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DOE OSTI2022

Uncertainty quantification in elastic constants of SiC f /SiC m tubular composites using global sensitivity analysis

Silicon carbide fiber and silicon carbide matrix (SiC f /SiC m ) tubes produced through the chemical vapor infiltration process have become a candidate cladding material in nuclear applications. The performance of this composite is influenced by many variables such as braiding angle, porosity, material properties, etc., which vary over a range of values due to the inherent fluctuations in the manufacturing process. In this study, the variability in elastic constants of SiC f /SiC m composite has been quantified through multiscale finite element (FE) simulations, variable screening, and high-fidelity surrogate modeling. The key variables dominantly affecting the elastic constants of SiC f /SiC m tubes were identified using global sensitivity analysis. A surrogate to the high-fidelity FE-based model was used in Monte Carlo simulations to generate a hundred thousand samples from which the uncertainty in elastic constants was assessed. It turned out that the coefficient of variation was less than 10%.

Materials Science↗

DOE OSTI2020

Criticality Control Overpack Fire Testing (Phase III)

This report will describe the one test conducted during phase III of the Pipe Overpack Container (POC) test campaign, present preliminary results from these tests, and discuss implications for the Criticality Control Overpack (CCO). The goal of this test was to see if aerosol surrogate material inside the Criticality Control Container (CCC) gets released when the drum lid of the CCO comes off during a thirty-minute long, fully-engulfing, fire test. As expected from POC tests conducted in Phase I and II of this test campaign, the CCO drum lid is ejected about one minute after the drum is exposed to fully-engulfing flames. The remaining pressure inside the drum is high enough to eject the top plywood dunnage a considerable distance from the drum. Subsequently, most of the bottom plywood dunnage supporting the CCC burns off during and after the fire. High pressure buildup inside the CCC and inside two primary containers holding the surrogate powder also results in damage to the filter media of the CCC and the filter-house, thread attachment of the primary canisters. No discernable release of surrogate powder material was detected from the two primary containers when pre- and post-test average mass were compared. However, when the average masses are corrected to account for possible uncertainties in mass measurements, error overlap does not preclude the possibility that some surrogate powder mass may have been lost from these primary canisters. Still, post-test conditions of the secondary canisters enclosing these two primary canisters suggest it is very unlikely this mass loss would have escaped into the CCC.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2022

Methods for Computing Physically Realistic Estimates of Electric Water Heater Demand Response Resource Suitable for Bulk Power System Planning Models

Demand response is commonly called on to reduce load during system peak times or to respond to contingency events. In future power systems with higher shares of wind and solar generation (which we describe together as variable generation [VG]), demand response could have more opportunities to provide energy shifting or operating reserve services. This report evaluates the ability of residential electric water heaters, both electric resistance water heaters (ERWHs) and heat pump water heaters (HPWHs), to provide such services starting from detailed whole-building energy models that realistically represent New England single family home stock. We use a parsimonious surrogate model to represent operational flexibility in a form suitable for linear and mixed integer programming. This enables relatively fast determination of aggregate contingency reserve resource, price-taking energy shifting outcomes, and in some cases the determination of aggregate models at the megawatt (MW) scale that can be directly included in large-scale grid models. After selecting modeling methods and parameters through various computational experiments, we find interquartile ranges of contingency reserve resource in ISO-NE for about 603,400 ERWHs of 45 MW - 69 MW for Claim10 (50 minute responses provided with 10 minutes of advanced notification) and 65 MW - 102 MW for Claim30 (30 minute responses provided with 30 minutes of advanced notification), and for about 619,000 HPWHs of 48 MW - 88 MW for Claim10 and 52 MW - 90 MW for Claim30. The overall reserve resource is up to 32% of total load for ERWHs providing Claim10 service, 47% for ERWHs providing Claim30 service, 93% for HPWHs providing Claim10 service, and 97% for HPWHs providing Claim30 service. More work is required to determine if HPWHs are inherently more suitable than ERWHs for providing contingency reserve or if these results reflect idiosyncrasies of the single family home stock model used in this study. The value of this contingency resource in a Near-term VG model of ISO-NE is $\$ 0.40$ to $\$1.20$ per water heater-year, and significantly larger, $\$ 3.80$ to $\$ 5.30$ per water heater-year in a Mid-term VG model of ISONE. Aggregating surrogate models to the MW-scale for energy shifting service is more challenging than for contingency service and we only present such results for ERWHs, because we were unable to determine satisfactory ways to deal with HPWHs' time-varying and path dependent operational characteristics. Individual surrogate models suitable for evaluating the energy shifting resource from both ERWHs and HPWHs are created, however, and dispatched against day-ahead prices from the Near-Term VG and Mid-Term VG models of ISO-NE. The individual surrogate models are able to access and potentially shift all 640 GWh of HPWH load and 1,547 GWh of ERWH load we modeled in two different single family home stock models. In contrast, the most effective model of aggregate ERWH shifting resource we created only captured 34.7% of the total ERWH load. Energy shifting affected by price-taking dispatch against modeled day-ahead energy prices produces per water heater year profits of $\$19.44$ - $\$22.93$ for individual HPWHs, $\$39.11$ - $\$40.54$ for individual ERWHs, and up to $\$4.00$ - $\$4.24$ for aggregated ERWHs, with the variations mainly due to grid conditions (more or less VG). When the supply-side response to these changes is accounted for, the per water heater year production cost savings for ISO-NE are $\$7.50$ to $\$17.70$ for the most effective set of endogenously dispatched aggregate ERWHs, $\$15.60$ to $\$15.70$ for individual ERWHs dispatched against the DA prices, and $\$10.70$ to $\$11.20$ for individual HPWHs dispatched against DA prices. Those ranges primarily represent the difference between Near-Term VG and Mid-Term VG grid conditions.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2022

Context-Aware Learning for Inverse Design in Photovoltaics

This document describes progress in the ARPA-E DIFFERENTIATE project titled “Context-Aware Learning for Inverse Design in Photovoltaics” during the period of May 2019 to May 2022. This project is being performed at Iowa State University, New York University, Stanford University, and National Renewable Energy Laboratory. The project aims to develop a new machine learning (ML) framework to significantly accelerate the design of organic microstructures for improved organic photovoltaic performance. In this project, we had developed an inverse design framework using Deep Learning called InvNets for generating microstructures with desired physics-driven properties. As a preliminary product, in Milestone 3, we demonstrated how InvNets show 20% improvement in the performance of the microstructures and over 100X speedup in the performance compared to traditional processes for physics-driven inverse design. Later, in Milestone 6, we demonstrated that InvNets work for more complex physics properties, specifically, generating microstructures for organic photovoltaic cells with desired current-voltage characteristics. Further, in Milestone 4, we explored the idea of using physics-aware surrogates for obtaining solutions of partial differential equations(PDE) called as DiffNets(now called as NeuFENets to avoid ambiguity of names). The connection between both frameworks is that DiffNet surrogates form the physics-aware surrogate in the InvNet framework. Finally in Milestone 8, we extend our framework for other physics domains. Specifically, we explore building geometry-aware NeuFENets by developing physics surrogates that exploit ideas from traditional immersed boundary finite element methods. With these updates, we are able to achieve all the Milestones.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Energy-efficient, Large-scale Molecular Dynamics Simulations via Hardware- and Algorithm-level Optimization

This work aims to develop a framework for energy-efficient computing that will enable molecular dynamics (MD) simulations of large-scale phenomena with atomic precision and simultaneously remove computational bottlenecks limiting the speed of MD simulations. We seek to implement such an approach through the development of surrogate models for the interatomic force calculation combined with the use of mixed numerical precision formats. For a model system of neutral atoms (only pairwise interactions), significant force calculation efficiency improvements were achieved, without detrimental effects on atomic structures or average energies, using single precision, by developing a surrogate model (deep neural network), and by quantizing this surrogate model. For a model system of charged atoms, the reciprocal-space calculation of electrostatic interactions was identified as the main bottleneck, and the development of a surrogate model should be pursued to achieve an estimated one-order-of-magnitude additional speedup.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2025

Computational materials reliability assessment of hydrogen fueled gas turbine power generation engines

The use of blended fuel sources in land based gas turbine engines drives variations in the resulting operational profile (temperatures and pressures) which can impact engine reliability. Furthermore, variability in the manufacture of components affects the resulting microstructure which directly impacts material performance and reliability. Currently, data-driven models are typically used for maintaining and inspecting fleets of engines. Without explicitly capturing material and operational sources of variability conservatism must be used in developing component-level reliability models. Therefore, there exists an opportunity to use information from materials-scale physics models to better inform reliability modeling and reduce conservatism; the impact is more cost-efficient operation and maintenance of current and future fleets. Specifically, this work establishes a computational framework for evaluating the probabilistic high temperature creep performance of hot-section Ni-based superalloys where uncertainty comes from both microstructural and operational variability. A novel high-fidelity physics model which phenomenologically captures grain-boundary sensitive phenomena has been established. A probabilistic calibration procedure was used to calibrate the model and capture uncertainty in the parameterized model coefficients. A design of experiments methodology was established for identifying informative microstructural digital representations for suitable for forward model evaluation. Results show that training a machine-learning surrogate using this design criteria outperforms random selection of microstructural representations. Finally, two surrogate models were developed: (1) a deterministic surrogate model which predicts the local field response given microstructure, constitutive model parameters, and operating conditions (stress, temperature) and (2) a probabilistic model, where uncertainty comes from constitutive law uncertainty, built using denoising diffusion probabilistic models which samples responses given (1) microstructure and (2) operating conditions. These surrogate models enable partner Siemens Energy to rapidly perform UQ analysis specific to creep deformation across a range of microstructures and operating conditions. The impact is that these ML and physics codes can be used to establish more advanced reliability models for the inspection, servicing, and maintenance of land based gas turbine engines.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Uncertainty quantification and sensitivity analysis of a nuclear thermal propulsion reactor startup sequence

The research presented in this article describes progress in applying stochastic methods, uncertainty quantification, parametric studies, and variance-based sensitivity analysis (also known as Sobol sensitivity analysis) to a full-core model of a nuclear thermal propulsion (NTP) system simulated via the radiation transport code Griffin to simulate neutronics. Our goal is to develop a reduced-order (surrogate) model that can be rapidly sampled with perturbations to multiple input parameters. In this NTP system, reactivity and power feedback affect the rotation of control drums (CDs), which is itself controlled by a hybrid proportional-integral-derivative (PID) controller actuated by the power demand and reactivity feedback from the numerical model. This model uses reactor kinetic feedback (mean generation time [Λ] and effective delayed neutron fraction [ β eff ] from a transient Griffin simulation executed via Griffin’s improved quasi-static solver to provide the kinetic parameters) as inputs to functions that control the CD rotation angle. By investigating numerous stochastic approaches, we developed a dual-purpose surrogate model of the NTP system, using polynomial regression in the Multiphysics Object-Oriented Simulation Environment (MOOSE) Stochastic Tools Module (STM). The trained model can be rapidly sampled while simultaneously perturbing various input parameters, such as coefficients on the PID control or temperature (directly affecting the neutron cross section). The surrogate model delivers accurate (within 5%) results at speeds orders of magnitude faster (minutes, not days of computational time) than the base model. Once the surrogate model has been trained, distributions of the uncertain parameters can be changed at will to investigate the effects of perturbing multiple inputs as well as the effects of these inputs on the model output. For example, coefficients used in the PID control system may vary due to some type of physical interference, or uncertainty may exist in the temperature of the neutron cross sections in various regions of the reactor. A distribution can be placed on these parameters, and operational boundaries can be determined. The goal of this work is to support development of an advanced control system for operating CDs in a functioning NTP system. This work is a scoping study of the MOOSE STM.

21 - SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLAN↗

DOE OSTI2022

Computational Workflow for Accelerated Molecular Design Using Quantum Chemical Simulations and Deep Learning Models

Efficient methods for searching the chemical space of molecular compounds are needed to automate and accelerate the design of new functional molecules such as pharmaceuticals. Given the high cost in both resources and time for experimental efforts, computational approaches play a key role in guiding the selection of promising molecules for further investigation. Here, we construct a workflow to accelerate design by combining approximate quantum chemical methods [i.e. density-functional tight-binding (DFTB)], a graph convolutional neural network (GCNN) surrogate model for chemical property prediction, and a masked language model (MLM) for molecule generation. Property data from the DFTB calculations are used to train the surrogate model; the surrogate model is used to score candidates generated by the MLM. The surrogate reduces computation time by orders of magnitude compared to the DFTB calculations, enabling an increased search of chemical space. Furthermore, the MLM generates a diverse set of chemical modifications based on pre-training from a large compound library. We utilize the workflow to search for near-infrared photoactive molecules by minimizing the predicted HOMO-LUMO gap as the target property. Our results show that the workflow can generate optimized molecules outside of the original training set, which suggests that iterations of the workflow could be useful for searching vast chemical spaces in a wide range of design problems.

Blanchard, Andrew↗

DOE OSTI2023

Adaptive Data-Driven Model Predictive Control for Heat Pipe Microreactors

To establish a technical basis for self-regulating microreactors, a model predictive control (MPC) system is investigated to proactively respond to anomalies and disturbances in anticipation of potential deviations from operating setpoints. Due to the difficulty of developing a physics-based surrogate model that can accurately match plant data in various operating conditions, machine learning algorithms are used in MPC, which allow for learning from both simulation and operation data, thus efficiently describing the targeted transient with arbitrary accuracy. However, one of the biggest concerns in applying ML algorithms like artificial neural networks (ANNs) is that the predictive capabilities of ANN are limited by training data. If there are gaps between the training and target domain, the accuracy of an ANN can degrade significantly when it is used to predict unseen data. To improve the predictive capability of ANN and enable a confident use of data-driven MPCs outside the training data, this study proposes an adaptive data-driven MPC framework. The system will monitor the discrepancy between plant responses and surrogate predictions, fine-tune the ANN-based surrogate when a large discrepancy is detected, and continue MPC operation with updated surrogates. The framework is demonstrated on a point kinetic model for microreactors. The hyperparameters of the update strategy, including layers to update, error thresholds, learning rate discount, and number of data points used for fine-tuning, are optimized so the simulated microreactor is able to follow changes in setpoint with the smallest of deviations.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2023

Adaptable Data Driven Model Predictive Control for Heat Pipe Microreactors

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2024

Rapid Inverse Parameter Inference Using Physics-Informed Neural Network

As Li-ion batteries become more essential in today's economy, tools need to be developed to accurately and rapidly diagnose a battery's internal state-of-health. Using a Li-ion battery's (high-rate) voltage response, it is proposed to determine a battery's internal state through Bayesian calibration. However, Bayesian calibration is notoriously slow and requires thousands of model runs. To accelerate parameter inference using Bayesian calibration, a surrogate model is developed to replace the underlying physics-based Li-ion model. Developing a surrogate model for rapid Bayesian calibration analysis is discussed for both the single particle model (SPM) and the pseudo two-dimensional (P2D) model. Surrogate models are constructed using physics-informed neural networks (PINNs) that encode the influence of internal properties on observed voltage responses. In practice, a neural network can be trained by: 1) using simulation results of the physics-based model (i.e., a data-loss approach); 2) using the residuals of the governing equations themselves (i.e., a physics-loss approach); or 3) using a combination of simulation results and governing equation residuals. In the present work, PINNs are developed using a variety of training losses and neural network architectures. In this analysis, it is shown that a PINN surrogate model can be reliably trained with only physics-informed loss. However, using a coupled data-informed and physics-loss approach produced the most accurate PINNs.

Bayesian calibration↗

DOE OSTI2025

MOOSE ProbML: Parallelizable Probabilistic Machine Learning and Uncertainty Quantification Capabilities

The Multiphysics Object Oriented Simulation Environment (MOOSE) is a widely used open- source finite element software for performing multiphysics multiscale simulations in a massively parallel fashion. Recently, the computational team at Idaho National Laboratory (INL) has implemented Probabilistic Machine Learning (ProbML) capabilities in MOOSE—in a parallelized fashion—and enable active learning with large-scale computational models for tasks such as surrogate model development, scale bridging, forward/inverse uncertainty quantification (UQ), Bayesian optimization, etc. This presentation summarizes these developments in MOOSE along with demonstrations on several real applications relevant to nuclear energy. At the fundamental level, samplers like Monte Carlo/Latin Hypercube, variance reduction, parallelized Markov Chain Monte Carlo (MCMC) support uncertainty propagation in both forward and inverse settings. These samplers can be integrated with the Gaussian processes (GP) suite in MOOSE, which offer several variants like scalar GPs, multi-output GPs, and deep GPs, to enable active learning. These GPs can be tuned using gradient-based optimization methods like Adam and its variants or gradient-free methods like the elliptical slice sampler (a variant of MCMC adept under Gaussian settings) for more complex covariance kernels or likelihoods whose gradient computations can be cumbersome. A variety of batch acquisition functions permit parallelized evaluation of the computational model and support different learning objectives with high efficiency like Bayesian inference, global surrogate development, optimization, etc. Furthermore, libtorch integration supports training, evaluation, and re-training of neural networks and other complex machine learning models in active learning settings. The impacts of these developments are shown on several real applications: (1) nuclear fuel inverse UQ and model inadequacy assessment using the Kennedy O’Hagan framework; (2) uncertainty aware surrogate modeling for additive manufacturing to predict field quantities; (3) nuclear reactor rare events analysis; and (4) complex fluid flow prediction using a global surrogate with quantified prediction uncertainty. Finally, the outlook of MOOSE ProbML is discussed for both outer-loop and inner-loop computations in the broad view to accelerate fuels and materials qualification, address gaps in knowledge and data, and assess new reactor/fuel systems.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2023

Cerium oxide impact on fresh and hardened properties of cementitious materials

Cements used in global nuclear waste treatment, storage, and disposal require thorough testing of fresh and cured properties to demonstrate regulatory compliance. Using actual radioactive wastes is often cost-prohibitive during early scoping tests necessitating the use of non-radiological surrogates. Cerium (Ce) is often used as a surrogate for actinides uranium (U) and plutonium (Pu) in spent nuclear fuel, yet few studies have explored how Ce impacts the properties used to qualify a cement for use. Here, this work compares the fresh and cured properties of three classes of cements – ordinary portland cements, ultra-high performance cement composites, and magnesium phosphate cements – each with and without ceria (CeO 2 ). Due to CeO 2 sorption of water (54 vol%) that effectively decreases the water available to hydrate and form binding cement phases, variations in key cement properties were detected that suggest surrogate CeO 2 –cementitious matrices may not be representative of matrix behaviors when using U and Pu sources.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Factorization Machine‐Based Active Learning for Functional Materials Design with Optimal Initial Data

The optimization of functional materials is important to enhance their properties, but their complex geometries pose great challenges to optimization. Data-driven algorithms efficiently navigate such complex design spaces by learning relationships between material structures and performance metrics to discover high-performance functional materials. Surrogate-based active learning, continually improving its surrogate model by iteratively including high-quality data points, has emerged as a cost-effective data-driven approach. Furthermore, it can be coupled with quantum computing to enhance optimization processes, especially when paired with a special form of surrogate model (i.e., quadratic unconstrained binary optimization), formulated by factorization machine (FM). However, current practices often overlook the variability in design space sizes when determining the initial data size for optimization. In this work, we investigate the optimal initial data sizes required for efficient convergence across various design space sizes. By employing averaged piecewise linear regression, we identify initiation points where convergence begins, highlighting the crucial role of employing adequate initial data in achieving efficient optimization. These results contribute to the efficient optimization of functional materials by ensuring faster convergence and reducing computational costs in FM-based active learning.

active learning↗

DOE OSTI2022

Dispersion-enhanced sequential batch sampling for adaptive contour estimation

In computer simulation and optimal design, sequential batch sampling offers an appealing way to iteratively stipulate optimal sampling points based upon existing selections and efficiently construct surrogate modeling. Nonetheless, the issue of near duplicates poses tremendous quandary for sequential learning. It refers to the situation that selected critical points cluster together in each sampling batch, which are individually but not collectively informative towards the optimal design. Near duplicates severely diminish the computational efficiency as they barely contribute extra information towards update of the surrogate. To address this issue, we impose a dispersion criterion on concurrent selection of sampling points, which essentially forces a sparse distribution of critical points in each batch, and demonstrate the effectiveness of this approach in adaptive contour estimation. Specifically, we adopt Gaussian process surrogate to emulate the simulator, acquire variance reduction of the critical region from new sampling points as a dispersion criterion, and combine it with the modified expected improvement (EI) function for critical batch selection. The critical region here is the proximity of the contour of interest. This proposed approach is vindicated in numerical examples of a two-dimensional four-branch function, a four-dimensional function with a disjoint contour of interest and a time-delay dynamic system.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Enhanced accuracy through ensembling of randomly initialized auto-regressive models for dynamical systems

Computational mechanics simulations using traditional finite element methods (FEM) require prohibitively expensive computational resources for real-time engineering applications, design optimization, and digital twin implementations. While machine learning (ML) surrogate models offer significant computational speedups, autoregressive ML models for time-dependent mechanical systems suffer from error accumulation that compromises long-term prediction reliability - a critical concern for engineering applications where accuracy over extended time horizons is essential for safety and performance assessments. Here, we propose a deep ensemble framework specifically designed to address this challenge in computational mechanics applications, where multiple ML surrogate models with random weight initializations are trained in parallel and their predictions aggregated during inference. This approach leverages statistical diversity to maximize information gain from a fixed set of training data and to mitigate error propagation, while maintaining the computational efficiency that makes ML surrogates attractive for engineering practice. We validate the framework on three representative problems spanning critical areas of computational mechanics: stress field evolution in heterogeneous microstructures under complex loading (relevant to advanced materials design and composite analysis), planetary-scale shallow water dynamics (applicable to environmental and geotechnical engineering), and Gray-Scott reaction-diffusion systems (relevant to mass transport and chemical process engineering). Across all test cases, the ensemble approach demonstrates consistent error reduction of 15-33% compared to individual models. The codes for this work are available on GitHub (https://github.com/Graham-Brady-Research-Group/AutoregressiveEnsemble_SpatioTemporal_Evolution).

autoregressive prediction↗

DOE OSTI2025

Sequence modeling of higher-order wave modes of quasi-circular, spinning, non-precessing binary black hole mergers

Higher-order gravitational wave modes from quasi-circular, spinning, non-precessing binary-black-hole (BBH) mergers encode rich information about the nonlinear dynamics of strong-field gravity. We present a transformer-based sequence-completion surrogate that, given an early-inspiral segment, forecasts the subsequent late inspiral, merger, and ringdown. The intended applications are (i) patching or completing expensive or interrupted numerical-relativity (NR) simulations and (ii) providing late-time cross-checks and rapid hybridization studies. The training set is built from the NRHybSur3dq8 surrogate, which provides spherical-harmonic modes up to $\ell$ ≤ 4 (excluding (4, 0) and (4,±1), and including (5, 5)) for mass ratios q ≤ 8, dimensionless spin components s$^{z}_{1,2}$ ϵ[–0.8, 0.8], and inclination angles θ ϵ [0, π]. Waveforms are supplied on the interval t ϵ [–5000M, –100 M) and the model autoregressively generates the plus and cross polarizations (h + , h x ) on t ϵ [–100 M, 130M]. Training on the Delta supercomputer with 16 NVIDIA A100 GPUs required ~15 h on more than 14 million hybrid waveforms. Evaluation on a held-out test set of 840,000 samples yields mean and median overlaps of 0.996 and 0.997, respectively, with respect to the surrogate ground truth.

black-hole merger↗

DOE OSTI2024

Efficient mapping between void shapes and stress fields using Deep Convolutional Neural Networks with sparse data

Establishing fast and accurate structure-to-property relationships is an important component in the design and discovery of advanced materials. Physics-based simulation models like the finite element method (FEM) are often used to predict deformation, stress, and strain fields as a function of material microstructure in material and structural systems. Such models may be computationally expensive and time intensive if the underlying physics of the system is complex. This limits their application to solve inverse design problems and identify structures that maximize performance. In such scenarios, surrogate models are employed to make the forward mapping computationally efficient to evaluate. However, the high dimensionality of the input microstructure and the output field of interest often renders such surrogate models inefficient, especially when dealing with sparse data. Deep convolutional neural network (CNN) based surrogate models have shown great promise in handling such high-dimensional problems. In this paper, a single ellipsoidal void structure under a uniaxial tensile load represented by a linear elastic, high-dimensional and expensive-to-query, FEM model. We consider two deep CNN architectures, a modified convolutional autoencoder framework with a fully connected bottleneck and a UNet CNN, and compare their accuracy in predicting the von Mises stress field for any given input void shape in the FEM model. Additionally, a sensitivity analysis study is performed using the two approaches, where the variation in the prediction accuracy on unseen test data is studied through numerical experiments by varying the number of training samples from 20 to 100.

surrogate modeling; convolutional neural networks;↗