness temperature measurements from the 19 GHz, horizontally polarized channel, separately for overpasses with 6 AM and 6 PM equatorial crossing times. Spatial and temporal patterns in regional freeze/thaw dynamics show distinct differences between North America and Eurasia, and boreal forest and Arctic tundra biomes. Annual anomalies in the timing of thawing in spring also correspond closely to seasonal atmospheric CO2 concentration anomalies derived from NOAA CMDL arctic and subarctic monitoring stations. Classification differences between AM and PM overpass data average approximately 5 days for the region, though both appear to be effective surrogates for monitoring annual growing seasons at high latitudes.

Sensor Microwave Imager (SSM/I)carbon cycle↗

NASA NTRS2004

Spaceborne Microwave Remote Sensing of Seasonal Freeze-Thaw Processes in the Terrestrial High Latitudes: Relationships with Land-Atmosphere CO2 exchange

net primary products↗

DOE OSTI2025

Efficient online quantum circuit learning with no upfront training

Optimization is a promising candidate for studying the utility of variational quantum algorithms (VQAs). However, evaluating cost functions using quantum hardware introduces runtime overheads that limit exploration. Surrogate-based methods can reduce calls to a quantum computer, yet existing approaches require hyperparameter pre-training and have been tested only on small problems. Here, we show that surrogate-based methods can enable successful optimization at scale, without pre-training, by using radial basis function interpolation (RBF) to construct an adaptive, hyperparameter-free surrogate. Using the surrogate as an acquisition function drives hardware queries to the vicinity of the true optima. For 16-qubit random 3-regular Max-Cut instances with the Quantum Approximate Optimization Algorithm (QAOA), our method outperforms state-of-the-art approaches, without considering their upfront training costs. Furthermore, we successfully optimize QAOA circuits for 127-qubit random Ising models on an IBM processor using 10 4 −10 5 measurements. Strong empirical performance demonstrates the promise of automated surrogate-based learning for large-scale VQA applications.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2022

A Framework for Deep Learning Emulation of Numerical Models With a Case Study in Satellite Remote Sensing

Numerical models based on physics represent the state of the art in Earth system modeling and comprise our best tools for generating insights and predictions. Despite rapid growth in computational power, the perceived need for higher model resolutions overwhelms the latest generation computers, reducing the ability of modelers to generate simulations for understanding parameter sensitivities and characterizing variability and uncertainty. Thus, surrogate models are often developed to capture the essential attributes of the full-blown numerical models. Recent successes of machine learning methods, especially deep learning (DL), across many disciplines offer the possibility that complex nonlinear connectionist representations may be able to capture the underlying complex structures and nonlinear processes in Earth systems. A difficult test for DL-based emulation, which refers to function approximation of numerical models, is to understand whether they can be comparable to traditional forms of surrogate models in terms of computational efficiency while simultaneously reproducing model results in a credible manner. A DL emulation that passes this test may be expected to perform even better than simple models with respect to capturing complex processes and spatiotemporal dependencies. Here, we examine, with a case study in satellite-based remote sensing, the hypothesis that DL approaches can credibly represent the simulations from a surrogate model with comparable computational efficiency. Our results are encouraging in that the DL emulation reproduces the results with acceptable accuracy and often even faster performance. We discuss the broader implications of our results in light of the pace of improvements in high-performance implementations of DL and the growing desire for higher resolution simulations in the Earth sciences.

Bayesian Deep Learning↗

DOE OSTI2022

Accurate Compression of Tabulated Chemistry Models with Partition of Unity Networks

Tabulated chemistry models are widely used to simulate large-scale turbulent fires in applications including energy generation and fire safety. Tabulation via piecewise Cartesian interpolation suffers from the curse-of-dimensionality, leading to a prohibitive exponential growth in parameters and memory usage as more dimensions are considered. Artificial neural networks (ANNs) have attracted attention for constructing surrogates for chemistry models due to their ability to perform high-dimensional approximation. However, due to well-known pathologies regarding the realization of suboptimal local minima during training, in practice they do not converge and provide unreliable accuracy. Partition of unity networks (POUnets) are a recently introduced family of ANNs which preserve notions of convergence while performing high-dimensional approximation, discovering a mesh-free partition of space which may be used to perform optimal polynomial approximation. In this work, we assess their performance with respect to accuracy and model complexity in reconstructing unstructured flamelet data representative of nonadiabatic pool fire models. Our results show that POUnets can provide the desirable accuracy of classical spline-based interpolants with the low memory footprint of traditional ANNs while converging faster to significantly lower errors than ANNs. For example, we observe POUnets obtaining target accuracies in two dimensions with 40 to 50 times less memory and roughly double the compression in three dimensions. We also address the practical matter of efficiently training accurate POUnets by studying convergence over key hyperparameters, the impact of partition/basis formulation, and the sensitivity to initialization.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

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 OSTI2025

Bayesian prior construction for uncertainty quantification in first-principles statistical mechanics

First-principles statistical mechanics enables the prediction of thermodynamic and kinetic properties of materials, but is computationally expensive. Many approaches require surrogate models to calculate energies within Monte Carlo or molecular dynamics simulations. Inexpensive surrogates such as cluster expansions enable otherwise intractable calculations by interpolating data from higher accuracy methods, such as Density Functional Theory (DFT). Surrogate models introduce uncertainty into downstream calculations, in addition to any uncertainty inherent to DFT calculations. Bayesian frameworks address this by quantifying uncertainty and incorporating expert knowledge through priors. However, constructing effective priors remains challenging. This work introduces and describes practical strategies for building Bayesian cluster expansions, focusing on basis truncation, hyperparameter selection, and ground state replication. We analyze multiple basis truncation schemes, compare cross-validation to the evidence-approximation for hyperparameter optimization, and provide methods to find and enforce ground-state-preserving models through priors. Additionally, we compare the uncertainties between different approximations to DFT (LDA, PBE, SCAN) against the uncertainty introduced with the use of cluster expansion surrogate models. These approaches are demonstrated on the BCC Li x Mg 1-x and Li x Al 1-x alloys, which are both of interest for solid-state Li batteries. Our results provide guidelines for constructing and utilizing Bayesian cluster expansions, thereby improving the transparency of materials modeling. Furthermore, the approaches and insights developed in this work can be transferred to a wide range of cluster expansion surrogate models, including the atomic cluster expansion and related machine-learned interatomic potential architectures.

Alloy theory↗

DOE OSTI2021

Train Like a (Var)Pro: Efficient Training of Neural Networks with Variable Projection

Deep neural networks (DNNs) have achieved state-of-the-art performance across a variety of traditional machine learning tasks, e.g., speech recognition, image classification, and segmentation. The ability of DNNs to efficiently approximate high-dimensional functions has also motivated their use in scientific applications, e.g., to solve partial differential equations and to generate surrogate models. In this paper, we consider the supervised training of DNNs, which arises in many of the above applications. We focus on the central problem of optimizing the weights of the given DNN such that it accurately approximates the relation between observed input and target data. Devising effective solvers for this optimization problem is notoriously challenging due to the large number of weights, nonconvexity, data sparsity, and nontrivial choice of hyperparameters. To solve the optimization problem more efficiently, we propose the use of variable projection (VarPro), a method originally designed for separable nonlinear least-squares problems. Our main contribution is the Gauss--Newton VarPro method (GNvpro) that extends the reach of the VarPro idea to nonquadratic objective functions, most notably cross-entropy loss functions arising in classification. These extensions make GNvpro applicable to all training problems that involve a DNN whose last layer is an affine mapping, which is common in many state-of-the-art architectures. In our four numerical experiments from surrogate modeling, segmentation, and classification, GNvpro solves the optimization problem more efficiently than commonly used stochastic gradient descent (SGD) schemes. Finally, GNvpro finds solutions that generalize well, and in all but one example better than well-tuned SGD methods, to unseen data points.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2017

The Use of a Satellite Communications System for Command and Control of the National Aeronautics and Space Administration Surrogate Unmanned Aerial System Research Aircraft

The NASA Langley Research Center has transformed a Cirrus Design SR22 general aviation (GA) aircraft into an Unmanned Aerial Systems (UAS) Surrogate research aircraft which has served for several years as a platform for unmanned systems research and development. The aircraft is manned with a Safety Pilot and a Research Systems Operator (RSO) that allows for flight operations almost any-where in the national airspace system (NAS) without the need for a Federal Aviation Administration (FAA) Certificate of Authorization (COA). The UAS Surrogate can be remotely controlled from a modular, transportable ground control station (GCS) like a true UAS. Ground control of the aircraft is accomplished by the use of data links that allow the two-way passage of the required data to control the aircraft and provide the GCS with situational awareness. The original UAS Surrogate data-link system was composed of redundant very high frequency (VHF) data radio modems with a maximum range of approximately 40 nautical miles. A new requirement was developed to extend this range beyond visual range (BVR). This new requirement led to the development of a satellite communications system that provided the means to command and control the UAS Surrogate at ranges beyond the limits of the VHF data links. The system makes use of the Globalstar low earth orbit (LEO) satellite communications system. This paper will provide details of the development, implementation, and flight testing of the satellite data communications system on the UAS Surrogate research aircraft.

Howell, Charles T.↗