Data-driven plasma equilibrium forecasting in magnetic fusion tokamak

Authors: Youngwoo Cho, Semin Joung, Jaemin Seo, Young-chul Ghim, Jaegul Choo
Primary area: applications to physical sciences (physics, chemistry, biology, etc.)
Keywords: nuclear fusion, plasma equilibrium, tokamak, video prediction

Abstract:
The most promising approach to achieving nuclear fusion is through tokamaks, which confine plasma using magnetic fields.
Understanding the current plasma equilibrium state in tokamaks is critical for effective plasma control.
Unlike previous studies, which reconstruct equilibrium from magnetic field information, our work forecasts future equilibrium based on past equilibrium states.
Specifically, we formulate the plasma equilibrium prediction task as a video prediction task, a well-explored problem in the machine learning community.
This formulation allows us to capture the spatio-temporal dynamics of plasma states and provides a foundation for multimodal modeling of data streams from tokamak operations.
Our methodology, incorporating a physics-inspired learning technique for physically reliable predictions, achieved plausible results in forecasting future plasma equilibrium up to 200 ms ahead compared to baselines.
This approach holds promise for predicting plasma instabilities and preventing disruptions, marking a significant step towards developing stable fusion reactors.

Decision: reject
Reviewer scores: 3, 3, 5

Reviews and discussion:
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creation date:
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creator: reviewer_jkqe

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summary:
This paper addresses the crucial issue of predicting plasma equilibrium in tokamaks, which are essential for advancing nuclear fusion technology. The authors propose a novel method that formulates this prediction task as a video prediction problem, enabling the capture of spatio-temporal dynamics of plasma states. By applying well-established video prediction algorithms, the authors aim to forecast future plasma equilibria based on past states and achieve promising results that contribute to the understanding of plasma instabilities and control.

strengths:
The approach of framing plasma equilibrium prediction as a video prediction task is new in this area, introducing a fresh perspective to the fusion community, which has been largely focused on magnetic field data. This formulation may inspire future research in related fields. The methodology demonstrates a solid understanding of both machine learning techniques and plasma physics, with the integration of a physics-inspired loss function showing potential for improving model predictions. The paper is generally well-organized, providing a clear explanation of the background and motivations behind the research, as well as a structured presentation of methods and results.

weaknesses:
The application of existing video prediction algorithms to the specific context of plasma equilibrium is straightforward and thus may not present sufficient novelty. Further differentiation from previous works is needed to establish the unique contribution of this study.
The selection of the loss function has not been illustrated and validated sufficiently. Equation (2), which should be crucial in this paper, looks strange without an essential explanation.

questions:
1. About the loss function: Why do the authors choose the ell-1 norm, rather than the more frequently used ell-2 norm? In eq. (2), what's the difference between $\Delta^* \psi_{pred}$ and $\Delta^*(\psi_{pred})$?
2. How does the resolution of discretization affect the accuracy of the prediction?
3. Could the authors elaborate on the choice of video prediction algorithms? What specific adaptations were made to ensure compatibility with the plasma equilibrium data?
4. Are there plans to extend this method to include a wider variety of tokamak data, such as temperature profiles or density distributions?
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creator: reviewer_t2ac

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summary:
The paper introduces a machine learning forecasting technique for applications in tokamak plasma predictions.  The data are spatio-temporal fields characterizing the plasma dynamics.  The method proposed makes use of equilibrium solutions from the past to predict the future states.

strengths:
As for applications, they do propose to apply this to an important problem in physics which is difficult to do forecasting on.  Certainly the characterization of plasmas is an important and challenging data set.

weaknesses:
While I do agree that they are proposing a new method, the comparatives to other methods just aren't up to the level required for ICLR.  Only convLSTM is really compared with for forecasting.  But I would argue there should have been a much richer set of comparatives.  For instance, there is the very simply DMD method for forecasting plasma dynamics:

https://pubs.aip.org/aip/pop/article/27/3/032108/929066

The dynamics they are looking have been shown to be pretty well characterized by a linear model in many application areas.  Using all this technology without comparison to a baseline linear model does not warrant the paper to move forward.  I work in spatio-temporal dynamic systems and just don't find their results compelling enough in terms of advancing the field, nor the results so compelling in terms of the application itself.

And there are other methods that should have been applied beside convLSTM:  

ResNet (He et al 2016)
PredRNN (Wang et al 2017)

Also, completely missed for the video prediction task idea is https://www.nature.com/articles/s43588-022-00281-6

Ultimately, I just don't think either the results or their method represent an innovative enough leap (either in the ML/AI architecture proposed or in the advancement of the application) for ICLR.

I cannot recommend the paper moving forward at this point.

questions:
The baselines and comparatives are simply not good enough in my view (see above).  There are other plasma reduced order models for forecasting that are completely ignored.  In addition, the method, while clever, does not signify an significant innovation for ICLR.
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creator: reviewer_gmlx

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summary:
In this work, the author considers an application for predicting plasma equilibrium, formulated as a video prediction task. The author proposes a physics-informed learning technique built upon an existing CNN-based model. This model can forecast future plasma equilibrium up to 200 ms ahead, outperforming baseline methods.

strengths:
- The author demonstrates an important application on plasma equilibrium forecasting.
- The author generates a new dataset, which can be a contribution if published.

weaknesses:
### Method
- The paper utilizes an existing method, simVP, which should be introduced in more detail.
- The physics-informed loss using finite differences is fairly standard [1].

### Scope
- Overall, I am concerned that the paper may lack sufficient contributions from the ML perspective, making it potentially more suitable for a journal in nuclear fusion.
- Alternatively, if the dataset can be published, it might be more effective to present this work as a benchmark paper comparing existing methods.

[1] Ren, Pu, et al. "PhyCRNet: Physics-informed convolutional-recurrent network for solving spatiotemporal PDEs." *Computer Methods in Applied Mechanics and Engineering* 389 (2022): 114399.

questions:
It seems quite standard to define the task as video prediction. What was the challenge preventing previous works from doing so? It could be helpful to discuss more the contribution from formulating the problem this way.
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title:
General response (1/3)

comment:
We appreciate all three reviewers for their constructive feedback and valuable comments.

All three reviewers recognized the following strengths of our work:
* The importance of addressing the plasma equilibrium forecasting problem.
* The novel and clever formulation of this problem as a video prediction task.
* A well-organized manuscript that demonstrates solid understanding of both machine learning (ML) and plasma physics.

The primary concerns raised by the reviewers focus on the contributions of our work and the baseline experiments. In this general response, we address these concerns, while more specific points will be discussed in separate comments.

## Contribution of our work
We would like to clarify several key aspects of the novelty and contributions of our study.

The plasma equilibrium reconstruction problem in fusion research has traditionally focused on reconstructing the current equilibrium state based on current magnetic field measurements. Our study takes a fundamentally different approach by forecasting future plasma equilibrium states based on past equilibrium states, without relying on magnetic field data.

The main reason this approach has not been attempted in fusion research is that the Grad-Shafranov (GS) equation, which physically describes plasma equilibrium states, is time-independent. In other words, the GS equation is designed to reconstruct the current equilibrium state from current measurements (i.e., magnetic field data), rather than predicting future equilibrium states. While temporal dynamics of plasma are studied, the corresponding equations are significantly more complex and computationally intensive than solving the GS equation. Consequently, fusion research, including plasma control and analysis, has primarily relied on GS equation-based methodologies, which provide reasonable results over short timeframes.

In this context, our motivation was to address temporal dynamics of plasma beyond the GS equation using a data-driven approach. The main contribution of our work lies in formulating this novel problem and demonstrating its feasibility through initial results. Given the underexplored nature of this direction, we deliberately formulated the problem as an intuitive video prediction task for our experiments.

One may question why we chose to present our results at an AI/ML conference such as ICLR, rather than nuclear fusion journals. This decision was motivated by the fact that our approach is straightforward for ML researchers, as noted by reviewer gmLx. We believe that ML researchers, who are familiar with video prediction tasks and are not constrained by traditional physics approaches, can offer fresh perspectives and potentially bring significant advances to fusion research.

Indeed, the ICLR call for papers explicitly invites submissions on "applications to physical sciences," and the conference has regularly published papers in areas like materials science and bioinformatics, advancing both ML methods and these scientific domains. We believe our work, which applies data-driven approaches to fusion problems, aligns well with the scope of ICLR conference. Unlike these more established domains, fusion research remains relatively unexplored in the AI/ML community. Following the example of previous work such as Spangher et al. [1], we believe ICLR provides an ideal platform for introducing the challenges of nuclear fusion to the ML community.

We acknowledge the reviewers' concerns regarding the limited contributions from an ML perspective. To clarify, our work expands the applications of ML to the underexplored fusion domain, analyzes how existing ML-based video prediction models perform on fusion data, and identifies challenges as well as future research directions. Specifically, we introduced a GS equation-based loss function to improve prediction consistency and demonstrated the current limitations in effectively incorporating tokamak control signals (e.g., heating information) into video prediction models. These findings contribute meaningful techniques and highlight challenges in applying ML to complex physical systems.

In summary, from a fusion research perspective, our key contribution is pioneering the prediction of future plasma equilibrium states and formulating this as a video prediction task. From an ML perspective, we contribute by extending ML applications to an underexplored scientific domain, demonstrating its feasibility, and establishing directions for future research.

[1] Spangher et al., “Position: Opportunities Exist for Machine Learning in Magnetic Fusion Energy”, ICML (2024), https://proceedings.mlr.press/v235/spangher24a.html
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title:
Paper revision

comment:
Based on the reviewers' feedback, **we have updated our manuscript** to better address their comments and concerns.

The main changes are summarized as follows:
* Enhanced clarity on our contribution and novelty.
* Revised GS-constraint loss equation with additional explanations.
* Added additional baselines, including DMD, Chronos, PredRNN, and PredRNNv2, with detailed descriptions and comparative analysis.
* Incorporated citations to the two papers suggested by the reviewers.

For your convenience, ***all the updated parts in the manuscript are highlighted in pink***.

We kindly invite you to review the revised manuscript for further details and the complete experimental results. We hope these revisions and our responses sufficiently address the reviewers' concerns. Any additional comments or suggestions would be greatly appreciated.
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Metareview:
metareview:
The authors present results on predicting the future plasma state in tokamak experiments from past state, which they claim is an advance beyond previous work on reconstructing current state from magnetic measurements. The reviewers agreed that the baseline comparisons were too limited for an ML venue, while the topic was potentially too far afield and more appropriate for a fusion journal. Additionally, the authors entirely ignore the field of physics-based forward equilibrium evolution. Forward evolutive solvers such as FGE (e.g. _Development of free-boundary equilibrium and transport solvers for simulation and real-time interpretation of tokamak experiments_, F. Carpanese 2021) are sufficiently mature that they can be used for model predictive control and deep reinforcement learning. Yet the authors don't even acknowledge the existence of these tools, let alone compare against them, which makes it unclear what if any advantage these tools would have over existing physics-based simulation approaches. I recommend against acceptance.