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DOE OSTI2025

Parameter uncertainties for imperfect surrogate models in the low-noise regime

Abstract Bayesian regression determines model parameters by minimizing the expected loss, an upper bound to the true generalization error. However, this loss ignores model form error, or misspecification, meaning parameter uncertainties are significantly underestimated and vanish in the large data limit. As misspecification is the main source of uncertainty for surrogate models of low-noise calculations, such as those arising in atomistic simulation, predictive uncertainties are systematically underestimated. We analyze the true generalization error of misspecified, near-deterministic surrogate models, a regime of broad relevance in science and engineering. We show that posterior parameter distributions must cover every training point to avoid a divergence in the generalization error and design a compatible ansatz which incurs minimal overhead for linear models. The approach is demonstrated on model problems before application to thousand-dimensional datasets in atomistic machine learning. Our efficient misspecification-aware scheme gives accurate prediction and bounding of test errors in terms of parameter uncertainties, allowing this important source of uncertainty to be incorporated in multi-scale computational workflows.

Swinburne, Thomas D. (ORCID:0000000232554257)↗

DOE OSTI2024

Genomic prediction of regional-scale performance in switchgrass ( Panicum virgatum ) by accounting for genotype-by-environment variation and yield surrogate traits

Switchgrass is a potential crop for bioenergy or carbon capture schemes, but further yield improvements through selective breeding are needed to encourage commercialization. To identify promising switchgrass germplasm for future breeding efforts, we conducted multisite and multitrait genomic prediction with a diversity panel of 630 genotypes from 4 switchgrass subpopulations (Gulf, Midwest, Coastal, and Texas), which were measured for spaced plant biomass yield across 10 sites. Our study focused on the use of genomic prediction to share information among traits and environments. Specifically, we evaluated the predictive ability of cross-validation (CV) schemes using only genetic data and the training set (cross-validation 1: CV1), a subset of the sites (cross-validation 2: CV2), and/or with 2 yield surrogates (flowering time and fall plant height). We found that genotype-by-environment interactions were largely due to the north–south distribution of sites. The genetic correlations between the yield surrogates and the biomass yield were generally positive (mean height r = 0.85; mean flowering time r = 0.45) and did not vary due to subpopulation or growing region (North, Middle, or South). Genomic prediction models had CV predictive abilities of –0.02 for individuals using only genetic data (CV1), but 0.55, 0.69, 0.76, 0.81, and 0.84 for individuals with biomass performance data from 1, 2, 3, 4, and 5 sites included in the training data (CV2), respectively. To simulate a resource-limited breeding program, we determined the predictive ability of models provided with the following: 1 site observation of flowering time (0.39); 1 site observation of flowering time and fall height (0.51); 1 site observation of fall height (0.52); 1 site observation of biomass (0.55); and 5 site observations of biomass yield (0.84). The ability to share information at a regional scale is very encouraging, but further research is required to accurately translate spaced plant biomass to commercial-scale sward biomass performance.

09 BIOMASS FUELS↗

DOE OSTI2023

An finite element analysis surrogate model with boundary oriented graph embedding approach for rapid design

Abstract In this work, we present a boundary oriented graph embedding (BOGE) approach for the graph neural network to assist in rapid design and digital prototyping. The cantilever beam problem has been solved as an example to validate its potential of providing physical field results and optimized designs using only 10 ms. Providing shortcuts for both boundary elements and local neighbor elements, the BOGE approach can embed unstructured mesh elements into the graph and performs an efficient regression on large-scale triangular-mesh-based finite element analysis (FEA) results, which cannot be realized by other machine-learning-based surrogate methods. It has the potential to serve as a surrogate model for other boundary value problems. Focusing on the cantilever beam problem, the BOGE approach with 3-layer DeepGCN model achieves the regression with mean square error (MSE) of 0.011 706 (2.41% mean absolute percentage error) for stress field prediction and 0.002 735 MSE (with 1.58% elements having error larger than 0.01) for topological optimization. The overall concept of the BOGE approach paves the way for a general and efficient deep-learning-based FEA simulator that will benefit both industry and Computer Aided Design (CAD) design-related areas.

42 ENGINEERING↗

DOE OSTI2020

Probabilistic neural networks for fluid flow surrogate modeling and data recovery

We consider the use of probabilistic neural networks for fluid flow surrogate modeling and data recovery. This framework is constructed by assuming that the target variables are sampled from a Gaussian distribution conditioned on the inputs. Consequently, the overall formulation sets up a procedure to predict the hyperparameters of this distribution which are then used to compute an objective function given training data. We demonstrate that this framework has the ability to provide for prediction confidence intervals based on the assumption of a probabilistic posterior, given an appropriate model architecture and adequate training data. The applicability of the present framework to cases with noisy measurements and limited observations is also assessed. To demonstrate the capabilities of this framework, we consider canonical regression problems of fluid dynamics from the viewpoint of reduced-order modeling and spatial data recovery for four canonical data sets. The examples considered in this study arise from (i) the shallow-water equations, (ii) a two-dimensional cylinder flow, (iii) the wake of a NACA0012 airfoil with a Gurney flap, and (iv) the NOAA sea surface temperature data set. Furthermore, the present results indicate that the probabilistic neural network not only produces a machine-learning-based fluid flow surrogate model but also systematically quantifies the uncertainty therein to assist with model interpretability.

42 ENGINEERING↗

DOE OSTI2024

Data-Driven Invertible Neural Surrogates of Atmospheric Transmission

We present Data-Driven Invertible Neural Surrogates of Atmospheric transmission, or DINSAT. DINSAT is a novel framework for inferring an atmospheric transmission profile from a spectral scene. This framework leverages a lightweight, physics-based simulator that is automatically tuned -- by virtue of autodifferentiation and differentiable programming -- to construct a surrogate atmospheric profile to model the observed data. The framework has utility in (i) performing atmospheric correction, (ii) recasting spectral data between various modalities (e.g. radiance and reflectance at the surface and at the sensor), and (iii) inferring atmospheric transmission profiles, such as absorbing bands and their relative magnitudes. We demonstrate the utility of these methods by performing a canonical atmospheric correction task for the purposes of further analysis - in this case, target detection within a scene.

Koch, James V.↗

DOE OSTI2024

Surrogate Distributed Radiological Sources—Part II: Aerial Measurement Campaign

In this second part of a multipaper series, we present results from outdoor aerial measurements of surrogate distributed gamma-ray sources. Here we detail the design, manufacture, and testing of 300 individual ~7 mCi Cu-64 sealed sources at the Washington State University (WSU) research reactor and their deployment in various source patterns (each comprising up to 100 point sources) during the aerial measurement campaign. We show the results of two such measurements, in which approximate source shapes and qualitative source intensities can be seen from the count rate versus position plots, even without performing reconstructions. We also detail our efforts in ground-truthing the deployed sources and comparing measured gamma-ray data to model predictions. In particular, we compare measured versus expected count data using the Poisson deviance formalism of Part I to evaluate whether the fielded surrogate point-source arrays “look like” their truly continuous distributed source analogs. More generally, we find that the point-source array technique provides high source placement accuracy, relative ease of quantifying the true source configuration, scalability to source dimensions of ≲100 m, ease of reconfiguration and removal, and relatively low dose to personnel. Finally, we consider potential improvements and generalizations of the point-source array technique for future measurement campaigns.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2026

Surrogate Distributed Radiological Sources—Part III: Quantitative Distributed Source Reconstructions

In this third part of a multi-paper series, we present quantitative image reconstruction results from aerial measurements of eight different surrogate distributed gamma-ray sources on flat terrain. Here, we show that our quantitative imaging methods can accurately reconstruct the expected shapes, and, after appropriate calibration, the absolute activity of the distributed sources. We conduct several studies of imaging performance versus various measurement and reconstruction parameters, including detector altitude and raster pass spacing, data and modeling fidelity, and regularization type and strength. The imaging quality performance is quantified using various quantitative image quality metrics. Our results confirm the utility of point source arrays as surrogates for truly distributed radiological sources, and advance the quantitative capabilities of Scene Data Fusion gamma-ray imaging methods.

Airborne survey↗

DOE OSTI2022

Propagating Parameter Uncertainty in Power System Nonlinear Dynamic Simulations Using a Koopman Operator-Based Surrogate Model

In this work, we propose a Koopman operator-based surrogate model for propagating parameter uncertainties in power system nonlinear dynamic simulations. First, we augment a priori known state-space model by reformulating parameters deemed uncertain as pseudo-state variables. Then, we apply the Koopman operator theory to the resulting state-space model and obtain a linear dynamical system model. This transformation allows us to analyze the evolution of the system dynamics through its Koopman eigenfunctions, eigenvalues, and modes. Of particular importance for this letter, the obtained linear dynamical system is a surrogate that enables the evaluation of parameter uncertainties by simply perturbing the initial conditions of the Koopman eigenfunctions associated with the pseudo-state variables. Simulations carried out on the New England test system reveal the excellent performance of the proposed method in terms of accuracy and computational efficiency.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2025

Micromechanical Surrogate Machine Learning Model for Creep Deformation Modeling

Process variability during the manufacture of gas turbine engine hot section components can significantly affect the material’s resulting microstructure. In casting, for instance, geometric variation within a component (thin sections versus thick sections, radial location) influences cooling rates and the resulting grain size. The high temperature creep response is known to be sensitive to grain size owing to a diffusional creep mechanism which occurs more readily along grain boundaries. Microstructural variation correspondingly drives mechanical behavior which propagates into component scale performance uncertainty. These factors are essential when planning inspection, maintenance, and repair strategies within a reliability framework. These benefits provide opportunities to increase overall energy efficiency through refined margins. Critically, there is an opportunity to bolster existing data-driven reliability models using physics-driven process-structure-property relations. Here we present recent work establishing a framework for evaluating the probabilistic creep performance of high-temperature materials. A novel microstructure-sensitive crystal plasticity finite element model is established that captures both grain boundary and crystallographic deformation effects. The computationally expensive physics model is calibrated using a statistical approach and this high-fidelity model is subsequently used to train a computationally efficient machine learning surrogate model. The surrogate model is essential for sampling a large ensemble of simulated structure-property pair results. The ensemble data are then mined to extract salient trends to be incorporated into a microstructure-sensitive reliability model. The proposed approach represents a novel way to capture microstructure-sensitive trends from physics-based models within a modern reliability framework.

Fernandez-Zelaia, Patxi [ORNL]↗

DOE OSTI2024

Material Model Parameters Optimization in Liquid Mercury Target Dynamics Simulation With Machine Learning Surrogates

A pulsed spallation target is subjected to very short (∼0.7μs) but intense loads (23.3 kJ) from repeated proton pulses, which knock away neutrons from the mercury atoms’ nuclei for a wide range application in physics, engineering, medicine, petroleum exploration, biology, chemistry, etc. The effect of this pulsed loading on the stainless-steel target module which contains the flowing mercury target material is difficult to predict not only due to its short but intense explosive-like physical reaction, but also the nonlinear material behavior of the liquid mercury in the structure. Injecting small helium bubbles in the mercury has been an efficient method of mitigating the pressure wave at high power level stage. However, prediction of the resultant loading on the target is more difficult when helium gas is intentionally injected into the mercury. A 2-phase material model that incorporates the Rayleigh-Plesset (R-P) model is expected to address this complex multi-physics dynamics problem by including the bubble dynamics in the liquid mercury. A parameter sensitivity study was firstly employed to understand their impact on the simulation strains. The investigated parameters included E, μ, γ, σ, n, VFgas, and gas cumulative volume curve control parameters a and b. Verification and validation results from sparse polynomial expansions (SPE) method and directional Gaussian smoothing (DGS) optimization show that the surrogate model had training error of ∼7% and validation error of ∼15%, indicating that machine learning methods and surrogate models can help optimize the uncertain parameters in the complex 2-phase material model. This approach is expected to fill the knowledge gap between unknown liquid-gas mixture material model and measured vessel strain responses.

Lin, Lianshan↗

DOE OSTI2026

Towards Generalizable and Efficient Circuit Topology Design: A Graph-Transformer-based Surrogate Model with Curriculum Learning

Unlike circuit parameter and sizing optimizations, the automated design of analog circuit topologies poses significant challenges for learning-based approaches. One challenge arises from the combinatorial growth of the topology space with circuit size, which limits the topology optimization efficiency. Moreover, traditional circuit evaluation methods are time-consuming, while the presence of data discontinuity in the topology space makes the accurate prediction of circuit performance exceptionally difficult for unseen topologies. To tackle these challenges, we design a novel Graph-Transformer-based Network (GTN) as the surrogate model for circuit evaluation, offering a substantial acceleration in the speed of circuit topology optimization without sacrificing performance. Our GTN model architecture is designed to embed voltage changes in circuit loops and current flows in connected devices, enabling accurate performance predictions for circuits with unseen topologies. To address the cold start problem when scaling GTN to large-scale circuits, we further introduce a curriculum learning strategy that progressively trains GTN from small-scale to large-scale circuits. This approach enables the model to first learn fundamental physical principles from simpler topologies and gradually adapt to complex configurations, effectively bridging the circuit complexity gap and improving prediction accuracy. Taking the power converter circuit design as an experimental task, our GTN model significantly outperforms an analytical approach and baseline methods directly utilizing graph neural networks. Furthermore, GTN achieves less than 5% relative error and 196× speed-up compared with high-fidelity simulation. Notably, our GTN surrogate model empowers an automatic circuit design framework to discover circuits of comparable quality to those identified through high-fidelity simulation while reducing the time required by up to 98.2%. With curriculum learning, the enhanced GTN achieves a 51% improvement for performance prediction of large-scale circuits compared to the GTN model without this strategy. These advancements establish GTN as a scalable framework for automated analog circuit design across varying circuit complexity levels.

Lu, Haoshu [New Jersey Institute of Technology (NJ↗

DOE OSTI2026

wa-hls4ml: A Benchmark and Surrogate Models for hls4ml Resource and Latency Estimation

As machine learning (ML) is increasingly implemented in hardware to address real-time challenges in scientific applications, the development of advanced toolchains has significantly reduced the time required to iterate on various designs. These advancements have solved major obstacles, but also exposed new challenges. For example, processes that were not previously considered bottlenecks, such as hardware synthesis, are becoming limiting factors in the rapid iteration of designs. To mitigate these emerging constraints, multiple efforts have been undertaken to develop an ML-based surrogate model that estimates resource usage of ML accelerator architectures. We introduce wa-hls4ml, a benchmark for ML accelerator resource and latency estimation, and its corresponding initial dataset of over 680,000 fully connected and convolutional neural networks, all synthesized using hls4ml and targeting Xilinx FPGAs. The benchmark evaluates the performance of resource and latency predictors against several common ML model architectures, primarily originating from scientific domains, as exemplar models, and the average performance across a subset of the dataset. Additionally, we introduce GNN- and transformer-based surrogate models that predict latency and resources for ML accelerators. We present the architecture and performance of the models and find that the models generally predict latency and resources for the 75% percentile within several percent of the synthesized resources on the synthetic test dataset.

Hawks, Benjamin [Fermilab] (ORCID:0000000157000288↗

DOE OSTI2022

ROMNet: Neural-Network-Based Surrogates for Reduced-Order Model Dynamics

SAND2023-05829O ROMNet is a toolbox built on the Tensorflow library for training reduced-order, neural operator surrogate models. The software is used for training reduced order neural operator surrogate models for dynamical systems applications. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

SciDAC↗

DOE OSTI2024

soogo (Surrogate-based 0-th Order Global Optimization) [SWR-24-57]

Surrogate-based 0-th Order Global Optimization for black-box problems. This software is comprised of active learning algorithms based on surrogate models to solve black-box optimization problems and other scientific applications. See also: https://pypi.org/project/soogo/

da Silva Pereira, Weslley↗

DOE OSTI2024

SysCaps (Language Interfaces for Simulation Surrogates of Complex Systems) [SWR-24-97]

You've found the official code repository for the paper "SysCaps: Language Interfaces for Simulation Surrogates of Complex Systems," presented at the Foundation Models for Science: Progress, Opportunities, and Challenges workshop at NeurIPS 2024. Our paper conjectures that interfaces (both text templates as well as conversational) makes interacting with simulation surrogate models for complex systems more intuitive and accessible for both non-experts and experts. "System captions", or SysCaps, are text-based descriptions of systems based on information contained in simulation metadata. Our paper's goal is to train multimodal regression models that take text inputs (SysCaps) and timeseries inputs (exogenous system conditions such as hourly weather) and regress timeseries simulation outputs (e.g. hourly building energy consumption). The experiments in our paper with building and wind farm simulators, which can be reproduced using this codebase, aim to help us understand whether a) accurate regression in this setting is possible and b) if so, how well can we do it. Paper: https://arxiv.org/abs/2405.19653

Emami, Patrick↗

DOE OSTI2026

GP Cosmology Surrogate v1.0

GP Cosmology Surrogate is a Python library for building and training a generalized multi-output Gaussian process (GP) framework of @takhtaganov2021cosmic. In this approach, the surrogate is constructed sequentially, guided by a Bayesian optimization acquisition function that targets reduction of emulation error in the regions most consistent with the observational data. This adaptive design concentrates computational resources where they have the greatest impact on inference accuracy. The library supports efficient training for separable GP kernels, which allows the use of Kronecker algebra to handle high-dimensional input spaces and large numbers of correlated outputs. This makes it well suited for applications such as modeling cosmological power spectra, large-scale physical simulations, and multi-output hyperparameter tuning. By combining scalable multi-output GP modeling with data-driven adaptive sampling, GPsurrogate enables parameter inference and optimization with substantially fewer simulations than conventional space-filling designs.

Lukic, Zarija [Lawrence Berkeley National Laborato↗

DOE OSTI2024

Spatially Local Surrogate Modeling of Subgrid-Scale Effects in Idealized Atmospheric Flows: A Deep Learned Approach Using High-Resolution Simulation Data

Abstract We introduce a machine learned surrogate model from high-resolution simulation data to capture the subgrid-scale effects in dry, stratified atmospheric flows. We use deep neural networks (NNs) to model the spatially local state differences between a coarse-resolution simulation and a high-resolution simulation. The setup enables the capture of both dissipative and antidissipative effects in the state differences. The NN model is able to accurately capture the state differences in offline tests outside the training regime. In online tests intended for production use, the NN-coupled coarse simulation has higher accuracy over a significant period of time compared to the coarse-resolution simulation without any correction. We provide evidence of the capability of the NN model to accurately capture high-gradient regions in the flow field. With the accumulation of the errors, the NN-coupled simulation becomes computationally unstable after approximately 90 coarse simulation time steps. Insights gained from these surrogate models further pave the way for formulating stable, complex, physics-based spatially local NN models which are driven by traditional subgrid-scale turbulence closure models. Significance Statement Flows in the atmosphere are highly chaotic and turbulent, comprising flow structures of broad scales. For effective computational modeling of atmospheric flows, the effects of the small- and large-scale structures need to be captured by the simulations. Capturing the small-scale structures requires fine-resolution simulations. Even with the current state-of-the-art supercomputers, it can be prohibitively expensive to simulate these flows when computed for the entire earth over climate time scales. Thus, it is necessary to focus on the larger-scale structures using a coarse-resolution simulation while capturing the effects of the smaller-scale structures using some parameterization (approximation) scheme and incorporating it into the coarse-resolution simulation. We use machine learning to model the effects of the small-scale structures (subgrid-scale effects) in atmospheric flows. Data from a fine-resolution simulation is used to compute the missing subgrid-scale effects in coarse-resolution simulations. We then use machine learning models to approximate these differences between the coarse- and fine-resolution simulations. We see improved accuracy for the coarse-resolution simulations when corrected using these machine learned models.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

Assessment of an E10 gasoline surrogate: Qualitative and quantitative comparisons of in-cylinder spray morphology

A minimum-component gasoline fuel surrogate that captures both chemical and physical behaviors of a full-distillate fuel is needed for high-fidelity CFD simulations. This study evaluates gasoline spray characteristics in a direct-injection spark-ignition engine under motored operation. Two fuels are compared; PACE-20, which is a 9-component surrogate formulation of RD5-87, is compared with its target fuel RD5-87, which is a full-boiling range research grade E10 gasoline. The spray morphologies of both fuels are recorded for a centrally-located direct-injection 8-hole spray subject to intake air cross-flow during the early part of the intake stroke. High-speed imaging recorded scattered light of the side and axial projections of the liquid spray. Quantitative metrics were developed and employed to facilitate comparison of spray morphologies as well as to identify the transition in spray morphology due to flash boiling. This paper builds on a previous study of RD5-87 where coolant temperature (20°C–100°C), in-cylinder pressure (40–110 kPa), engine speed (650–1950 rpm), and injection pressure (60–180 bar) were systematically changed to span operating conditions with and without flash boiling. Images of the PACE-20 morphology are selected for a sub-set of operating conditions from the previous study where distinctive morphology changes occurred. Visual inspection of the images and quantitative metrics demonstrate that the PACE-20 spray morphology is equivalent to that of the RD5-87 in most cases. The exception was for changes in the ambient-gas pressure where the flash-boiling transition occurred at ∼5 kPa higher in-cylinder pressure for PACE-20. Three empirical metrics, Merging Index, Asymmetry, and Flash Index are proposed here and they were found to be useful both as quantitative comparisons of the fuel morphologies, and for identifying the transition in spray morphology due to flash boiling.

Kim, Namho↗