Experiment data-driven modeling of tokamak discharge in EAST

07/21/2020 ∙ by Chenguang Wan, et al. ∙ 0

A model for tokamak discharge through deep learning has been done on EAST tokamak. This model can use the controlled input signals (i.e. NBI, ICRH, etc) to model normal discharge without the need for doing real experiments. By using the data-driven methodology, we exploit the temporal sequence of controlled input signals for a large set of EAST discharges to develop a deep learning model for modeling discharge diagnose signals, such as electron density n_e, store energy W_mhd and loop voltage V_loop. Comparing the similar methodology, we pioneered a state-of-the-art Machine Learning techniques to develop the data-driven model for discharge modeling. Up to 95 achieved for W_mhd. The first try showed very promising results for modeling of tokamak discharge by using data-driven methodology. This is a very good tool for the ultimate goal of machine learning applied in fusion experiments for plasma discharge modeling and discharge planning in the future.

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1 Introduction

A reliable model of tokamak is critical to magnetic confinement fusion experimental research. It is used to check the feasibility of pulse, interpret experimental data, validate the theoretical model, and develop control technology.

The conventional physical-driven modeling tools come from empirical models or derivations based on first principles, which is the so-called "Integrated Modeling". "Integrated Modeling" is a suite of module codes that address the different physical processes in the tokamak, i.e. core transport, equilibrium, stability, boundary physics, heating, fueling, and current drive. Typical codes are PTRANSP [5], TSC [13], CRONOS [2], JINTRAC [17], METIS [3], ASTRA [16], TOPICS [9] etc. The reliability of the first-principles model depends on the completeness of the physical processes involved. In the past few decades, sophisticated physical modules have been developed and integrated into these codes for more realistic modeling results. Typical simulation of a full discharge on tokamak using sophisticated modules takes a few days. Due to the nonlinear, multi-scale, multi-physics characteristics of tokamak, high-fidelity simulation of the whole tokamak is still a great scientific challenge [4].

Increasingly, researchers are turning to data-driven approaches. The previous history can be traced back to the research of disruption prediction using neural networks since the 1990s, i.e. JET

[6, 23], ASDEX-Upgrade[7], JT-60U[28] and J-TEXT [21]. The disruption prediction is a binary classification problem. One neural network was trained with several selected experimental signals to identify the presence of incoming disruption. Recently, the application of deep learning paradigms has expanded prediction capabilities and shown encouraging results [12, 27]. Neural-network-based models are also used to accelerate theory-based modeling [11, 15]. One neural network was trained with a database of modeling and successfully reproduced approximate results with several orders of magnitude speedup.

Physics-driven approaches reconstruct physical high-dimensional reality from the bottom-up and then reduce them to the low-dimensional model. Alternatively, data-driven approaches discover the relationships between low-dimensional quantities from a large amount of data and then construct approximate models of the nonlinear dynamical system. When focusing only on the evolution of low-dimensional macroscopic features of complex dynamic systems, data-driven approaches can build models more efficiently. In practical applications, control and diagnostic signals of tokamak usually appear as temporal sequence of low-dimensional data, most of which are zero-dimensional or one-dimensional profile and rarely two-dimensional distribution. If we consider tokamak as a black box, these signals can be considered as inputs and outputs of a dynamic system. It is reasonable to assume that a neural network model trained with historical experimental signal data can be used to reproduce or predict the external dynamic behavior of the tokamak system.

In the present work, a neural network model is trained with the temporal sequence of control and diagnose signals for a large data set of EAST discharges [26, 24, 14]. It can be used to model discharge main parameters, such as electron density , store energy and loop voltage .

The rest of this letter consists of four parts. Section 2 shows the model details of this letter. The detailed data preprocessing and model training process can be found in section 3. Then an in-depth analysis of the model validation is put forward in section 4. Finally, a brief conclusion and discussion are made in section 5.

2 Model

Experiment data can be divided into three categories, configure parameters, diagnose signals, and control signals. Configuration parameters describe constants related to device construction, such as major radius , minor radius , etc. Diagnostic signals give physical information about the plasma state, such as stored energy , electron density , or loop voltage . Control signals are provided by the plasma control system (PCS) and external auxiliary systems. (e.g. Neutral Beam Injection (NBI), Lower Hybrid Wave (LHW), Poloidal magnetic field coil current, etc.) The purpose of tokamak discharge modeling is to predict the plasma response to external control. In practical applications, that is to build the relationship between control signals and diagnostic signals. If it is not to build a cross-device model, the configuration parameters need not be taken into account.

For tokamak discharge modeling, mapping the control signals to diagnostic signals in the configuration parameters not change. That is somewhat like natural language processing (NLP) rather than classification (e.g. disruption prediction), an important direction of machine learning. The main work of NLP is to translate a natural language sequence into another natural language sequence. In the abstract, mapping a word sequence to another word sequence while in the NLP problem doesn’t need to consider the “time”, a very important characteristic of tokamak signals. In the machine learning field, the modeling of general the temporal sequence signals basically uses Recurrent Neural Network (RNN) and its variants (e.g. Gated Recurrent Unit (GRU), Long Short-Term Memory (LSTM)). In this letter, LSTM was chosen as a fundamental component. And stacking LSTM as an encoder-decoder

[19] deep learning model.

In the deep learning model of this letter, when ignoring dropout layers, the encoder hidden states are computed using this formula:

(1)

This simple formula represents the result of an ordinary recurrent neural network. As you can see, we just apply the appropriate weights to the previously hidden state

and the input vector

. The encoder vector is the final hidden state produced from the encoder part of the model. It is calculated using the formula above. This vector aims to encapsulate the information for all input elements to help the decoder make accurate predictions. It acts as the initial hidden state of the decoder part of the model.

In decoder a stack of several recurrent units where each predicts an output at a time step . Each recurrent unit accepts a hidden state from the previous unit and produces and output as well as its hidden state. In the simulation of tokamak discharge, When ignoring dropout, the output sequence is a collection of all time steps from the . Each time step is represented as where is the order of that word. Any hidden state is computed using the formula:

(2)

As you can see above, we are just using the previous hidden state to compute the next one. The output at time step t is computed using the formula:

(3)

We calculate the outputs using the hidden state at the current time step together with the respective weight

(The weight of the dense layer). Dense is used to determine the final outputs. Activation function had been tried a variety of functions, the best function is the linear function.

In terms of components, The main component of our architecture is long short-term memory (LSTM) [10], because the LSTM can use trainable parameters to balance long-term and short-term dependencies. This feature is suitable for tokamak data, tokamak discharge response is always strongly related to short-term input changes but it is also affected by long-term input changes. The dropout layer which is a common trick to prevent over-fitting. Final component is the dense layer to match the high-dimensional decoder output with the real target dimension.

In terms of the overall deep learning model architect, the architecture is based on the sequence to sequence model (seq2seq) [20], When ignoring dropout layers and dense layer, our architect can be regarded as four LSTM layers stacked. The first two LSTM layers can be considered as encoders, and the last two layers can be regarded as decoder. In this work, the encoder is to learn the high-level representation (cannot be displayed directly) of input controlled signals (tab 1 input signals). The hidden state of the encoder is used to initialize the hidden state of the decoder. The decoder plays the role of decoding the information of encoder. Encoder-decoder is built an end-to-end model, it can learning information directly without manually extracting features.

In tokamak device, almost all the diagnostic signals can be divided into three segments, namely ramp-up, ramp-down and flat-top. Flat-top segment is a stable segment while ramp-up segment and ramp-down segment is not as stable as flap-top segment and different diagnostic signals also have different performances in the three segments, for example, compared with , and remain relatively stable in three segments. So different resampling methods is used for modeling different diagnose signals.

For the diagnose signals that are relatively stable in all three segments can use uniform resampling method (using the same resample rate in all the segments) and for the diagnose signals have different change speed, adaptive resampling method are used. Adaptive resampling method is used higher resampling rate for the segments of interest to physicists or areas that change more quickly, when using this method, the higher resampling rate of the segments can make the loss function have more weight and driven deep learning model “learning more hard” in these segments than other segments. And then all the resampled signals should be standardized and input to the deep learning model.

The input and output signals using in this letter are shown in table 1.

Signals Physical meanings
Output Signals
Electron density
Loop voltage
Stored energy
Input Signals
Plasma current
NBI Neutral Beam Injection System
ICRH Ion Cyclotron Resonance Heating System
LHW Lower Hybrid Wave Current Drive and Heating System
ECRH/ECCD Electron Cyclotron Resonance Heating/Current Drive System
GPS Gas puffing system
SMBI Supersonic Molecular Beam Injection
Magnetic field Poloidal field and Toroidal field
Table 1: Input and output signals of the model.

In the signal selection, a very trivial principle was adopted that is regarding tokamak as a non-linear dynamic system selected all the available control signals (Eliminate interference from experience bias) as model input, some typical diagnose signals as output. Almost every control signal in tokamak has two categories: processed data (Physical signals) and raw data (electrical signals), which one is richer (more reliable) and more concise (more information) will be selected. In this letter we only choose , and as a demonstrate work, it is shown a promise direction in the future from the results.

Figure 1: Workflow of our work. (a). Uniform resampling signals preprocessing and training. (b). Adaptive resampling signals preprocessing and training.

After the deep learning model had been trained, the model can model future data as shown in figure 2. At the beginning of using the trained model should obtain all the 65 channels raw signals and then aligning all the data on the time axis. The aligned data should be standardized by the same parameters of the training set. All the standardized data will be flew into the trained model and get the modeling sequence of diagnostic signals.

Figure 2: Using of trained model.

3 Training

In the training stage, as shown in figure 1. the training model can be divided into 5 steps as follows:

  1. Obtaining the data of 68 channels of the selected signals from the EAST source database.

  2. Using different resampling methods base on the signal characteristics that would be modeled.

  3. Standardizing the data with z-scores.

  4. Data flow into the deep learning model for training.

  5. Using the loss between model output and real experimental output as backing propagation metric and then update parameters for the training model.

Sampled simultaneous throughout t all shot numbers in the range of 70000-80000 tokamak discharges shot in the 2016-2018 campaign on EAST [26, 25, 14]. 3476 normal discharge shots are selected and divide the data into a training set, a validation set, and a test set. The data set only include normal discharge shots. It was sampled starting at and continuing until the end of the discharge. (Typical EAST normal discharge shot duration range from 5s to 8s.).

For each tokamak discharge shot, signals from 68 different channels (include input and output signals as shown in table 1

) are resampled by linear interpolating to have the same sample rate and same sample time points. If the shot disruption, duration time in the flat-top segment is too short or without complete magnetic field confinement signals,

or model output signals data will be regarded as abnormal shot and discarded it, because, for a tokamak shot, disruption and duration time in the flat-top segment is too short, it is an abnormal status not taken account by the normal discharge experimental proposal. If there is no certain magnetic field configuration, plasma is impossible to be constrained and without or output signals are no meaning for our model or tokamak discharge experiment.

For modeling and , they change slowly in the ramp-up segments and ramp-down segments, so the same sampling rate can be used in ramp-up, ramp-down and flat-top . Then all signals of input are resampled to have the same sample rate of 1, 1 is the original sampling rate of and . This sampling rate can balance speed up model training and accuracy if there is no special stage we want to model.

For modeling , it changes rapidly in the ramp-up segment and ramp-down segment, so to model the ramp-up segment and ramp-down segment of , a higher resampling rate is required. The different sampling rates are used in ramp-up, ramp-down and flat-top, 10 sample rate is used in ramp-up segment and ramp-down segment and 1 sample rate is used in the flat-top segment. Then all signals of inputs are resampled to the same sample rate.

When all source data was obtained the z-scores will be applied for standardization. and then all the data had preprocessed will be input to the deep learning model for training. The deep learning model uses an end-to-end training was executed on 8x Nvidia P100 GPUs with Keras

[22]

and TensorFlow

[1] in Centos7 system in local computing cluster and remote computing cluster.

The training of the deep learning model starts with kernel initializer is glorot uniform initialization [8], the recurrent initializer is orthogonal [18], bias initializer is zeros, and optimizer is Adadelta [29]

for solving gradient explosion. Our model trains about 12 days, 40 epochs. Then use callbacks and checkpoints to choose the best performing model in

and modeling best epoch is 15, while modeling best epoch is 7. In per epoch, all the data in the training set will be put into the model for one time.

Shuffle method (a common generalization method) in not used in all data sets, training set validation set and test set are separated according to time order, to prevent data leakage caused by multiple adjacent experiments with the same parameters that are frequency in tokamak discharge experiment. But inside the training set shuffle shot is necessary for the reason of generalization.

The training of our model is executed several times. Most of these trials considered as fail because of the bad performance of unsuitable hyper-parameters. In the training of the model, different epochs with different learning rates, different optimization methods, and different initialization configurations were tried. Such as the dropout rate in the encoder and decoder should balance regularization and accuracy. Finally, the best hyper-parameters were found and shown in table 2.

Hyper-parameters Explanation Best value
Learning rate
Adadelta decay factor 0.95
Optimizer Optimization scheme Adadelta
Dropout

Dropout probability

0.1
Epochs Epochs 10
dt time step 0.001s
Batch_size batch size 1
LSTM type Type of LSTM CuDNNLSTM
Initializer for the kernel of LSTM weights matrix Glorot uniform
Initializer for the recurrent kernel of LSTM weights matrix Orthogonal
Initializer for the kernel of dense matrix Glorot uniform

Initializer for the bias vector

Zeros
Number of LSTMs stacked in encoder 2
Number of LSTMs stacked in decoder 2
Dimensions of LSTM output 128
Table 2: Hyper-parameters in our model

4 Results

Two data sets of typical EAST discharge shots, shot #77873 and #78461, are selected to check the accuracy of the model trained in this article. Figure 3(a) shows the modeling result for shot #77873, which has two LHW injections during discharge. Figure 3(b) shows the result for shot #78461, which has NBI, LHW, ICRF injection. As mentioned in the previous section, raw experiment signal data are used as inputs, and physical signal data (,,) are used as outputs.

Experimental data and modeling results are displayed together in figure 3. The comparison shows that they are in good agreement in most regions of discharge, from ramp-up to ramp-down. The slope of the ramp-up and the amplitude of the flattop are accurately reproduced by the model. The vertical dash dot lines indicate the rising and falling edges of the external auxiliary system signal and the plasma response, which show the time accuracy of the model.

Compared with experimental signals, the modeling results are more sensitive to changes in external drives. For example, after the external drive is turned off, the experimental signal continues to decrease with a fixed slope, but the modeling results show a step-down. The high sensitivity of the model is helpful to improve the fineness of the model. However, it will also cause the deviation of the modeling result and the experimental data when the external drive changes rapidly. How to adjust the sensitivity of the model is still an open question.

Figure 3: Comparison of modeling result and EAST experiment data, shot #77873 (a) and #78461 (b).

A test data set with 695 shots were used to quantitatively evaluate the reliability of the model. The similarity is quantitative measuring the correlation between experimental data and modeling data which is pearson correlation coefficient. The statistical results of the similarity between model results and the experimental data are shown in the figure 4.

Figure 4: The similarity distribution and average similarity in the test set. show the similarity distributions of (a) (b) and (c) , respectively. Figure (d) is a joint scatter plot of three parameters.

is the best performance parameters, with the similarity concentrated at more than 95%. In other words, can be considered to have been almost completely modeled. The almost similarity of is greater than 85%. is the worst performing parameter, but many of the errors are due to the plasma start-up pulse in the ramp-up segment and the plasma shutdown pulse in the ramp-down segment. However, in the ramp-up and ramp-down sections is not the key factor for the operation of the experiment.

The joint distribution of the three parameters is shown in figure

4(d). Most shots are concentrated in a limited range, which reflects the consistency of the model on three target signal. It also shows that these shots belong to the same tokamak operating mode. In other words, those points far away from the center area indicate that the experiment is running in abnormal mode. The cause of these deviations may be due to abnormal equipment conditions or different plasma confinement modes.

5 Conclusion

In the present work, we showed the possibility of modeling the tokamak discharge process using experimental data-driven methods. A machine learning model based on the LSTM was established and trained with the EAST experimental data set. This model can use the controlled input signals (i.e. NBI, ICRH, etc.) to reproduce the normal discharge process (i.e. electron density , store energy and loop voltage ) without introducing physical models. Up to 95% similarity was achieved for . The first try showed very promising results for modeling of tokamak discharge by using the data-driven methodology. This model can be easily extended to more physical quantities, and then a more comprehensive tokamak discharge model can be established. And all the controlled data can be designed in the experimental proposal stage, so the model can be used to validate the validity of the proposal.

Compared with the physically-driven method, the data-driven method can build models more efficiently. We also realize that there are many challenges before the practical application of this method. For example, the impact of model sensitivity on modeling results has been recognized. How to adjust the sensitivity of the model is still an open question. Cross-device modeling is more important for devices under design and construction such as ITER and CFETR. Introducing device configuration parameters and performing transfer learning is a feasible solution to this problem. Our next step is to model the time evolution of the one-dimensional profile and the two-dimensional magnetic surface.

The author would like to thank all the members of EAST Team for providing such a large quantity of past experimental data. The author Chenguang Wan sincerely thanks Yong Guo, Dalong Chen for explaination of experimental data, Cristina Rea, and Professor Robert Granetz for technical discussion. This work was supported by the National MCF Energy R&D Program under Contract No.2018YFE0304100 and the Comprehensive Research Facility for Fusion Technology Program of China under Contract No. 2018-000052-73-01-001228.

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