Surrogate Modeling for Fission Cross Sections using Artificial Neural Networks
This work explores the application of Artificial Neural Networks (ANNs) in surrogate modeling for fission cross sections and criticality studies within the nuclear domain. Leveraging past simulations and data-driven ML techniques, the goal is to reduce the costs of uncertainty quantification, identify key regions of data uncertainty, and inform future targeted measurements. The use of Dense Feed-Forward Networks and training on laptop CPUs with open-source software demonstrates the potential for accelerated computation. Critical benchmarks such as Godiva, Jezebel, and PU_MET_FAST_036 are modeled, with the task being to emulate ARDRA using ML models trained on the collected data.
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Surrogate Modeling for Fission Cross Sections and Criticality Studies using Artificial Neural Networks (ANNs) Christian Brazell Texas A&M University, LLNL With Kay Kolos & Andrew Ratkiewicz Jan 29, 2021 LLNL-PRES-813688 This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract DE-AC52-07NA27344. Lawrence Livermore National Security, LLC
Overview Motivation ML Approach Results Takeaways and areas for future work 2 LLNL-PRES-813688
Motivation Uncertainty in nuclear data yields uncertainty in nuclear data applications Current UQ/Sensitivity Studies require thousands of full simulations this is an expensive procedure My goal here is to develop a data-driven ML surrogate for ARDRA (deterministic neutron transport code) Reduce costs of UQ Identify key regions of uncertainty in data Inform future targeted measurements 3 LLNL-PRES-813688
Artificial Neural Networks (ANNs) can leverage past simulations to achieve these goals. Dense Feed-Forward Networks model highly non- linear functions of as a series of matrix multiplications with a twist Interjected element-wise nonlinear functions warp the manifold onto which data is projected Because the surrogate model is built on linear operations, GPUs can be used to accelerate training and computation All the ANNs in this work were trained on a laptop CPU using opensource software (Python, TensorFlow 2.0) 4 LLNL-PRES-813688
I have applied ML to simulations of nuclear criticality experiments. Three critical benchmarks are modeled: Godiva is a critical sphere of uranium Jezebel is a critical sphere of plutonium PU_MET_FAST_036 is critical reflected sphere of plutonium The nuclear data of interest are fission CXs Realizations sampled from covariance matrices Application of interest is keff Computed for each realization using ARDRA The task now is to emulate ARDRA with a ML model by training on this data. 5 LLNL-PRES-813688
A Feed-Forward Neural Network can map the CX data to keff for Godiva. The 95-bin U-235 fission CX is mapped directly to keff with a series of fully connected layers We now train on 20,000 training samples (each sample is a CX realization and its corresponding keff) 6 LLNL-PRES-813688
The results show a high-fidelity surrogate model for the Godiva experiment. Evaluating the model on a test set shows promising results. Results: Mean Squared Error = 9.1E-10 Mean Absolute Error = 2.4E-05 (2.4 pcm) Most of the uncertainty comes from under-represented regions in the training set 7 LLNL-PRES-813688
This model has serious limitations. It only models the relationship between U-235 fission and keff. It only works for the specific binning structure used in the training/test set. It is reliable only within the domain of the training input space, i.e. within a Gaussian distribution of the real CX. It is specific to Godiva and cannot accurately predict keff for other criticality benchmarks. THE GOOD NEWS: these limitations are all addressable! My next step was to build a hybrid model will work on multiple benchmarks. 8 LLNL-PRES-813688
A hybrid model can learn the neutronics of multiple benchmarks. An ANN that can compute keff for various geometries is shown in the graph. The left branch of this graph takes the CX as input. The right branch takes a class label as input, denoting the geometry of the sample. The ANN learns to represent the relationship between CX, geometry, and the neutronics of the system. In this problem, the Pu-239 fission CX was considered for Jezebel and PU_MET_FAST_036. 9 LLNL-PRES-813688
The hybrid ML model was able to learn two distinct representations of keff. The ML model computed keff with MSE=4.57E-07 The two distinct peaks correspond to the two geometries in the dataset. A significant portion of the error comes from outliers in the Jezebel data This could likely be combatted with pre-processing Class-wise L1 Normalization 10 LLNL-PRES-813688
This is an important proof-of-concept. ML models can learn complex relationships between reaction and geometric data, and how these relate to neutronics. 11 LLNL-PRES-813688
Conclusions Machine Learning is well suited to solve many extant nuclear data problems. We can leverage past simulations to build fast, accurate, and flexible surrogate models. These surrogate models can be trained to high levels of fidelity and can accommodate multiple criticality problems. By using these ML models, future computations can be done in a matter of seconds, rather than weeks! This reduces the cost of this research and accelerates the performance of nuclear data research. 12 LLNL-PRES-813688
Future Work Extend the hybrid model to account for more than two benchmarks Including benchmarks with similar distributions of keff Build a hybrid model to learn different reactions for the same benchmark Could be implemented using the existing hybrid architecture Reveal relative contribution of each CX to overall uncertainty in keff Apply the methodology to more complex geometries, more uncertain cross sections, and other quantities of interest Identify number of training samples needed to build an effective surrogate Bound the extrapolation errors of the model using ResNets 13 LLNL-PRES-813688
Acknowledgments Kay Kolos and Andrew Ratkiewicz Peter Brown Kelli Humbird 14 LLNL-PRES-813688
Questions? 15 LLNL-PRES-813688
This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. Disclaimer This document was prepared as an account of work sponsored by an agency of the United States government. Neither the United States government nor Lawrence Livermore National Security, LLC, nor any of their employees makes any warranty, expressed or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States government or Lawrence Livermore National Security, LLC. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States government or Lawrence Livermore National Security, LLC, and shall not be used for advertising or product endorsement purposes.
