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Tracking Blobs in the Turbulent Edge Plasma of Tokamak Fusion Reactors
Woonghee HanMIT
Randall A. PietersenMITCEE
Rafael Villamor-LoraMITCEE
Matthew BeveridgeMIT
Nicola OffedduEPFL
Theodore GolfinopoulosMIT
Christian TheilerEPFLSPC
James L. TerryMIT
Earl S. MarmarMIT
Iddo DroriMIT
Abstract
The analysis of turbulent flows is a significant area infusion plasma physics. Current theoretical models quantifythe degree of turbulence based on the evolution of certainplasma density structures, called blobs. In this work wetrack the shape and the position of these blobs in high fre-quency video data obtained from Gas Puff Imaging (GPI)diagnostics, by training a mask R-CNN model on syntheticdata and testing on both synthetic and real data. As a result,our model effectively tracks blob structures on both syn-thetic and real experimental GPI data, showing its prospectas a powerful tool to estimate blob statistics linked withedge turbulence of the tokamak plasma.
1. Introduction
In tokamak fusion reactors, plasmas are magneticallyconfined and heated up to produce energy from nuclearfusion. In order to maximize the rate of fusion, it is vi-tal to maintain an energy confinement as high as possi-ble. The quality of this confinement is closely related tothe turbulence at the edge region of the plasma core. Cur-rent theoretical models quantify the degree of this turbu-lence from the evolution of certain structures, known asblobs, within the plasma density field. This is an evolv-ing area of research, and the different models require theanalysis of different blob statistics that can be derived fromimage data (e.g. blob velocity, size, and intermittent). For
example, the fluctuations in the plasma may be describedby a stochastic model as the superposition of uncorrelatedLorentzian pulses, which is parameterized by the intermit-tency of blobs [4, 5]. Furthermore, the radial velocity andthe size of blobs may be used to determine the theoreticalblob propagation regime and the dependence of its proper-ties on various plasma parameters [8]. Thus, it is crucial tohave a reliable method for estimating statistics of blobs inorder to study turbulences in the edge of tokamak plasmas.
In this work, we develop a deep neural network trainedon synthetic data to track the shape and the position of blobsin experimentally obtained low-resolution (12 × 10 pixel),high-frequency (2 MHz) video data from Gas Puff Imaging(GPI) diagnostics [6, 12] on the Tokamak a ConfigurationVariable (TCV), shown on Figure 1. GPI is an edge diag-nostic tool that measures the spatially-resolved fluctuationsof plasma light emission, which can be used as a proxyfor plasma density fluctuation measurements. Figure 2(b)shows a snapshot of the GPI data that captures a blob mov-ing radially outwards after crossing the plasma edge (i.e.the Last Closed Flux Surface (LCFS)).
Currently, blob-like structures in GPI data are trackedby conventional algorithms such as brightness thresholding[9]. However, these methods do not generalize well due tothe presence of measurement noise and varying experimen-tal conditions. For instance, threshold values change be-tween individual experiments, and experimental noise mayresult in structures that resemble blobs appearing in isolatedframes. Conventional tracking algorithms fail to distinguishsuch noise fluctuations from actual blobs.
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Figure 1. The schematic of the Tokamak a Configuration Variable (TCV) (left) and its interior (right). Credits: EPFL (left) and A. Herzog,EPFL (right).
Figure 2. (a) Cross-section of a plasma in the Tokamak a Configuration Variable (TCV) with the locations of Gas Puff Imaging (GPI)views near the Last Closed Flux Surface (LCFS). (b) Snapshot of experimental GPI data (drawn to the actual scale) capturing a blob onthe right-hand-side moving radially outward. Here empty spots correspond to dead GPI views. The brightness level is color-coded, low asblue and high as yellow. (c) Snapshot of synthetic data capturing a blob moving radially outward. The blob is represented by a Gaussianellipse with a major and minor axis marked by perpendicular black lines.
We therefore propose the use of a convolutional neu-ral network (CNN) to track blobs, improving upon existingmethods. While using CNN may be straightforward, ourapplication domain introduces a level of complexity whichmay create a significant barrier to entry for non domain ex-perts. The current process of finding an appropriate algo-rithm, altering it for a specific use case, debugging errors,and then optimizing its performance to achieve useful re-sults, is by no means trivial and may inhibit, or completelydiscourage, its use in certain contexts. Indeed, the associ-ated time required by subject matter experts with limitedcoding experience, but who have a use for a specialized al-gorithm, is oftentimes very discouraging under the currentparadigm. OpenAI Codex [2] is a Transformer trained onboth text and code. Although it was originally intended asa means of converting textual descriptions, by designers forexample, into code; in this work we apply it in a novel work-flow so that non-domain experts may efficiently construct
state of the art models for our highly specialized domain.Specifically, we use Codex to aid implementing a Mask
Region-based Convolutional Neural Network (Mask R-CNN) [7] combined with a loss function that computes thepairwise cost between each object from the previous frameand each object in the current frame [3]. Our modified al-gorithm is able to segment blobs in a three dimensional vol-ume by preserving the spatiotemporal features in the GPIvideo data. We discuss the qualitative utility of using Codexto help with our code implementation, as well as present theresults of this process with the model’s performance on bothsynthetic training data and real-experimental data.
Our methodology, including the model architec-ture, training approach, and hyperparameter tuning withBayesian optimization, is described in Section 2. We thendiscuss the result of training and performance on experi-mental GPI data in Section 3, with our main conclusionssummarized in Section 4.
2. Methodology2.1. Base model: mask R-CNN
We implement a Mask R-CNN [7, 10] as a base model.The output from the Mask R-CNN consist of boundingboxes, masks, labels of the object class, and confidencescores. The model identifies three distinct classes: thebackground, the shear layer region, and blobs. Mask R-CNN is an extension of Faster Region-based CNN (FasterR-CNN) [11], which is designed to produce two outputs foreach candidate object: a class label and a bounding box.Mask R-CNN extends this by an additional branch that pre-dicts segmentation masks on each bounding box. The train-ing is performed on a pre-trained off-the-shelf model.
2.2. Datasets and Training
Each experimental GPI dataset is composed of a seriesof 2D images, 12× 10× t, where t is the number of framesin the video. A snapshot of GPI data is shown in Figure2(b) which shows a blob (as a bright spot on the bottom-right), and the LCFS, which is approximately the positionof a shear layer, across which the plasma flow reverses di-rection. The masks of these two types of objects, blobs andshear layer, are what we aim to predict. Due to the limitedamount of experimental data available and the current lim-itations for adequately labeling real world data, our modelis trained using synthetic data. A snapshot of this syntheticdata is shown in Figure 2(c). For these synthetic data, weare able to simulate complex instances which appear in thereal GPI data, such as merging and splitting of blobs.
Although the GPI sensors output data with 12×10 pixelsper frame, it is standard practice to use interpolation algo-rithms to upsample this resolution, in the present case to256 × 256 pixels per frame. This degree of upsampling al-lows adequate detail during analysis without being too com-putationally demanding. Aligning with this convention, thesynthetic data generated for training is also kept at 256×256pixels per frame and the model is designed to receive inputsand produce outputs at this resolution.
2.3. Tracking-by-detection algorithm
After blobs are detected in each frame, temporal coher-ence between frames the is enforced based on a tracking-by-detection workflow [3]. The algorithm of a typical tracking-by-detection method is illustrated in Figure 3, and consistsof four steps:
1. Object detection from the trained mask R-CNNmodel. Given an input data, the bounding boxes andthe masks of blobs are predicted for each frame by thetrained mask R-CNN model.
2. Feature extraction. We select the objects to be tracked(i.e., blob objects). Predictions with scores below a
certain threshold are discarded.
3. Pairwise cost. In this critical step, we exploit the tem-poral coherence of the images. Using a cost function,we compute the pairwise cost between the objects inthe current and previous frames. There are differentalternatives for the cost function, and we use the volu-metric intersection over union (VIoU) as described inSection 2.4.
4. Matching. Using the cost matrix from the previousstep, we assign unique correspondence between ob-jects with the constraint that no object receives morethan one assignment. If a new object appears in an iso-lated frame (i.e. it has no correspondence either in theprevious or the next frame), then the object is ignoredand discarded as a noise fluctuation. Moreover, whena new object appears in the current frame with no cor-respondence in the previous frame, but a match in thenext frame, we start a new tracklet [3]. By bookkeep-ing of the active and finished tracklets we are able tocount the number of blobs in the video and record theirtrajectories.
2.4. Volumetric IoU
To quantify the loss during (1) the training of the MaskR-CNN detector, and (2) the pairwise cost step in thetracking-by-detection algorithm, we use volumetric IoUas our evaluation metric. In object detection algorithmsit is customary to use intersection over union (IoU) met-rics to evaluate the goodness of the prediction. For theprediction/ground-truth pair (e.g., bounding boxes, mask),the IoU is computed as the ratio between the area of inter-section and the area of the union. While this approach isquite robust when dealing with the mask detection of solidobjects with well-defined, sharp boundaries, IoU can mis-lead the score for our application when the area of inter-section has low brightness level which is intuitively a poorprediction.
Note that the boundary definition of blob structureswithin the plasma is a function of the brightness threshold.Since this threshold may vary from experiment to experi-ment, in our case, it is more appropriate to describe the blobshape as a volume, with volumetric IoU (VIoU), being thebrightness level the third axis, as shown in Figure 4.
2.5. Data Augmentation
In order to improve the generalization performance ofthe model, a set of data augmentation transformations areapplied to the training data with corresponding probabili-ties as shown in Figure 5. Specifically, given random num-bers xhorizontalF lip, xscale, xtranslate, xshear, and xrotate
between 0.0 and 1.0, we perform the following transforma-tions:
t = 2
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1) Object detection using a pre-trained off-the-shelf detector
(Mask R-CNN)
2) Feature extraction 3) Pairwise cost 4) Matching
Costij = C(Oi, Oj)
t = 1
t = 2
t = 3
t = 4
Sets of 2D images,
XY, with a t
temporal coherence Cost12 = C(O1, O2)
Cost23 = C(O2, O3)
Cost24 = C(O2, O4)
Cost35 = C(O3, O5)
Cost45 = C(O4, O5)
Figure 3. Tracking-by-detection algorithm consisting of four steps: (1) Object detection within each frame using a pre-trained detector.Here the mask R-CNN produces three outputs for each candidate object: a label, a bounding box, and a mask. The model distinguishesbetween three classes: background, shear layer, and blobs. (2) Extraction of features of interest (i.e. blob objects). (3) Computation ofpairwise costs between objects in the current and previous frame. (4) Matching between object assigning unique correspondence.
Figure 4. Volumetric Intersection over Union (VIoU) computed for a prediction on an image containing a blob (top) using the volumeunder the profile of the brightness (bottom).
• Flip: horizontally flips with fhorizontalF lip probabilitywhen xhorizontalF lip < PhorizontalF lip,
• Scale: scales with random scaling factor between 0.8and 1.2 when xscale < Pscale,
• Translation: translates with random translating factorbetween 0.0 and 0.2 when xtranslate < Ptranslate,
• Shear: shears with random shearing factor between−0.2 and +0.2 when xshear < Pshear, and
• Rotation: rotates with random angle between −10 and+10 deg when xrotate < Protate.
The transformation probabilities PhorizontalF lip, Pscale,Ptranslate, Pshear, and Protate are hyperparameters whichare optimized by Bayesian optimization as described in Sec-tion 2.6.
Original
Ground-truthBox predicted
Horizontal flip Scale Translation
Shear Rotation All
(a) (b) (c) (d)
(e) (f) (g)
Figure 5. A set of data augmentations in (b)-(f) applied to the original image (a) with their corresponding probabilities. (g) Application ofall transformations in (b)-(f) to the original image (a).
2.6. Bayesian Optimization of Hyperparameters
Hyperparameter tuning is a key step in optimizing theperformance of machine learning algorithms, however, thecomputational demands of such an analysis vary greatly de-pending on the dimensionality of the parameter space andcomplexity of the algorithm being evaluated. In our model,Bayesian optimization is used to find the hyperparametervalues that minimize the loss of the CNN trained to detectblob objects in GPI data.
We apply Bayesian optimization [1] as two levels of hy-perparameters: (1) learning rate, momentum, weight decay,and number of epochs; and (2) data augmentation transfor-mations PhorizontalF lip, Pscale, Ptranslate, Pshear, Protate,as well as dropout probability Pdropout for each dropoutlayers added after ReLU layers in later parts of the modelwhich detect regions of interest.
The exploration ranges for each hyperparameters areshown in Table 1. We first optimize first the group one hy-perparameters, and then keep those values fixed while opti-mizing the second group of hyperparameters.
2.7. Co-programming using Codex
OpenAI Codex [2] is a large scale Transformer trainedon both text and code. Recently, the toolbox of moderncoding has been extended to include using OpenAI Codexor Github co-Pilot to aid and guide the implementation pro-cess. In the spirit of best coding practices and these ad-vances in automation, this work is the first to use programsynthesis to improve performance by automatically writingarchitectural components and hyperparameters. To do sowe provide prompts including part of our model code toOpenAI’s Codex [2] and incorporate the architectural andhyperparameter changes generated. Therefore, instead of
setting the model architecture and hyperparameter valueson an ad hoc basis, we use OpenAI Codex. For ad hoc val-ues, the horizontal flipping factor fhorizontalF lip (probabil-ity of flipping when the horizontal flip is practiced) and scal-ing factor (percentage of the scaling) in data augmentationwere suggested by Codex as 1.0 and 0.5, respectively. Formodel structures, Codex suggests replacing the ReLu lay-ers with leaky ReLu layers, and plain dropout layers (ran-domly zeroes some of the elements of the input tensor) with2D dropout layers (randomly zeroes entire 2D channels ofthe input tensor, e.g., 2D with the channel and the batch).We find that providing guidance through human code snip-pets allows Codex to make these decisions by automaticallymodifying existing code. These decisions would have beenchallenging for programmers to make unless they try costlyruns for every different combinations, without the aid ofCodex.
2.8. Conventional Algorithm for Labeling Experi-mental GPI Data
One of the aims of this study is to improve upon the per-formance of the conventional tracking algorithm based onimage thresholding [9]. The conventional tracking algo-rithm generates blob sizes and trajectories from GPI data,by tracking the contours that exceed a user-defined thresh-old. With these, one can directly determine the distribu-tions of speed, size, and frequency of blobs. While thisalgorithm is a common approach for blob analysis, it in-herently has two primary shortcomings that our approach isdesigned to address: (i) It does not generalize well acrossmultiple experiments and variations in data, which requiresto carefully oversee the tracking process and continuouslyadjust values during data processing steps. Implementing a
BO Lv. 1 - Parameters LR: initial val LR: reduction period LR: decay Momentum Weight decay nepochs
Exploration range 1e-6—5e-2 1—40 0.1—1.0 0.0—1.0 0.0—1e-3 2—40BO Lv. 2 - Parameters PhorizontalF lip Pscale Ptranslate Pshear Protate Pdropout
Exploration range 0.0—1.0 0.0—1.0 0.0—1.0 0.0—1.0 0.0—1.0 0.0—0.5
Table 1. Exploration ranges of hyperparameters used in Bayesian optimization. BO level 1 hyperparameters: learning rate initial value,learning rate reduction period, learning rate decay factor, momentum, weight decay and number of training epochs. BO level 2 hyperpa-rameters: probabilities for horizontal flip, scaling, translation, shearing, rotation, and dropout.
Mask R-CNN model for our approach makes this processmore invariant to changes in blob representation. (ii) It isincapable of instance-level object recognition and cannotadequately characterize the merging and splitting of blobs,which is critical for the understanding of the nature of theplasma edge turbulence. Mask R-CNN is able to performthis instance-level recognition [3]. Although this conven-tional algorithm is what our model aims to outperform, weused it for labeling blobs in experimental GPI data in orderto test the performance of our model (trained with syntheticdata) on the real GPI data.
Uncertainty estimates. We estimate uncertainty usingdropout by training the network using dropout and then test-ing each example by running multiple forward passes withdropout weights.
3. Result3.1. Result of Bayesian optimization
As described in Section 2.6, hyperparameters are tunedby two levels of Bayesian optimization (BO) with each ofthe exploration ranges shown in Table 1. The optimal valuesand importance found for each hyperparameter are summa-rized in Table 2 and 3. The convergence of VIoU in thehyperparameter space is shown for the three most impor-tant hyperparameters in BO level 1 (Figure 6 (a)) and inBO level 2 (Figure 6 (b)). Here, the VIoU score drivingBO is 0.7 ∗ V IoUblob + 0.3 ∗ V IoUshear, where V IoUblob
and V IoUshear are the average volumetric IoU for bloband shear layer predictions, respectively. This weightingemphasizes the importance of blob predictions over predic-tions for the shear layer. The importance is estimated as themutual information regression for the resulting VIoU scorefrom each BO trial. For BO level 1, the learning rate re-duction period is the most important hyperparameter. TheVIoU increases from 0.77 and converges to 0.89 as shownin Figure 6 (a). For BO level 2, the optima in Table 3 areshallow since there is not much change in VIoU for trialsshown in Figure 6 (b). The VIoU’s are around 0.89, whichis similar to the convergent value of BO level 1. Our con-clusion from these results is that we found optimal valuesof hyperparameters in BO level 1 which greatly improve
BO Lv.1 - Parameters Optimum Importance
Learning rateInitial value 0.0500 0.1334Reduction period 12 0.3957Decay factor 0.4020 0.2798
Momentum 0.2956 0.3347Weigh decay 2.7289e-5 0.3824Training epochs 28 0.2884
Table 2. Optimal values and importances of the BO level 1 hyper-parameters.
BO Lv.2 - Parameters Optimum Importance
Pdropout 1.2834e-17 0.2701PhorizontalF lip 0.3413 0.1649Pscale 0.5597 0.0336Ptranslate 0.2614 0.0946Protate 0.3679 0.0188Pshear 0.5644 0.0000
Table 3. Optimal values and importances of the BO level 2 hyper-parameters.
the performance of the model. In contrast, we conclude thatdata augmentation, as well as the addition of dropout layersto the model, have not much effect on the overall perfor-mance of the model.
3.2. Training of the model on synthetic data withoptimized hyperparameters
The model is trained on synthetic data using the opti-mized hyperparameters found in Section 3.1, and the re-sult is shown in Figure 7. The size of the training datasetis twice as large as the dataset used in Bayesian optimiza-tion. Figure 7 shows VIoU’s evaluated with held-out testdata (20% of the dataset) for each epoch for blob and shearlayer predictions. The uncertainties are estimated by MonteCarlo (MC) dropout with dropout probability 0.3 and 100MC passes. The score gradually increases up to ∼ 0.88 forblob predictions and ∼ 0.80 for blob predictions. The un-certainty also gets smaller in the later epochs (0.08 for blob
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Figure 6. Convergence of volumetric IoU score in (a) BO level 1 and (b) BO level 2. In both cases, the three most important hyperparametersare plotted.
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Figure 7. Result of the training of the model showing volumet-ric IoU’s from test data for each epoch, for blob and shear layerpredictions.
and 0.04 for shear layer) compared to the earlier. As a con-clusion, the model trained on synthetic data with the opti-mized hyperperameters does achieve a high score in testingwith synthetic data, comparable to the score achieved in theBayesian optimization.
3.3. Testing of the trained model on real experimen-tal GPI data
Using the resultant weight matrices for the model trainedon synthetic data, real experimental GPI data is then in-putted to test performance. While performance metrics forthe experimental data are valuable, it is important to under-stand that unlike the synthetic data, the conventional track-ing algorithm used to generate ground truth labels for theexperimental data often has errors and may therefore be un-reliable. One such example is shown in Figure 8, wherethe black mask, which is the label from the conventional al-gorithm, is inaccurate compared with the red mask, which
is the prediction from the model. In this case, the VIoUbetween black and red masks is low but the ground truthis not good enough, which makes the model’s performanceto be underestimated from this low VIoU. For this reason,only VIoU’s higher than 0.5 are considered. The mean ofsuch VIoU’s is 0.61 with a standard deviation of 0.08, sothe model performs fairly well on experimental GPI data.Figure 9 shows the model’s tracking ability for the case ofsplitting blobs, which is not captured by the conventionaltracking algorithm. Here, the blob ID in pre-splitting (Blob16) is preserved after the splitting and a split-off blob has anew ID (Blob 17), showing the efficacy of the tracking-by-detection algorithm described in Section 2.3. In conclusion,these results show good performance of the model on realexperimental GPI data, and these also highlight the limita-tions of the conventional tracking algorithm which is over-come by our proposed model.
4. Conclusion
We present a model for blob tracking which is trainedwith hyperparameters found by Bayesian Optimization andan architecture design guided by OpenAI Codex for improv-ing performance. It effectively predicts the shape and thelocation of turbulent structures in the edge of tokamak fu-sion reactors, called blobs, in both synthetic and real exper-imental GPI data. This new model will serve as a reliabletool for tracking blobs, which allows estimation of variousstatistics of blob dynamics connected to the level of turbu-lence in the edge of tokamak plasmas. Having this char-acterization of the edge turbulence based on blob statisticshelps us understand turbulent modes which are harmful tothe plasma confinement, thereby improving the generationof fusion energy.
Figure 8. An example of experimental GPI data with a groundtruth mask (black) labeled by conventional tracking algorithmwhich is not as good as predicted mask (red) by the model.
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