Demonstration of ideas from scientific machine learning and informed ML
Tokamaks are donut-shaped magnetic-confinement fusion devices that keep plasma stable using strong magnetic fields. These plasmas can undergo disruptions-rapid loss of confinement events that can dump heat and induce forces on the vessel and first-wall components, risking serious damage if not mitigated [1,2,3]. On large devices (e.g., JET/ITER-like walls), disruptions and runaway-electron events pose substantial load and operational constraints [4,5].
If operators can detect impending or ongoing disruption states (ideally, the type of disruption) with enough lead time, mitigation systems (e.g., impurity injection) can trigger to limit damage [1]. Historically, real-time prediction/avoidance has relied on hand-crafted features and thresholds, plus classical ML (SVM/Random Forest/GBMs) integrated into control systems on several machines [6–10]. Deep-learning predictors and transfer-learning across devices are active research fronts [7,9,11].
Why "informed" classification? Many disruptive/nominal regimes have partial physics models, but real-time deployment can be constrained by missing physics or computational cost. Nominal plasma behavior is described by MHD/equilibrium theory (e.g., Grad–Shafranov) [12,13], while for statistical time-series modeling, Gaussian processes (GPs) are a flexible way to encode priors over trajectories [14,15].
In reality, we rarely have complete knowledge about the trajectories our dynamic system's states come from. If we knew nothing, it's clear that a traditional discriminative approach would be the best choice (NN, SVM, Random Forest, ...). If we knew the conditional distributions of nominal and disrupted/anomalous states, the optimal choice would be to use those as a Bayes classifier [16]. But what if we only knew the distribution of one state? Partial knowledge of a time-varying mean vector based on known physics? The covariance of the two states over time?
The question this repo explores is: when does using approximate knowledge about the conditional distributions beat generic discriminative baselines? This aims to cut at an ongoing question in hybrid-ML (physics-/knowledge-informed), particularly for disruption prediction for nuclear fusion devices.
We study a controlled two-class time-series classification problem that mirrors “nominal vs disrupted” plasma states:
- Two hidden states generate length-T trajectories:
- Nominal: a finite-time Gaussian process with mean μA(t) and covariance ΣA.
- Disrupted: a finite-time Gaussian process with mean μB(t) and covariance ΣB.
- We can sample labeled trajectories from each class and wish to predict the class of a new trajectory.
- We then vary how much of the true generative structure we "know" and compare to a purely discriminative baseline.
As a sanity check: if you knew the true class-conditional distributions, the Bayes classifier attains the minimal achievable error (Bayes risk) [17,18].
We sweep the spectrum from "oracle knowledge" to "no prior knowledge":
-
Bayes (oracle) - uses the true
$\mu_A,\Sigma_A$ and$\mu_B,\Sigma_B$ to compute class-conditional likelihoods and the Bayes decision rule. This is the optimal classifier. -
Informed generative models (fitted GPs) — we estimate parts of the generative structure from data:
- FittedGaussianModel: estimate both mean and covariance for each class (μ̂, Σ̂).
- FittedMeanGaussianModel: estimate only means; use true covariance of the underlying process.
- FittedCovGaussianModel: assume the mean; estimate covariances.
These form a family of Informed Classifier classifiers; performance tracks the quality of μ̂, Σ̂.
-
Discriminative baseline - a standard SVM (RBF) trained on trajectories (with simple normalization/whitening). This represents no physics prior and serves as a control.
How much partial generative knowledge is enough to consistently outperform a generic discriminative model?
By sweeping what we fit (mean only, cov only, both) and the size of the labeled dataset, we chart where informed Informed Classifier wins versus an SVM.
We generate synthetic time-series under two GPs:
- Nominal uses an RBF-dominant kernel with small noise.
- Disrupted uses a higher-variance kernel and added short-range structure (e.g., periodic/RQ component) to mimic extra spectral content and variability.
See informed_classification/generative_models.py for exact kernels and sampling. The GP kernel zoo is inspired by Distill’s GP visual exploration [19].
The GIFs below animate progressive fits of the informed models.
Row-normalized confusion matrices on the held-out validation set (rows = true class, columns = predicted class).
| Oracle Bayes (true GP) | Informed Classifier (fitted GP) | SVM baseline |
|---|---|---|
 |
 |
 |
How to read these: diagonal = correct predictions; off-diagonal = misclassifications.
Typical pattern we observe:
- Oracle Bayes is near-identity (upper-left/lower-right bright), setting the ceiling.
- Fitted GP (Informed Classifier) approaches the oracle as mean/covariance estimates improve with more data.
- SVM baseline tends to confuse classes when separability is primarily in covariance rather than mean differences; whitening helps but doesn’t fully close the gap.
Takeaways (see report for more details):
- The oracle Bayes is the optimal classifier and sets the performance ceiling.
- When the GP fit is not ill-conditioned due to low data, fitted generative models often outperform SVM, especially when classes differ primarily in covariance structure (a classic weak spot for margin methods on raw trajectories).
- Normalization helps SVM, but when separability is mostly in covariance, the informed models have a clear edge.
- As data grows and the fitted
$\hat\mu,\hat\Sigma$ improve, Informed Classifier approaches the oracle.
Python
Install Poetry:
curl -sSL https://install.python-poetry.org | POETRY_VERSION=1.3.2 python -Install informed_classification:
poetry install
Run tests:
poetry run pytest
First generate the data:
poetry run python scripts/gen_data.py --config config_filename_in_config_dir
Then run the script to evaluate the models based on the generated data:
poetry run python scripts/evaluate_{MODEL_CLASS}.py --config config_filename_in_config_dir
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