Efficient dataset construction using active learning and uncertainty-aware neural networks for plasma turbulent transport surrogate models

(2) UKAEA Culham Centre for Fusion Energy; (3) Radboud University; Aaron Ho (1); Abingdon; Bram de Leeuw (3); Cambridge; Fusion Center; Lorenzo Zanisi (2); Nathaniel T. Howard (1) ((1) MIT Plasma Science; Netherlands)

REVIEW 4 major objections 4 minor 9 references

Efficient dataset construction using active learning and uncertainty-aware neural networks for plasma turbulent transport surrogate models

T0 review · 4 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Active learning with uncertainty-aware networks can build compact tokamak turbulence surrogate datasets, reaching F1 around 0.8 and R2 around 0.75 with about ten thousand labels and beating random sampling.

desk verdict A solid, honest proof-of-principle that active learning with uncertainty-aware single models can build QuaLiKiz surrogates as efficiently as the ADEPT ensemble pipeline, with the caveat that the efficiency is only demonstrated in the same Gaussian-distributed pool used for training. read the letter →

arxiv 2507.15976 v1 pith:UFPHOAC5 submitted 2025-07-21 physics.plasm-ph cs.LG

Aaron Ho (1) , Lorenzo Zanisi (2) , Bram de Leeuw (3) , Vincent Galvan (1) , Pablo Rodriguez-Fernandez (1) , Nathaniel T. Howard (1) ((1) MIT Plasma Science , Fusion Center , Cambridge

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USA (2) UKAEA Culham Centre for Fusion Energy Abingdon UK (3) Radboud University Nijmegen Netherlands)

This is my paper · ORCID

classification physics.plasm-phcs.LG

keywords activelearninguncertainty-awareneuralnetworksplasmaturbulenttransportQuaLiKizsurrogatetokamakfusionBayesiannetworkFisher-Raodistancedatasetconstruction

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Active learning, with a physics simulator acting as the label provider, is proposed as a way to build small training sets for surrogate models of plasma turbulent transport. The paper demonstrates this on the QuaLiKiz quasilinear gyrokinetic transport code, starting from 100 labelled inputs and adding roughly 200 points per iteration over 45 iterations to reach a final set of about $10^{4}$ points. The resulting classifier and regressor networks reach $F_1$ around 0.8 and $R^2$ around 0.75 on an independent test set that follows the same distribution as the unlabelled pool, and this is better than randomly sampling an equivalently sized dataset from that pool. The relevance is that more expensive gyrokinetic codes could, in principle, be treated the same way, making surrogate training affordable at higher fidelity while replacing an ensemble of networks with a single uncertainty-aware model per output.

What carries the argument

The pipeline is built on Bayesian last layer architectures: a spectral-normalized Gaussian process classifier produces a mode-presence probability with an uncertainty output, and a Bayesian neural network with noise-contrastive prior regressor returns a mean prediction, a model-uncertainty estimate, and a data-uncertainty estimate. A custom acquisition function combines classifier uncertainty with a weighted sum of absolute and relative regressor uncertainties, and a low-discrepancy sampler generates random weight vectors so that multiple transport outputs compete fairly in a multi-objective selection. A closed-form Fisher-Rao distance metric replaces the asymmetric KL-divergence in the regressor loss, improving training robustness, and physics-based filters clean the labelled outputs before they are appended. The loop works by evaluating the current models on a random subset of a very large unlabelled pool, scoring candidates, sending the top-scoring inputs to QuaLiKiz for labelling, and growing the training set.

What would settle it

Run the identical active-learning pipeline with the unlabelled pool drawn from a uniform distribution over the same input bounds while the test set remains Gaussian, and compare final F1 and R2; the paper's own mismatch study says the Gaussian-pool/uniform-application combination collapses the regressor, so if the uncertainty-aware pipeline shows the same collapse the reported efficiency is pool-specific, and if it does not the method is more general than the paper claims.

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Extended reading notes

Core claim

The central claim is that a single-model, uncertainty-aware architecture can drive an active-learning loop that constructs a QuaLiKiz surrogate dataset about as efficiently as the earlier ensemble-based pipeline, but with only one network to train, store, and load per output variable. Starting from a 100-point seed set and adding roughly 200 labelled points per iteration over 45 iterations, the classifier-regressor pairs reach $F_1$ around 0.8 and $R^2$ around 0.75 on a test set drawn from the same distribution that generated the unlabelled pool. The paper presents this as a proof-of-principle for smaller datasets, explicitly framed as a proxy for more expensive gyrokinetic codes, and states that the final performance is notably better than random acquisition from the pool at the same dataset size.

Load-bearing premise

The load-bearing premise is that the hand-fitted multivariate Gaussian distribution used to generate the unlabelled pool describes the domain where the surrogate will actually be applied; the test set is drawn from that same distribution, and Appendix B shows regressor performance degrades sharply when the application distribution does not match the pool.

Editorial extensions

If this is right

If the claim holds, a surrogate for a costly gyrokinetic code can be trained with roughly 10,000 high-value simulator runs instead of relying on a comparably performing random dataset of the same size.
Deployment keeps one trained network per output instead of an ensemble, reducing memory, training time, and loading overhead in integrated transport solvers.
The multi-objective acquisition scheme means one active-learning campaign can simultaneously improve classification and multiple flux regressors for all three turbulence modes.
The Fisher-Rao loss replacement, if it generalizes, gives other uncertainty-aware regression models a more stable training signal in low-data regimes.
The same simulator-in-the-loop design can be ported to other expensive physics codes as long as a suitable unlabelled pool and physics filters exist.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

An implication the paper leaves implicit is that the 45-iteration schedule and fixed candidate buffer may not be the main driver of efficiency; the same pipeline with adaptive batch sizes or an adaptive acquisition-function schedule could show faster convergence, since the paper itself notes diminishing returns.
A testable extension would swap the pool distribution while holding all other components fixed; the appendix's mismatch study suggests regressors are the fragile part, so a production version should validate the pool against the target machine's expected operating space before trusting the reported numbers.
Because classifier and regressor outputs are blended, classifier errors can feed into regressor acquisition in later iterations; the paper flags this feedback risk but does not quantify it, so tracking per-iteration classifier F1 as a real-time gate could be a cheap safeguard.
The single multi-output Bayesian network experiment failing while single-output models succeed suggests the covariance information between transport channels is not captured; an explicit covariance-aware loss or a small final correlation layer would be a natural next step to recover that information.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The real news here is that the ADEPT ensemble trick can be replaced by single uncertainty-aware models: SNGP for classification, BNN-NCP for regression, with a Fisher-Rao loss replacing KL divergence and a Sobol-weighted multi-objective acquisition. That is a genuine, if incremental, advance. The paper earns credit for measuring against a random-sampling baseline, for documenting the pool construction and hyperparameters in enough detail to reproduce, and for shipping code. It also explicitly flags its own limitations: the BNN occasionally collapses, large fluxes are underpredicted, the ETG Qe channel is weak, and the classifier barely improves with dataset size. That honesty is rare and useful.

The central result holds up in-distribution: AL beats random sampling for most regressors and classifiers, reaching roughly F1=0.8 and R2=0.75 on a test set drawn from the same hand-fitted multivariate Gaussian used to generate the pool. I do not buy the stress-test claim that this invalidates the paper—it is a proof-of-principle, and the authors themselves warn that the pool must match the application domain. But the caveat is real and should be stated loudly: the headline efficiency is conditional on that match. Appendix B shows regressor collapse when the application distribution differs from a Gaussian pool, and their response (oversampling the same Gaussian to 5e8 points) does not solve the mismatch problem—it just makes the Gaussian denser. So the 'broadly defined pool' claim is overstated.

Other soft spots, in proportion: the headline metrics are single-run point estimates with no seed averaging or error bars; the ADEPT parity claim is extrapolated, not measured head-to-head; and the acquisition function hyperparameters are tuned on a validation set drawn from the same distribution, which contributes a mild circularity. None of these break the paper. The flat classifier F1 and weak ETG Qe are honestly reported and plausibly explainable.

Who should read it: anyone building surrogates for expensive plasma physics codes, and machine-learning practitioners working on active learning for scientific simulators. It deserves a serious referee. I would accept it for peer review and ask for seed-averaged results and a more honest treatment of the distribution-mismatch limitation. The core method is sound, and the paper is a legitimate upgrade to the ADEPT program rather than a new paradigm.

Referee Report

4 major / 4 minor

Summary. This paper presents a proof-of-principle active-learning pipeline for constructing training datasets for QuaLiKiz turbulent transport surrogates. It combines an SNGP classifier for instability presence with a BNN-NCP regressor for each flux channel, evaluates uncertainty-based acquisition functions over a large unlabelled pool generated from a hand-fitted multivariate Gaussian, and labels selected candidates with in-the-loop QuaLiKiz simulations. After 45 iterations growing the training set from 100 to roughly 10^4 points, the authors report F1 around 0.8 and R2 around 0.75 on a test set drawn from the same Gaussian distribution, and argue this is notably better than random sampling and extrapolates toward the earlier ADEPT ensemble approach. The paper also introduces a Fisher-Rao replacement for the KL-divergence terms in the BNN loss and a Sobol-weighted multi-objective acquisition function.

Significance. If the in-distribution result is taken at face value, the paper makes a useful contribution: it demonstrates that single-model uncertainty-aware architectures can replace deep ensembles in an active-learning loop for a high-dimensional plasma physics surrogate, with open-source code, physics-based filtering, and honest reporting of failure modes in Appendix B. The multi-objective acquisition and the Fisher-Rao based robust training loss are practical innovations. However, the headline efficiency claims are conditional on the unlabelled pool and test set sharing the same hand-fitted Gaussian, the metrics are single-run point estimates with some channels much weaker than others, and the ADEPT parity is extrapolated rather than measured. The significance is therefore that of a well-scoped proof-of-principle, not a validated general-purpose methodology.

major comments (4)

[Section 3.2 / Appendix A / Appendix B] The efficiency claim is demonstrated only in-distribution. The unlabelled pool (Section 3.2) and the test set are both drawn from the same hand-fitted multivariate Gaussian defined in Appendix A (Eqs. 18-20), and Appendix B's Figure 12 shows that when the application distribution is uniform while the pool is Gaussian, the regressor performance collapses catastrophically. Because the stated goal is a multi-machine surrogate built from a JET-fitted pool, this is a load-bearing assumption behind the Section 5 statement that the AL result is notably better than randomly sampling an equivalently sized dataset. The paper itself acknowledges this in Appendix B by advising that the high-probability region of the Gaussian must cover the application domain, but it does not remove the limitation. I request either an additional experiment measuring AL versus random sampling under a distribution shift, or a revised claim that explicitly scopes the efficiency result to the case where the pool distribution matches the application distribution.
[Section 4.1, Figures 6-7] The headline F1 around 0.8 and R2 around 0.75 are single-run point estimates with no error bars or multiple-seed variability. Figure 7 shows the classifier F1 is essentially flat as the training set grows, and Figure 6 (top right) shows the ETG Qe regressor is markedly weaker than the other channels, sometimes at or below zero. The abstract and conclusion state these metrics across all outputs, which overstates what is shown. Please report per-output final metrics, ideally with means and standard deviations over at least three to five seeds, and clarify that the summary metrics are not uniform across modes and channels.
[Section 5] The comparison with the ADEPT ensemble is extrapolative, not measured. The text says that by extrapolating the observed performance trajectory, the AL methodology appears to approach the previous ADEPT performance, and no ADEPT model is evaluated on the same test set in this paper. This extrapolation is reasonable as a discussion point, but it should be presented explicitly as an extrapolation rather than as an established equivalence. If feasible, a head-to-head comparison on a common test set would substantially strengthen the claim.
[Section 3.3 and Section 4.1] The efficiency comparison does not include an analysis of sensitivity to acquisition hyperparameters or to the manual per-iteration adjustment of the candidate buffer size. Because these choices directly affect the number and location of labels, their absence leaves open the possibility that part of the reported AL advantage over random sampling stems from these manual choices rather than from the uncertainty-aware acquisition itself. A brief sensitivity study, or at least an explicit statement of which results depend on manual tuning, would make the efficiency claim more robust.

minor comments (4)

[Figure 16 caption] The caption refers to the ion heat flux, Pi_i, but Pi_i was defined in Section 3.2 as the ion momentum flux; please correct the caption.
[Section 3.3] The sentence 'QuaLiKiz executions continued to simultaneous produce the necessary output' contains a typo; 'simultaneous' should be 'simultaneously'.
[Table 5 caption] The caption states that gamma_abs,d and gamma_rel,d are equal across channels, but the main text explains why negative values are useful; adding one sentence on this to the caption would improve readability.
[Figure 6 caption] The caption says that models with R2 <= 0 are set to zero, which visually inflates the apparent improvement; please state how many such points occur, or plot the negative values explicitly.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the AL-versus-random result is an empirical comparison on an independent, simulator-labelled test set, and the pool/test distribution match is an explicitly stated limitation rather than a definitional reduction.

full rationale

The paper's central claim—that uncertainty-aware active learning constructs more efficient QuaLiKiz surrogate training sets than random sampling—is an empirical measurement, not a derivation that reduces to its inputs. The reported F1 and R2 values are evaluated on a held-out test set of 1000 QuaLiKiz-labelled points (Section 3.3), while the acquisition function (Equations 13–16) is driven by model uncertainty outputs and Sobol-weighted multi-objective scores; the random baseline is correctly drawn from the same unlabelled pool. The multivariate Gaussian pool in Appendix A is fitted to JET-based statistics, but the surrogate targets are QuaLiKiz outputs, not values computed from that fitted distribution or from the paper's prior publications. The test set is intentionally sampled from the same distribution as the pool, and Appendix B explicitly quantifies the resulting limitation under distribution mismatch, including catastrophic regressor degradation when the application is uniform; this is an external-validity caveat, not a circular identity. Self-citations to ADEPT [27], QLKNN [17], and EuroPED-NN [57] are used as motivation, architecture choices, and baselines, but the improvement over random sampling is demonstrated with data and models produced in this study. The validation set is used to scale acquisition hyperparameters (Section 3.3), which is standard model selection and could introduce optimism, but it does not rename a fitted parameter as a prediction, and the test set remains independent. No quoted equation is equivalent to another by construction, and no fitted parameter is relabelled as a predicted result. Thus the derivation chain is self-contained for the in-distribution proof-of-principle it claims.

Assumptions & free parameters 7 free parameters · 6 assumptions · 0 invented entities

The central claim rests on the pool distribution, the fidelity of QuaLiKiz as label source, the validity of uncertainty-based acquisition, and the filters. None of these are derived from first principles; they are domain assumptions, but the paper tests the acquisition assumption against a random baseline.

free parameters (7)

Pool distribution moments (Eqs. 18-20) = Means, stds, correlations as polynomial/exponential functions of x
Manually fitted to the JET-based QuaLiKiz dataset [17]; used to generate the 5e8-point unlabelled pool. The central efficiency claim depends on this distribution matching the application domain.
Acquisition function hyperparameters (Table 5) = gamma_cls=2, gamma_reg=1e-5 to 1e-4, gamma_rel=1e4, gamma_abs,d=-0.5, gamma_rel,d=-0.5
Chosen to bring 90th percentile acquisition values to f~1 on a validation set (Section 3.3); the paper calls this an educated guess, not rigorous tuning.
Modified NLL mixing parameter gamma_s = 0.1
Introduced in Eq. (11) to stabilize BNN training; the authors state it is unclear whether it has undesired effects on uncertainty estimates.
Classifier-regressor blending threshold sigma_thr = 0.1
User-defined in Eq. (12); controls transition into stable regions and affects final flux predictions.
Physics filter thresholds (Table 2) = epsilon values 0.05, 0.1; flux caps
Post-hoc exclusion rules inherited from Ref. [17]; preferentially remove unstable points and affect which candidates enter the training set.
Candidate buffer size (manual per iteration) = 20-200 per iteration
Manually adjusted to target ~100-300 added points; this is a hand-tuned schedule.
OOD width and prior uncertainties for BNN = OOD width 0.5, epistemic/aleatoric priors 1e-3
Hyperparameters from prior BNN application [57]; calibrate model and data uncertainty terms.

assumptions (6)

domain assumption QuaLiKiz quasilinear gyrokinetic outputs are treated as ground truth for the turbulent transport fluxes and mode stability.
Section 3.2: QuaLiKiz is the in-the-loop labeller; all labels and the test set come from it. Errors in QuaLiKiz itself are not modeled.
domain assumption The 16 dimensionless input parameters fully constrain the local plasma state for electrostatic turbulence with the chosen species mix.
Table 1 and Section 3.2; the surrogate learns a function on this 16D space, implicitly assuming no unlisted physics variables matter.
domain assumption The multivariate Gaussian pool distribution fitted to JET data covers the intended application domain.
Appendix A, Eqs. (18)-(20); Appendix B shows performance degrades if the application distribution diverges from the pool, so this coverage assumption is load-bearing.
domain assumption The post-labelling physics filters remove numerical noise without removing informative signal.
Table 2, Section 3.2; filters preferentially reject unstable points and the paper notes they make dataset growth semi-stochastic.
domain assumption Model uncertainty from SNGP/BNN-NCP is a useful proxy for regions of poor predictive accuracy.
Section 3.3 acquisition functions use sigma_cls, sigma_reg; the AL-vs-random comparison supports this empirically but it remains an assumption about the architectures.
domain assumption The independent test set drawn from the same distribution as the pool measures the performance relevant to the target application.
Section 3.3 test set construction; Appendix B mitigates but does not eliminate distribution mismatch concerns.

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Cite this review

Pith. "Pith review of Efficient dataset construction using active learning and uncertainty-aware neural networks for plasma turbulent transport surrogate models." pith.science (2026). https://pith.science/paper/UFPHOAC5

@misc{pith2026250715976,
  author       = {Pith},
  title        = {Pith review of: Efficient dataset construction using active learning and uncertainty-aware neural networks for plasma turbulent transport surrogate models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UFPHOAC5}},
  note         = {Machine review of arXiv:2507.15976}
}

abstract

This work demonstrates a proof-of-principle for using uncertainty-aware architectures, in combination with active learning techniques and an in-the-loop physics simulation code as a data labeller, to construct efficient datasets for data-driven surrogate model generation. Building off of a previous proof-of-principle successfully demonstrating training set reduction on static pre-labelled datasets, using the ADEPT framework, this strategy was applied again to the plasma turbulent transport problem within tokamak fusion plasmas, specifically the QuaLiKiz quasilinear electrostatic gyrokinetic turbulent transport code. While QuaLiKiz provides relatively fast evaluations, this study specifically targeted small datasets to serve as a proxy for more expensive codes, such as CGYRO or GENE. The newly implemented algorithm uses the SNGP architecture for the classification component of the problem and the BNN-NCP architecture for the regression component, training models for all turbulent modes (ITG, TEM, ETG) and all transport fluxes ($Q_e$, $Q_i$, $\Gamma_e$, $\Gamma_i$, and $\Pi_i$) described by the general QuaLiKiz output. With 45 active learning iterations, moving from a small initial training set of $10^{2}$ to a final set of $10^{4}$, the resulting models reached a $F_1$ classification performance of ~0.8 and a $R^2$ regression performance of ~0.75 on an independent test set across all outputs. This extrapolates to reaching the same performance and efficiency as the previous ADEPT pipeline, although on a problem with 1 extra input dimension. While the improvement rate achieved in this implementation diminishes faster than expected, the overall technique is formulated with components that can be upgraded and generalized to many surrogate modeling applications beyond plasma turbulent transport predictions.

Figures

Figures reproduced from arXiv: 2507.15976 by the authors.

**Figure 1.** Representative schematic of the Bayesian last layer (BLL) architecture class, which is identical to a standard feed [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗

**Figure 2.** Loss curves for the BNN architecture training on [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

**Figure 3.** Workflow diagram outlining the general steps taken [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

Figures from the paper (12 more)

**Figure 4.** Figure 4: Sample acquisition from an AL iteration targeting [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]

**Figure 5.** Figure 5: Sample acquisition from an AL iteration targeting [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]

**Figure 6.** Figure 6: Regressor NN model performances, as measured by the [PITH_FULL_IMAGE:figures/full_fig_p016_6.png]

**Figure 7.** Figure 7: Classifier NN model performance, as measured by [PITH_FULL_IMAGE:figures/full_fig_p017_7.png]

**Figure 8.** Figure 8: Comparison of the predicted electron heat flux, [PITH_FULL_IMAGE:figures/full_fig_p018_8.png]

**Figure 9.** Figure 9: KL-divergence metric, DKL, as a function of the dataset size, ND, of the 1D parameter distributions of the ion temperature ratio, Ti/Te (left), magnetic shear, s (center), and the radial variable, x (right), computed between the constructed dataset, D, and the unlabell…

**Figure 11.** Figure 11: Performance of an ensemble of FFNN classifiers [PITH_FULL_IMAGE:figures/full_fig_p029_11.png]

**Figure 12.** Figure 12: Performance of an ensemble of FFNN regressors [PITH_FULL_IMAGE:figures/full_fig_p030_12.png]

**Figure 13.** Figure 13: Comparison of the predicted ion heat flux, [PITH_FULL_IMAGE:figures/full_fig_p030_13.png]

**Figure 14.** Figure 14: Comparison of the predicted electron particle flux, [PITH_FULL_IMAGE:figures/full_fig_p031_14.png]

**Figure 16.** Figure 16: Comparison of the predicted ion heat flux, Π [PITH_FULL_IMAGE:figures/full_fig_p032_16.png]

**Figure 17.** Figure 17: KL-divergence metric, DKL, as a function of the dataset size, ND, of the remaining 1D parameter distributions in [PITH_FULL_IMAGE:figures/full_fig_p033_17.png]

Discussion (0). Continue with ORCID to comment.

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