Data-driven prediction of scaling and ignition of inertial confinement fusion experiments Open Access

Throughout the 50-year history of inertial confinement fusion (ICF) experiments^1–3 researchers have faced a significant challenge: how can data from complex and expensive experimental facilities inform predictions of future experiments? What are the uncertainties in those predictions? Making progress on these questions has been challenging since ICF datasets are sparse and difficult to diagnose, making pure data-driven approaches infeasible, while physics-based simulations often fail to predict experimental outcomes based on pre-shot information alone. We present a hybrid statistical approach that aims to combine information from high-yield experiments at the National Ignition Facility (NIF),^4–6 large-scale radiation hydrodynamics simulation studies,⁷ and statistical learning into a probabilistic prediction for the outcome of proposed designs.

Inertial confinement fusion research relies on large-scale radiation hydrodynamics simulations^8–14 for the design,^15–18 optimization,^19,20 and interpretation^21–24 of experiments. These simulations integrate a full suite of physics models^25,26 relevant to the evolution of ICF and high energy density physics (HEDP) experiments, allowing a complete prediction of the assembled plasma and diagnostic signals from the initial target design and drive parameters. Nevertheless, state-of-the art simulations are not truly predictive of individual ICF experiments: simulations will typically overpredict performance even with all the information available before a shot is fired. As a result, pre-shot predictions usually rely on expert-driven, ad hoc modifications that degrade the performance to reflect the expectations of the experimental team. This reliance on expert priors introduces biases that are difficult to quantify and remove from the design process, and is inherently limited to a handful of performance degradation mechanisms. Scaling to high-dimensional design studies, and integrating existing experimental data in a formal manner, remain significant challenges in ICF research.

We take a Bayesian model calibration approach that provides a principled framework to combine data from past experiments into a single statistical model that predicts the outcome of future shots. The approach infers probability distributions over unknown simulation inputs for each shot in the series and links them together into a common, jointly informed “variability” model that describes the statistical variations between shots at the NIF. By introducing simulations into the analysis, we explicitly include known physics in the analysis, allowing us to make efficient use of the available experimental data and to ensure that predictions are always physically correct and consistent. Taking a Bayesian approach ensures that all sources of uncertainty can be accounted for and propagated to quantities of interest in order to place rigorous uncertainty bounds on predictions.

Data-driven approaches like the one reported here are a potentially powerful tool in ICF research, high energy density, and plasma physics and are being investigated by several groups.^27,28 Statistical and machine learning²⁹ models, trained only on experimental data, have been used to predict the performance and sensitivity of ICF implosions^30–34 and to propose new experiments.³⁵ Bayesian methods have been used with relatively simple physics models to infer parameters in implosion experiments,^36–41 laser-driven opacity⁴² and equation-of-state^43,44 experiments, and others. For an introduction and review of current work, see a recent review by Knapp and Lewis.⁴⁵ Transfer learning⁴⁶ has been used to combine simulations and experiments into a single model which reliably describes data^47–49 but compromises the interpretation of the model inputs. In contrast to those works, our ICF models are designed to allow the use of very sparse NIF data and the best fidelity simulations possible while retaining the interpretability of the physics at work.^24,50,51

In this work, we describe our statistical approach and its application to the prediction of fusion ignition in recent NIF “Hybrid-E” experiments. We have used the model to perform a joint Bayesian analysis of 9 sub-ignition NIF shots, driven with 1.9 MJ of laser energy, and then to predict the onset of ignition in larger 2.05 MJ drive shots. We performed this analysis prior to any 2.05 MJ experiments, and can therefore use subsequent ignition shots to validate our predictions. We will describe our model calibration approach and the design decisions that motivated it, discuss the Bayesian postshot analysis of performance and variability in 1.9 MJ shots, and then present our predictive model for 2.05 MJ shots. Finally, we will discuss the uncertainties in our analysis and their impact on the predicted probability of ignition.

The Bayesian approach provides a framework to extract information from NIF shots, in the form of posterior distributions over uncertain parameters, and use it as prior information to make predictions for future shots. This process formalizes the ad hoc institutional knowledge currently used in pre-shot design and simulation work. The fundamental building block of the approach is the Bayesian inference of posterior distributions based on experimental data, which can be approached with standard methods but nevertheless faces practical challenges due to the nature of ICF data.²⁴ 

Constraining variations in performance across NIF shots is challenging due to the highly nonlinear onset of fusion reactions and their impact on the overall dynamics of the implosion, the large number of design and physics parameters, and the expense of experimental shots. As a result of these challenges typical NIF datasets are too sparse to constrain performance variability on their own (Fig. 1). We have solved this problem by framing our Bayesian inferences as a model calibration, allowing us to introduce a second constraint in the form of high-fidelity simulations. The simulations provide significant information on the nonlinearities of the response, allowing the experimental data to be used more efficiently to constrain only the most uncertain aspects of the implosion physics rather than known physical scaling results and correlations.

We select input calibration Eq. (4) for three main reasons. First, the calibration parameters $θ$ have a clear meaning (in the context of the simulation code), meaning that the calibration provides an interpretable explanation for the observed performance. Second, predictions from the calibrated model are always valid outputs of the simulation and therefore they will automatically obey known physical laws and correlations between observations. Third, the interpolation and extrapolation behavior of the calibrated model (i.e., as a function of x) is determined by the known physics of the problem, potentially modified by $θ$⁠, meaning that nonlinear behavior emerges in predictions even when experimental data are not sufficient to show it. The joint advantages of interpretability, consistency, and physics-based extrapolation are not available from the output calibration, making input calibration the clear choice for our purpose.

Our predictive model uses a series of Bayesian postshot procedures to independently calibrate capsule simulation inputs for each shot in an NIF experimental campaign. Each shot has its own inferred distribution of simulation inputs, which varies across the experimental campaign; we use these variations to constrain a second statistical model for the shot-to-shot variability for a given design. The combined variability and postshot models form a hierarchical model, which we represent as a Bayesian network in Fig. 2. The inferred shot-to-shot variations, which we call our variability model, can then be used to aid in the prediction of new shots by exposing simulations of the new design to the same (or suitably modified, see Sec. IV C) variations. In this manner, our first stage of analysis extracts information from existing shots through model calibration, which is then used to make informed predictions or extrapolations. The stages of analysis are described in more detail in Secs. III A–III C.

The posterior distribution Eq. (6) is the distribution of simulation inputs, which are consistent with the observed data. The analysis proceeds by stochastically sampling values of $θ$ from the posterior using Markov chain Monte Carlo (MCMC).^52,59 In principal, the MCMC algorithm can sample from arbitrary posterior distributions and can therefore support complex correlations between elements of $θ$⁠, as well as multiple peaks in probability, which arise when multiple values of $θ$ can produce a match to the data. These features of the MCMC approach are significant advantages when dealing with ICF data since the simulated outputs are highly correlated by the physics at work and the calibration problem tends to be underdetermined by the available diagnostic quantities.

The final practical challenge in applying our model calibration approach is the computational expense of the MCMC algorithm. MCMC generates samples iteratively by proposing values of $θ$ and accepting or rejecting according to Eq. (6), which in our case requires a radiation-hydrodynamics simulation. High-probability regions are repeatedly sampled by simulations with almost the same $θ$⁠, while low-probability regions require very long MCMC runs to reach. As a result, converged MCMC samples require millions of simulation runs performed in serial, a completely infeasible task with any realistic ICF simulation.

We solve this problem by pre-running a large number of simulations in parallel on a large high performance computing (HPC) resource^7,60–62 and using the resulting ensemble of input–output pairs to build a rapid interpolator or surrogate. The surrogate can then be used during MCMC inference to predict the simulation output very quickly, and by choosing a differentiable surrogate model, we can further improve performance using gradient accelerated MCMC sampling techniques.⁶³ Together, these two improvements allow a Bayesian calibration, which would be impossible without a surrogate, to be completed in a matter of minutes on a desktop computer. Our chosen method of surrogate modeling is through deep neural network (DNN) interpolation, which has several advantages over more traditional methods. We will describe this approach in detail in Sec. IV.

Sampling from the postshot and variability posteriors, Eqs. (6) and (8), is performed simultaneously by implementing the full Bayesian network shown in Fig. 2 using the Bayesian modeling library pymc.⁶⁵  We obtain samples of the variability parameters $μθ$ and $Σθ$ along with simulation inputs for each shot in the experimental campaign ${θi}$⁠. We have found that rapid convergence is possible if short, independent Bayesian postshot inferences are performed before attempting to tune the full problem.

Finally, we will comment on the approximations introduced to our shot-to-shot variability model. Although we have introduced a normal approximation for the variability distribution in Eq. (7), the inferred shot-to-shot input variations—obtained by integrating over MCMC samples $μθ$ and $Σθ$—are not constrained to be normal. The inferred distribution can in fact be quite complex; however, it should be noted that the normal approximation does have a smoothing effect on the variability posterior. This smoothing is important in the application to ICF since it makes the problem more numerically tractable when there are very few experiments; however, the normal approximation may need to be revisited for other problems where more data are available.

The Bayesian postshot procedure we have described generates a data-driven model for the shot-to-shot variations seen over a series of NIF experiments. Using this model, we may make a prediction for a future shot, for example, one at a new value of the independent variables $x=x∗$⁠, by propagating the shot-to-shot variation distribution through new simulations. This is achieved by evaluating the new simulations at a set of samples from the variability distribution generated during MCMC inference. This evaluation would be trivial if the desired $x∗$ was included in the original simulation study since the previous surrogate can be used; however, this is rarely the case in practice.

To make the propagation of variability samples through new simulations tractable, we require a new surrogate that emulates simulations of the proposed design. This second surrogate may be produced in the same way as the first, that is, by using millions of CPU-hours (and months of wall time) to run thousands of new simulations. While computationally feasible, we have found this approach to be incompatible with experimental timescales; the details of a shot are often confirmed only a week or less before a prediction is required, meaning that new surrogate models must be trained in a few days. To be useful for experimental planning we must reduce the number of simulations needed to create a new surrogate by several orders of magnitude.

We have shown that new surrogates, suitable for generating predictions for new designs, can be reliably trained on only 10–100 new simulations using a deep learning technique known as transfer learning.⁴⁶ Transfer learning uses the structure of a deep neural network to identify subsets of an existing model that can be updated, or retrained, using a new (but related) dataset. Applications in computer vision provide an intuitive example: a neural network can be trained to “understand” images on open-source data, extracting information that can be re-used to understand more specialized datasets like medical images. In an ICF context, these ideas have been used to update a simulation surrogate using small experimental^47,49 and synthetic datasets.⁴⁸ Here, we transfer learn from the previous design to the new one using a small set of new simulations.

While the transfer-learned surrogate typically has much lower accuracy than the source surrogate it is still sufficient for our prediction tasks. In the postshot analysis, where the surrogate is used to match observational data, we require a surrogate accuracy and precision comparable to the experimental uncertainties. For prediction, the surrogate is used to propagate the shot-to-shot variability model, which is very broad and quite uncertain (see Sec. IV C for a discussion), and so the surrogate accuracy requirements are correspondingly relaxed.

Recent high-yield experiments at the NIF have demonstrated significant heating by fusion alphas and fusion energy gain using the so-called Hybrid-E implosion design. Hybrid-E implosions combine advances in target design¹⁸ and capsule manufacturing quality with tuned laser drives to provide robust megajoule energy yields, often exceeding the laser energy required to drive the implosion.⁶⁶ 

Our data-driven predictive model for high-yield, 2.05 MJ drive Hybrid-E shots is informed by a series of sub-ignition experiments performed with 1.9 MJ of laser energy. The series consists of shot N210808, the first experiment to demonstrate a Lawson criteria greater than one, and a subsequent set of near repeats that aimed to test performance variability and sensitivity to key degradation mechanisms. These experiments, which we referred to as the “210808+R” campaign, are the largest run of experiments of similar design and provide a high-quality dataset for our data-driven variability model. We give a short summary of the shots in the 210808+R set in Table I 

We aim to calibrate a single capsule-only simulation model, performed with the radiation-hydrodynamics code HYDRA,⁸  across the 210808+R dataset. This requires that the calibrated inputs $θ$ span both the known design changes and the unknown drivers of variability. To define this parameter set we start with a nominal N210808 HYDRA simulation, derived from NIF drive tuning data and integrated hohlraum simulations, which are then modified with a set of parameters that define $θ$⁠. We have developed a set of nine input parameters that capture the expected variations and allow high-quality fits to all shots in the 210808+R series (discussed at length in Sec. III A). These parameters include modifications to the timing, energy, and peak power of the x-ray drive on the capsule (three parameters), a multiplier on the nominal fraction of x-ray energy in the gold emission M-band, $P1$ and time-dependent $P2$ drive asymmetries (three parameters), and compression degradation through a fall-line mix model and preheat of the DT fuel layer (two parameters). They define a 9-dimensional simulation input space $Θ$ which we sampled using an ensemble of 30 000 HYDRA simulations performed using approximately 20 × 10⁶ cpu-hours on the Trinity supercomputer at Los Alamos National Laboratory.⁶⁷ 

The HYDRA simulation ensemble consists of a set of simulation input–output pairs $(θ,ys(θ))$ in which the input values are selected through a combination of space-filling latin hypercube sampling and an adaptive scheme that aims to optimally sample the posterior distributions for shot N210808.^68, We use the resulting dataset to construct a fast emulator of the full simulated response $ys(θ)$⁠. We have found that deep neural networks (DNNs) provide a fast and reliable approach to emulate our simulations with the added benefit of differentiability and the opportunity to leverage new approaches like transfer learning.⁴⁶ In this work, we use the DJINN architecture,⁶⁹ which allows a high-quality surrogate model to be found by tuning a single hyperparameter. Our final DNN has six hidden layers with widths [11, 15, 23, 39, 71, 135], ReLU activations, and no dropout regularization, and predicts ten scalar output quantities. The average performance on both train and test datasets is excellent for all output features (Table II), and we have further confirmed that the prediction uncertainty (the standard deviation in the differences between predictions and ground truth) is comparable to or smaller than experimental uncertainties. This second check ensures that surrogate uncertainties do not overwhelm the experimental data during the Bayesian inference.

With a complete and verified set of MCMC samples, we can validate the physics in our Bayesian postshot analyses and variability models and also make extrapolated predictions for ignition-scale shots. These applications are discussed in Secs. IV A–IV C.

The Bayesian postshot attempts to match multiple experimental observables with strong physics-driven correlations between them. As a result of these complex target data, it is not guaranteed that a given simulation and choice of calibrated inputs $θ$ is capable of simultaneously matching the full set of observables for a given shot. We, therefore, begin our analysis by validating that the HYDRA simulations, combined with input parameters described previously, can successfully match the experimental data. We then move on to a discussion of the quality of the inferred shot-to-shot variability distribution.

The fit to experimental data is excellent across all shots in the 210808+R dataset for all of the output features of interest. Figure 3 compares experimental and posterior-predictive distributions and shows that they overlap within error bars with high likelihood. This level of high-quality match to multiple observables is far better than can be achieved by hand-tuning a small number of parameters.

The present Bayesian postshot also performs well on observables that were not explicitly fit by the MCMC algorithm. Figure 3 includes hold-out features (marked with a $†$ symbol in plot titles), which serve as an after-the-fact check against the MCMC procedure finding the “right answer for the wrong reason.” In some previous analyses, this check has found fits that reproduce target data well but failed to match or have very large posterior uncertainties on kept-out features. In the present analysis, we see encouraging agreement across all of the output features considered.

The variability model accurately reproduces the experimental shot-to-shot distributions. Figure 4(a) shows the predicted joint distribution of $4π$ DSR and $Ye$⁠, compared with the N210808+R dataset. The agreement is qualitatively very good; the calibrated simulations reproduce the strong linear correlation in the data and predict a strong peak in yield close to the experimental median. We further validate the $Ye$ distribution through a detailed comparison of the cumulative probabilities from the model and experiment (Fig. 5), which demonstrates that our model correctly reproduces the bulk of the empirical data distribution. The main discrepancy is in the predicted long tail at low performance, which is a consequence of our assumed normal distribution over simulation inputs and the very sparse nature of the NIF data.

The shot-to-shot variability model provides information about the drivers of performance variations through the inferred covariance over simulation inputs $Σθ$⁠. The diagonal elements of the covariance describe the degree to which different inputs vary from shot-to-shot, and the off diagonal elements describe physics-driven correlations. The absolute values of these entries are determined by the sensitivity of simulated outputs to each input, which complicates the interpretation of the covariance itself. Instead, we identify the most important contributions to the yield variation by “switching off” variations of specific inputs and quantifying the change in the predicted yield distribution. This is achieved by fixing the values of certain inputs at the distribution mean (for example) and conditioning the variability model on the fixed values; successively applying this approach to each set of simulation inputs allows us to compare the impact of variations over the experimentally relevant scales.

We find that the mix, which we define as the combination of fall-line mix and preheat, is the only degradation that, when removed, results in a noticeable reduction in shot-to-shot yield variability (Fig. 6). Other inputs are sufficiently correlated that removing one set in isolation is not enough to significantly change the predicted yield. Further analysis of the high-dimensional variability model is possible through dimensional reduction techniques or by linear projection; however, this detailed interpretation of the postshot variability model is beyond the scope of this work. Instead, we will proceed to discuss the use of the model to predict the outcome of future experiments.

Our approach predicts the outcome of future shots by propagating samples from the trained shot-to-shot variability model through simulations of the new design to predict the distributions of observables before experiments are performed. We have used this approach to extrapolate from the 1.9 MJ drive Hybrid-E experiments used to train the model to new 2.05 MJ drive experiments. In this section, we will present the predicted performance based on the 210808+R dataset, then use experiments performed with a 2.05 MJ drive to validate the model. Finally, we will quantify the uncertainty in our predictions due to the sparsity of both experimental and simulation datasets.

The first step of our predictive workflow is to generate a DNN surrogate of HYDRA simulations for the new shot design. To make this computationally tractable on a timescale useful to experiments we use transfer learning to re-train the initial DNN to the new task. In transfer learning, an existing DNN is updated for a new (but related) task by re-training a subset of the network layers using a small amount of new data. In this work, we have found that effective transfer learning can be achieved with only $∼100$ new simulations, resulting in a new surrogate in just a few hours of HPC time. With this very small number of simulations the transfer-learned 2.05 MJ surrogate model has lower performance than the original one (test $R2∼0.9$⁠); however, we have confirmed that prediction uncertainties are small compared to the variability model we aim to propagate. With this capability we can respond quickly to the demands of the experimental facility, potentially producing new predictions as critical decisions are made in the days prior to a high-value experiment.

The shot-to-shot variability distribution, propagated through our transfer-learned surrogate model for the 2.05 MJ design, predicts a significantly higher performance than with a 1.9 MJ drive and that 2.05 MJ drive experiments begin to access the robust compressive ignition regime [Fig. 4(b)]. The predicted distribution of yield and $4π$ DSR shifts upward along the ignition cliff (the negatively correlated region around 100 kJ to 1 MJ of yield) and begins to turn the corner into the positively correlated robust ignition regime.

We can quantify the increase in performance by integrating the predicted distributions into a probability of ignition for each design. For the analysis shown in Figs. 4(a) and 4(b), the ignition probability increases from $∼5%$ to $∼50%$ (we discuss the uncertainties in these probabilities later in this section). We present these metrics, along with several others, in Table III.

We may validate our predictions [Fig. 4(b)] by comparing them with subsequent NIF experiments performed with a 2.05 MJ drive (recall that no data with this drive were used to produce the prediction). Comparison with five NIF shots performed with the 2.05 MJ drive to date, including the first fusion experiments to ignite, shows excellent agreement with the prediction with three shots igniting and a median yield in excellent agreement with our predictions (Table III). While the comparison between 50% intervals from the prediction and model is less good, the estimate of percentiles from only five NIF shots is very uncertain, and so more NIF data will be required to properly validate the tails of our predicted distribution.

Finally, we can quantify the uncertainty in our predictions that arises due to the small datasets available. We investigate the impact of two uncertainty sources: first, surrogate prediction uncertainty arising due to the limited number of simulations available and, second, the sparsity of NIF data used to train the variability model. In both cases, we take an ensemble approach by training multiple models on different data realizations and treating the distribution of models as a measure of uncertainty. We have produced 50 different predictions with different DNN surrogates and experimental datasets (described below) and use the range of predictions to measure the uncertainty in our performance model.

We measure the impact of surrogate uncertainty by training 50 DNN surrogates using different test/train data splits, initial weights and biases, and seeds for random number generators. Since the DNN training process is typically non-convex, with many local minima, this procedure produces 50 distinct DNN surrogates with comparable performance on test and train data but different functional forms. It should be noted that while this procedure is commonly used for this purpose, the distribution of predictions is not a true uncertainty (for example, the standard deviation may not be properly calibrated); however, the procedure still serves to measure the sensitivity of our predictions to this uncertainty source.

The impact of the sparsity of experimental data is investigated by re-sampling from the shot-to-shot variability model described previously to produce 50 synthetic datasets. Effectively, we use the result of a single inference as a reference solution and measure the sensitivity of that solution to the sparsity of a typical NIF dataset. Similar to the surrogate sensitivity, this procedure is not a true measurement of uncertainty since the ground-truth experimental distribution is not known; however, we can still measure sensitivity and compare it with the shot-to-shot and surrogate distributions.

Data sparsity introduces significant uncertainty in the details of our predictions; however, we have found that the fluctuations in predictions for 1.9 and 2.05 MJ shots are correlated (Fig. 7). As a result, while the precise ignition probability for a given design has an absolute uncertainty of 10%–20%, the relative performance gain between designs is quite robust. This is an encouraging result since it suggests that even sparse datasets can be meaningfully used to design new high performance and robust implosions.

We have described a novel data-driven predictive model for the performance and variability of inertial confinement fusion experiments. The model combines past experimental data with large-scale ensemble simulation studies to produce a calibrated distribution for shot-to-shot variations posed in terms of simulation inputs. Our Bayesian model calibration approach affords several advantages over other methods by jointly informing the model with experiments and simulations and allowing for a complete quantification of uncertainty in predictions. Our model is interpretable, physically consistent, makes physics-based extrapolations to new designs, and captures uncertainty from multiple sources.

Each stage of the Bayesian analysis and prediction approach has been validated through detailed comparison with the available experimental data. When applied to nine recent “Hybrid-E” ICF experiments at the National Ignition Facility with 1.9 MJ of laser drive, the model accurately matches multiple observed quantities across all shots as well as the full performance distribution across the whole campaign. When used to extrapolate and predict new experiments with a 2.05 MJ drive, the calibrated model predicts a significant (⁠ $∼10×$⁠) increase in ignition probability, which has been confirmed by subsequent experiments. While the higher drive data are insufficient to validate the predicted distribution in detail, the central distribution moments are in excellent agreement with NIF data.

The sparsity of simulation and experimental data, which arises due to the expense of collecting new samples, has an important impact on the details of the predicted distributions for individual designs but not on the expected increase in ignition probability between designs. We have quantified the impact of data sparsity through an ensemble technique where multiple models are trained using different realizations of the data, and the variations in ignition probability are used as a proxy for sensitivity. We find that while individual ignition probabilities vary across ensemble members, predictions for different designs are correlated such that comparisons between designs are consistent. This is an encouraging result for future data-driven design studies using our techniques.

Deep learning plays an essential role in making the present approach computationally tractable and in enabling predictions on a timescale relevant to experiments. Deep neural network surrogate models allow expensive radiation-hydrodynamic simulations to be decoupled from Bayesian inference steps and to be performed in a massively parallel manner, enabling our analysis to include state-of-the-art physics. The use of transfer learning to update existing surrogate models to new implosion designs allows us to make new predictions in a matter of days in order to respond to on-the-ground experimental changes as they occur.

The methods and results presented here are a prototype for several new types of data-driven design and analysis studies for ICF. The Bayesian postshot, which forms the first step of the prediction model, can be used to calibrate and place uncertainties on unobserved parameters like x-ray drives, implosion velocities, etc. The calibrated shot-to-shot variability model, combined with transfer learning or other multi-fidelity approaches, can be used to evaluate performance variability during automated design optimization studies. These “design-for-robustness” studies would enable new implosion designs that can hit yield targets with a low probability of failure with many applications in ICF and high energy density physics. Finally, our use of deep learning in the framework provides an exciting potential for the inclusion of non-scalar data like capsule metrology, x-ray images, and neutron spectra.

This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA27344. Lawrence Livermore National Security, LLC. LLNL-JRNL-862855.

The authors have no conflicts to disclose.

Jim A. Gaffney: Conceptualization (equal); Data curation (equal); Methodology (equal); Software (equal); Validation (equal); Visualization (equal); Writing – original draft (equal). Kelli Humbird: Conceptualization (equal); Investigation (equal); Project administration (equal); Writing – review & editing (equal). Andrea Kritcher: Investigation (equal); Writing – review & editing (equal). Michael Kruse: Conceptualization (equal); Investigation (equal); Writing – review & editing (equal). Eugene Kur: Conceptualization (equal); Data curation (equal); Investigation (equal); Writing – review & editing (equal). Bogdan Kustowski: Conceptualization (equal); Data curation (equal); Investigation (equal); Software (equal); Writing – review & editing (equal). Ryan Nora: Conceptualization (equal); Data curation (equal); Investigation (equal); Software (equal); Writing – review & editing (equal). Brian Spears: Conceptualization (equal); Investigation (equal); Writing – review & editing (equal).

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