🔬 physics

The Fusion Equilibrium Challenge: Inferring Magnetic Geometry Without Magnetic Diagnostics

The Fusion Equilibrium Challenge introduces a new open-access benchmark dataset and competition for the NeurIPS community to develop machine learning models that accurately reconstruct plasma equilibrium parameters using only non-magnetic diagnostics, addressing the critical need for robust equilibrium inference in future neutron-rich fusion reactors.

Original authors: Tapan Ganatma Nakkina, Matthew Waller, Craig Michoski, Brian Sammuli, David R. Hatch, William Boyes, Mitchell Clark, Raffi Nazikian, Sterling Smith

Published 2026-09-03

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Tapan Ganatma Nakkina, Matthew Waller, Craig Michoski, Brian Sammuli, David R. Hatch, William Boyes, Mitchell Clark, Raffi Nazikian, Sterling Smith

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

For half a century, the quest to harness the power of the stars has relied on a delicate dance of invisible forces. Inside the doughnut-shaped machines known as tokamaks, superheated gas called plasma is held in place by powerful magnetic fields, preventing it from touching the walls and cooling down. To keep this fusion reaction stable and safe, engineers must constantly know the exact shape and position of the plasma. Traditionally, they have done this by placing magnetic sensors on the walls of the machine to feel the magnetic field lines. However, the next generation of fusion reactors, designed to produce net energy, will operate in an environment so filled with high-energy neutrons that these sensors will likely fail or be destroyed. If the sensors die, the machine loses its eyes, and without knowing the shape of the plasma, the reactor cannot be controlled.

This looming problem has sparked a new challenge for the scientific community: can we teach computers to "see" the shape of the plasma using only the information that will survive the harsh reactor environment? A team of researchers has launched a competition to find the answer, inviting experts in artificial intelligence to solve a difficult puzzle. They have gathered a massive collection of data from two existing fusion machines, one in California and one in the United Kingdom, and asked participants to build a system that can reconstruct the entire two-dimensional structure of the plasma using only electrical currents and measurements of heat and density, completely ignoring the magnetic sensors.

The challenge, known as the Fusion Equilibrium Challenge, is built on a simple but profound idea. In a fusion reactor, the shape of the plasma is determined by the balance between the pressure of the hot gas and the magnetic forces holding it. While magnetic sensors have been the standard way to measure this balance, the researchers realized that the electrical currents used to create the magnetic fields, combined with direct measurements of the plasma's temperature and density, contain enough information to figure out the shape without ever touching a magnetic sensor. The goal is to create a digital model that can predict the plasma's configuration in real-time, a capability that will be essential for the future of clean energy.

To test this idea, the organizers assembled a curated dataset containing over eleven thousand distinct experimental runs, or "shots," from two very different types of fusion machines. The first machine, DIII-D, is a conventional design with a large central column and a plasma shape that looks like a letter D. The second, MAST, is a spherical tokamak with a much thinner central column and a plasma that wraps around it like a kidney bean. These two machines are topologically distinct, meaning their shapes and the way the magnetic fields wrap around them are fundamentally different. The dataset includes detailed records of the electrical currents in the coils surrounding the machines and the electron temperature and density profiles measured by a laser-based diagnostic tool called Thomson scattering. Crucially, the magnetic sensor data was stripped away for the purpose of the challenge, forcing the participants to rely solely on the remaining inputs.

The task for the participants is to take these non-magnetic inputs and reconstruct a two-dimensional map of the magnetic flux, which essentially acts as a blueprint for the plasma's shape. From this map, the system must also deduce specific numbers that describe the plasma's stability and energy content. The researchers are not just looking for a rough guess; they require a high-fidelity reconstruction that can accurately locate the outer boundary of the plasma, the center of the magnetic field, and the overall volume of the gas. The evaluation is rigorous: the computer's prediction is compared against the known truth from the original experiments, and the score is based on how closely the predicted shape matches the actual shape, as well as how well the derived numbers align with reality.

What makes this challenge particularly difficult is the requirement for the solution to work across different machines. A model trained on the data from the DIII-D machine must be able to apply what it has learned to the MAST machine without any additional training. This "zero-shot" transfer is the ultimate test of whether the artificial intelligence has learned the underlying physics of fusion or if it has simply memorized the specific quirks of one device. Early tests with simple methods showed that a straightforward approach failed miserably when moving from one machine to the other, dropping in accuracy from a high level to near zero. This suggests that the problem requires a deep understanding of the universal laws governing plasma, rather than just pattern matching.

The organizers have provided a set of baseline models to help participants get started, ranging from simple statistical tools to more complex neural networks. These baselines serve as a starting point, demonstrating that while the problem is hard, it is not impossible. The competition is structured in two phases, with a public leaderboard allowing teams to track their progress against a hidden test set. The ultimate goal is to identify a method that can serve as a backup system for current machines if their sensors fail, and as the primary control system for future reactors where magnetic sensors cannot survive.

The implications of a successful solution extend far beyond the competition itself. If machine learning can reliably infer the state of the plasma without magnetic diagnostics, it could revolutionize how fusion reactors are operated. It would provide a robust safety net for current experiments and pave the way for the construction of commercial power plants that are immune to the radiation damage that plagues traditional sensors. By forcing the scientific community to confront the loss of a century-old diagnostic tool, this challenge is pushing the boundaries of what artificial intelligence can achieve in the realm of complex physical systems. It asks a fundamental question: can a computer learn the language of the stars well enough to keep the fire burning, even when the traditional tools of measurement are gone? The answer, if found, will be a critical step toward a future powered by fusion energy.

Technical Summary: The Fusion Equilibrium Challenge

Problem Statement

The paper addresses a critical operational bottleneck for next-generation magnetic confinement fusion reactors (e.g., SPARC, ARC, CFETR). These devices will operate in extreme neutron environments where traditional magnetic sensors (Mirnov coils, pickup loops, Rogowski coils) suffer severe degradation due to radiation-induced electromotive force and conductivity, as well as structural transmutation. Consequently, the standard method for reconstructing plasma equilibrium—the Grad–Shafranov solution via codes like EFIT—becomes infeasible because it relies heavily on magnetic flux loop and pickup coil data.

The core challenge is an inverse problem: reconstruct the two-dimensional poloidal flux function $\psi(R, Z)$ and key scalar equilibrium parameters using only non-magnetic diagnostics. Specifically, the challenge requires inferring the equilibrium state from:

External poloidal-field coil currents.
Thomson-scattering electron temperature ( $T_e$ ) and density ( $n_e$ ) profiles.

This task is complicated by the need for cross-machine generalization. The solution must work not only on the training machine (DIII-D, a conventional D-shaped tokamak) but also transfer "zero-shot" to a topologically distinct machine (MAST, a spherical tokamak with a kidney-bean plasma profile and a hollow central column), where simple coil-mapping transfers fail catastrophically.

Methodology and Data Infrastructure

Dataset and Curation

The organizers have released the first open-access, harmonized multi-machine benchmark for fusion equilibrium reconstruction.

Sources: Data is drawn from the DIII-D National Fusion Facility (General Atomics) and the MAST (Culham Centre for Fusion Energy).
Scale: The dataset contains 9,113 DIII-D shots and 2,416 MAST shots (filtered for Thomson diagnostic availability and EFIT reconstruction quality).
Format: Data is stored in single-row Parquet files containing nested NumPy arrays. Each shot includes:
- Targets: EFIT flux maps ( $\psi$ ) at $\sim313$ (DIII-D) or $\sim77$ (MAST) time steps per shot.
- Inputs: Coil currents (18 F-coils + ECOILA for DIII-D; 10 P-coils + solenoid for MAST), Thomson scattering profiles (core and edge), and machine-specific geometry (coil positions, chord locations).
- Constraints: Only diverted plasma timeslices are included to ensure the Last Closed Flux Surface (LCFS) is defined by magnetic topology rather than wall contact.
Tools: A cross-platform desktop application, the Data Fusion Labeler (dFL), is provided to visualize flux maps, coil currents, and Thomson profiles interactively.

Evaluation Metrics

The scoring system is designed to prevent "gaming" via scalar-only predictions. Participants submit the flux map $\hat{\psi}$ and two scalars ( $q_{95}$ and $\beta_N$ ) that cannot be derived from $\psi$ alone. All other metrics are derived from the submitted flux map by the scorer using the same functional applied to the ground truth.

The composite intra-machine score ( $S_{model}$ ) is a weighted sum of four terms:

Flux Reconstruction Accuracy ( $R^2_\psi$ ): Coefficient of determination over the $(R, Z)$ grid (Weight: 0.55).
Predicted-Scalar Fidelity ( $R^2_{q95, \beta_N}$ ): Accuracy of the submitted $q_{95}$ and $\beta_N$ (Weight: 0.15).
LCFS Alignment ( $D_{LCFS}$ ): Normalized symmetric Hausdorff distance between the true and predicted LCFS contours (Weight: 0.10).
Flux-Map Consistency: Agreement of seven derived geometric scalars (magnetic axis, elongation, triangularity, volume, internal inductance) calculated from the submitted flux vs. ground truth (Weight: 0.20).

A secondary metric, Generalization Ratio ( $G_{ratio}$ ), measures the fraction of DIII-D performance retained when the model is applied zero-shot to MAST.

Baselines

Four reference baselines are provided to establish performance floors:

PCA + Ridge: Linear mapping of coil currents to PCA coefficients of flux maps.
PCA + Gradient Boosted Trees: Captures non-linear coil coupling.
MLP on PCA Targets: A 3-layer fully connected network predicting PCA coefficients.
Convolutional Decoder: An encoder-decoder architecture mapping inputs to a 65x65 flux grid.

Key Contributions

First Open Multi-Machine Benchmark: The paper transitions tokamak equilibrium reconstruction from a closed-access institutional task to a standardized, open-science benchmark, releasing a curated dataset of over 11,000 shots.
Novel Challenge Design:
- Non-Magnetic Inference: Explicitly removes magnetic signals, forcing models to learn the physics of the Grad–Shafranov equation from kinetic and coil data alone.
- Topologically Distinct Transfer: The DIII-D (D-shape) to MAST (spherical/kidney-bean) transfer serves as a rigorous stress test for machine-agnostic learning, where simple coil-mapping transfer fails (SSIM drops from 0.83 to 0.10).
- Consistency-Based Scoring: By deriving all geometric parameters from the submitted flux map, the challenge ensures that a model cannot achieve high scores by predicting scalars independently of the physical flux surface.
Reactor-Ready Pipeline: The challenge is framed as a direct path to developing primary equilibrium inference pipelines for reactor-class devices where magnetic diagnostics are unreliable.

Results and Claims

The paper does not present a winning solution but rather establishes the framework and baselines for the NeurIPS competition.

Baseline Performance: The linear PCA + Ridge baseline achieves an SSIM of 0.84 on a small demo set in under 0.1 seconds, suggesting that linear approximations capture significant variance. However, the simple coil-mapping transfer baseline collapses on MAST (SSIM $\approx$ 0.10), highlighting the difficulty of cross-machine generalization.
Feasibility: The organizers assert that the challenge is solvable, noting that the "compute-light" baselines (Ridge, small CNN) can train in under two hours on a single GPU/CPU, making the problem accessible to a broad range of participants.
Scientific Goal: The paper claims the challenge will determine if machine learning can learn a universal representation of plasma equilibrium that survives the loss of magnetic diagnostics, moving beyond device-specific engineering minutiae to capture fundamental physics.

Significance

The paper positions this challenge as a pivotal step toward reactor-ready equilibrium inference. Its significance lies in three areas:

Operational Resilience: Providing a backup estimator for current machines when magnetic sensors fail and a primary inference path for future reactors where such sensors may not survive.
Physics Discovery: Testing whether learned models can capture the universal physics of the Grad–Shafranov equation rather than overfitting to the specific geometry of a single device.
Community Building: Creating a standardized, open platform to accelerate the integration of scientific machine learning (physics-informed networks, neural operators) into fusion energy research, bridging the gap between the fusion-ML subcommunity and the broader scientific ML community.

The challenge is explicitly framed as a benchmark for research, not a deployment-ready system, with a focus on reproducibility, uncertainty quantification, and ethical compliance.