Machine learning methods for fission product identification from Bragg curves

Improved nuclear data from fission were identified as a nuclear-data gap during the Nuclear Data Roadmapping and Enhancement Workshop (NDREW) in 2018.¹ Although neutron-induced fission cross sections of major actinides (e.g., ²³⁵U, ²³⁸U, and ²³⁹Pu) have been studied for many years,^2–4 improved neutron-induced fission data for these and other isotopes of U, Pu, and Np at a wider range of incident neutron energies are still needed.¹ Fission product yield data and evaluations were also identified as a nuclear data need. This has prompted a review of the available fission product yield (FPY) data and fission models in an effort to modernize an upcoming evaluation by replacing the historic England and Rider⁵ fission model with a more complete model of the fission process.^6,7 The improvements to fission cross sections and FPYs will benefit many applications, including nuclear reactors, stockpile stewardship, and astrophysics.⁸ 

A collaborative effort was made to address these nuclear data needs using a time projection chamber (TPC) to provide precise measurements of neutron-induced fission for several major actinides. The Neutron Induced Fission Fragment Tracking Experiment (NIFFTE) collaboration built a dual-chamber time projection chamber, the fission-TPC,⁹ to make precision fission cross section measurements, and it has provided several new fission cross section measurements to date.^10–13 Recent work has been focused on extracting FPY data from these measurements as well.¹⁴ The aim of this work was to find a novel method to determine the fission product associated with a specific energy-loss profile (Bragg curve) extracted from fission-TPC data.

The use of machine learning (ML) in nuclear physics experimentation can provide improved sensitivity of current instrumentation and increased accuracy of the data while also decreasing the computation time for analysis and simulations.¹⁵ This work aims to provide improved sensitivity to the fission-TPC for future fission measurements by enabling the fission product classification based upon their energy-loss (-dE/dx) profiles. Other TPCs have successfully applied machine learning techniques for a variety of applications.^16–18 The work by Kuchera et al. used a convolutional neural network (CNN) to identify specific types of events from the active-target time projection chamber, which improved the data processing speed and accuracy when compared to conventional analysis and data selection criteria.¹⁶ Acciari et al. used a CNN on simulated data from MicroBooNE, a liquid argon TPC, to perform particle classification and rare event classification.^17,19 In addition, deep neural networks have successfully been applied to data from EXO-200 to reconstruct relevant data parameters (energy and position) from digitized waveforms.¹⁸ Machine learning has also been applied to Bragg curve spectroscopy for pulse-shape analysis.²⁰ Here, we present results from a CNN algorithm to perform elemental identification based on energy loss profiles from the fission-TPC.

In this work, the simulated data used for training, testing, and validation of the ML algorithm will be discussed along with their performance for classifying extracted −dE/dx curves. The structure of the algorithm and metrics used to assess its performance will be described in Sec. II. In Sec. III, the results from the algorithms trained on both light and heavy fission fragments will be presented. Future improvements to the algorithm as well as a discussion of the applications within the fission-TPC analysis framework are discussed in Sec. IV.

Understanding the structure of the data of interest is the first step to being able to apply machine learning to any problem. The type of data (i.e., 1D, 2D, and multiple source) guides the appropriate type of the algorithm for ML application. The fission-TPC and data will be described, followed by a description of the simulated datasets for training, testing, and validation of the ML algorithm. Finally, various metrics used to assess performance will be presented.

The complete details of the fission-TPC can be found in Ref. 9, but a brief description is provided here. The fission-TPC consists of two equivalent detector volumes separated by a central cathode, which also acts as the target holder. Each volume has an anode, positioned 54 mm from the central cathode, with 2976 hexagonal pads and a 2 mm pitch, as well as a MICRO-MEsh GAseous Structure (MICROMEGAS)²¹ above the pad plane for gas amplification. The drift chamber is filled with a mixture of 95% Ar:5% isobutane at 550 Torr²² and has a diameter of 150 mm. The fission-TPC is operated at the Los Alamos National Laboratory’s Neutron Science Center on the 90L flight path, which can provide fast neutrons from 0.1 to 100 MeV.²³ 

When a neutron interacts with the central target and a fission event occurs, the fission fragments enter the gas volumes and ionize the drift chamber gas, generating an image charge on the cathode that is used as a fast timing signal.²⁴ The resulting electron cloud drifts toward the anode and is multiplied by the MICROMEGAS and detected by the anode pad plane. These data, along with the pad plane signals, provide enough information for three-dimensional track reconstruction.^10,24

Through track reconstruction and fitting, various parameters, including track length and energy, are determined and can be used to separate protons, alphas, and recoiling ions from fission fragment signals. The reconstruction uses principal component analysis to determine the axes of the track based on the reconstructed charge cloud.¹⁰ Various requirements are placed on the reconstructed data prior to 2D and stopping force analysis,^10,13,14 including the track origination vertex point, number of tracks per event, minimum energy deposited, and angular emission of the track. The selection criteria ensure that the tracks come from the correct isotope (some fission-TPC targets contain multiple isotope regions¹⁰) and contain only binary fission events, ensuring data quality.

After the reconstruction, a dE/dx or Bragg curve profile can be created by projecting the measured energy loss per length onto the main axis. Because the properties of the Bragg curve depend on the atomic number, Z, its shape can be used to extract this information regarding the fission fragment.²⁵ Therefore, the Bragg curves from fission-TPC measurements could provide additional valuable FPY data.

At present, the only Bragg curve analysis available for fission-TPC data is the stopping force analysis, developed by Moore et al.¹⁴ This work aims to provide a streamlined approach to the Bragg-curve analysis in the fission-TPC that could be integrated into the current analysis procedures to extract elemental FPYs.

To facilitate the development of the machine learning algorithm, labeled data are needed for training, testing, and validation purposes. Labeled data for Bragg curve classification were created using the 2013 version of the Stopping and Range of Ions in Matter (SRIM) and TRansport of Ions in Matter (TRIM) simulation software.²⁶ TRIM calculates the interactions of energetic ions with other materials such as solid targets of gas volumes using Monte Carlo techniques.²⁶ 100 isotopes selected from 24 peak fission product yield elements from both light and heavy yield peaks from ²³⁵U(n, f) were selected and simulated through a single volume of fission-TPC drift gas. Light fragments from Br to As and heavy fragments from Cs to Sb were simulated. For each of the 100 total isotopes, 10 000 energy loss curves were generated. The fission fragment kinetic energy for each isotope was taken from the study by Baba et al.²⁷ The curves produced from TRIM simulations do not contain observed detector effects, such as resolution. Therefore, a smearing factor was applied to the TRIM outputs to match the measured resolution of the fission-TPC detector. To mimic the data structure that is generated by the fission-TPC data reconstruction and analysis, the Bragg curve data points were interpolated and rebinned into 96 bins, representing 50 mm of the drift gas volume. This step ensures the ML algorithm can be included into the established fission-TPC software framework.

Figures 1 and 2 show the median energy loss curves with respect to particle track length for the selected light and heavy fission fragment elements, respectively. These curves show the distribution of the inputs to the element classification algorithm, where each point is the median energy loss with the associated standard deviation plotted as the error bars. While several isotopes of each element were simulated, the energy loss of each should be dominated by the atomic number, Z, and be mostly independent of the neutron number. The charge states of the fission fragments in the fission-TPC are not known, but they could influence the extracted Bragg curves. However, this investigation was beyond the scope of this work.

The ResNet architecture adapted for the one-dimensional data was chosen for this work.²⁸ A convolutional neural network (CNN), specifically a VGG-16,²⁹ was found to be useful for particle classification for the active-target time projection chamber at Michigan State University.¹⁶ ResNet is a modern CNN, which has been shown to be an improvement over the VGG-16 in the computer vision literature, demonstrating a 28% relative improvement in object detection.²⁸  Table I gives a summary of the model architecture. The main portion of the architecture is 15 ResNet BasicBlocks, which, for this work, were defined as a sequence of 2 (BatchNorm1d, ReLU, Dropout, and Conv1dPadSame) groups followed by a maximum pooling layer.

The architecture resulted in 683 340 trainable parameters. The same architectures were used for both the light and heavy datasets. However, the model was trained separately for each of the datasets as they are easily separable after particle reconstruction. The simulated data were split for each algorithm using a 80:10:10 ratio for training, testing, and validation, respectively. The algorithm was trained for 200 epochs for both the light and heavy dataset. A k-fold cross-validation function was used to evaluate the performance of the algorithms. Cross entropy loss was used as this was a fully supervised classification problem. An ADAM optimizer, with the learning rate initially set to 1 × 10⁻³, was applied, where the learning rate was divided by ten every 50 epochs. Training was considered done after no decrease in the loss was noted after 50 epochs. Figure 3 shows the cross entropy as a function of epoch where the loss decreases exponentially with increasing epoch, with a large decrease occurring at 50 epochs.

The light and heavy fragment algorithms yielded promising results for this technique. Light fission fragments, from Br to As, can be easily differentiated from one another. From Fig. 1, most of the elements can be classified by comparing the maximum energy loss measured between the track lengths of 13 and 18 mm. Further along the track length, differentiating between particles becomes more challenging as the energy loss curves overlap with one another. Inspection of the energy loss curves shows that Nb, Rb, and Zr should be the most challenging fragments to differentiate in the light fragment dataset, but these are still accurately distinguished. The resultant accuracy for the light-fragment algorithm was 100%, as shown in detail in Fig. 4. The confusion matrix details the accuracy for each classification of the algorithm, which in this case is light-fission fragments. For all trained light elements, the algorithm was able to accurately identify the correct element. This may not actually be surprising since for many of the light-fragment energy loss curves, the peak energy loss can be differentiated by the naked eye, so it is expected that the classification accuracy is 100%.

The heavy fission fragments elements are more challenging to differentiate from one another. Figure 2 shows the energy-loss curves with respect to track length. Again, most of the classification could be performed using the measured energy loss between 12 and 17 mm, but accurate classifications require use of a larger portion of the track length for the heavy fragment elements than the light fragment elements. The prediction accuracy of the heavy fission fragment algorithm is 84.8%. This is due to misclassifications between several heavy fission fragments.

Misclassifications are likely to occur when there is significant overlap in the energy loss curves. Figure 5 details the true vs predicted labels from the algorithm for heavy fission fragments and can be used to determine where misclassifications are common. Be, Pr, La, and Ce contain the largest percentage error between the true and predicted label. 100 individual energy loss curves as a function of track length for Pr and Ce (Fig. 6) and Ba, La, and Ce (Fig. 7) are shown to demonstrate the similarities between the misclassified fragments. Both figures show a significant overlap in the energy loss curves, which is likely responsible for the classification behavior shown in Fig. 5.

The results of this work demonstrate that elemental classification of fission fragments in the fission-TPC can be achieved using a CNN optimized for 1D data. The classification accuracy could make this technique viable for use in assigning experimental data from the fission-TPC to provide further fission product yield information to improve upon the historic England and Rider compilation.⁵ 

A machine learning algorithm has been developed to classify energy loss vs track length data from the fission-TPC for the first time. Bragg curves were generated using SRIM/TRIM simulations of a single volume of the TPC.²⁶ The simulated data were used to train, test, and validate a machine learning algorithm, which used the ResNet architecture optimized for 1D data. Because light and heavy fission fragments are easily separated in fission-TPC data, these were treated separately in two separate algorithms. The results for the light-fission fragments were extremely accurate owing to a differentiation in the peak energy loss for different elements in the Bragg curve. The heavy fission fragments did not perform as well as the light-fission fragments did, with 85% classification accuracy, mainly due to overlap within their expected energy-loss curves. The main overlap occurred between Ba, La, Ce, and Pr. Based on these initial results, a machine learning algorithm for Bragg curve identification could be an effective analysis technique in the future.

As with most initial studies, there are several potential improvements to fully develop this type of analysis. While SRIM is currently the foremost used software used to understand the ion stopping power through various media, it is not able to fully capture the complexity of the fission fragment interactions in the target and detector gas, for example, secondary and tertiary nuclear reactions, nucleon evaporation, and charge exchange. In addition, known detector response effects from the fission-TPC were included in post-processing of the SRIM data. It is recognized by the authors that a Geant4³⁰ validated simulation of the fission-TPC would be preferred for the generation of labeled data, but this was being developed in parallel with this work, so it was not available at the time of this work. Other approaches may be looked into in the future that do not require fully labeled data, which are not presently available from current experiments. Progress with semi-supervised learning may enable the use of physical constraints to help guide the model training and could result in improved accuracy. For example, performing a simultaneous machine learning analysis of both fragments simultaneously, including basic conversation rules, could enhance the accuracy of the heavy fragment analysis and provide a more complete picture of fission events from the fission-TPC.

Future work on the development of a Bragg curve classification ML algorithm should include the use of fission-TPC simulation generated data along with modifications such that experimental data can be used. This would help to capture effects from fission fragment charge states in the algorithm as well. This work demonstrates that elemental classification is possible with machine learning techniques to progress the current capabilities of the NIFFTE fission-TPC.

The authors would like to thank Dr. Aaron Luttman for his guidance at the beginning of this work, as well as the NIFFTE Collaboration for stimulating conversations related to the fission-TPC operation and data processing. L. Snyder was funded by U.S. Department of Energy through Lawrence Livermore National Laboratory, through Grant No. DE-AC52-07NA27344. Pacific Northwest National Laboratory is operated for the U.S. Department of Energy by Battelle, under Contract No. DE-AC05-76RL01830. This work was funded by the Office of Defense Nuclear Nonproliferation Research and Development within the U.S. Department of Energy’s National Nuclear Security Administration and the Laboratory Research and Development Program at Pacific Northwest National Laboratory. The views expressed here do not necessarily reflect the opinion of the United States Government, the United States Department of Energy, or the Pacific Northwest National Laboratory. Distribution A is cleared for public release. The distribution is unlimited (PNNL-SA-178019).

The authors have no conflicts to disclose.

S. M. Lyons: Conceptualization (lead); Formal analysis (equal); Methodology (lead); Validation (equal); Writing—original draft preparation (lead); Writing—review & editing (equal) C. G. Britt: Data curation (equal); Formal analysis (equal); Methodology (equal); Software (lead); Visualization (lead); Writing—original draft preparation (lead); Writing—review & editing (equal) L. S. Wood: Conceptualization (equal); Data curation (lead); Project administration (lead); Supervision (lead); Writing—original draft preparation (equal); Writing—review & editing (equal) D. L. Duke: funding acquisition (lead); Project administration (equal); Writing—review & editing (equal) B. G. Fulsom: Conceptualization (equal); Methodology (equal); Validation (equal); Writing—review & editing (equal) M. E. Moore: Conceptualization (equal); Validation (equal); Writing—review & editing (equal) L. Snyder: Funding acquisition (lead); Project administration (equal); Supervision (equal); Writing—review & editing (equal)

The data that support the findings of this study are available from the corresponding author upon reasonable request.