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arxiv: 2411.02740 · v5 · submitted 2024-11-05 · 💻 cs.LG · cond-mat.mtrl-sci· physics.app-ph· physics.comp-ph· physics.data-an

An information-matching approach to optimal experimental design and active learning

Yonatan Kurniawan (1) , Tracianne B. Neilsen (1) , Benjamin L. Francis (2) , Alex M. Stankovic (3) , Mingjian Wen (4) , Ilia Nikiforov (5) , Ellad B. Tadmor (5) , Vasily V. Bulatov (6)
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Vincenzo Lordi (6) Mark K. Transtrum (1 2 3) ((1) Brigham Young University Provo UT USA (2) Achilles Heel Technologies Orem (3) SLAC National Accelerator Laboratory Menlo Park CA (4) University of Electronic Science Technology of China Chengdu China (5) University of Minnesota Minneapolis MN (6) Lawrence Livermore National Laboratory)
This is my paper

Pith reviewed 2026-05-23 18:11 UTC · model grok-4.3

classification 💻 cs.LG cond-mat.mtrl-sciphysics.app-phphysics.comp-phphysics.data-an
keywords information matchingoptimal experimental designactive learningFisher Information Matrixquantities of interestsloppy parametersconvex optimization
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The pith

An information-matching criterion selects training data that constrain only the parameters needed for quantities of interest.

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

The paper introduces an information-matching criterion based on the Fisher Information Matrix to select the most informative training data from a candidate pool. Models often contain many unidentifiable parameters, yet quantities of interest typically depend on fewer parameter combinations. The criterion ensures selected data supply enough information to learn only those relevant combinations. Formulated as a convex optimization problem, the method scales to large models and is demonstrated in power systems, underwater acoustics, and active learning for material science, where small optimal datasets suffice for precise predictions.

Core claim

The central claim is that an information-matching criterion based on the Fisher Information Matrix selects the most informative training data from a candidate pool such that the selected data contain sufficient information to learn only those parameters that are needed to constrain downstream QoIs; the criterion is formulated as a convex optimization problem.

What carries the argument

The information-matching criterion based on the Fisher Information Matrix, which matches the information content of candidate data points to the information required to constrain the QoIs.

If this is right

  • A relatively small set of optimal training data suffices to achieve precise QoI predictions.
  • The convex formulation makes the selection scalable to large models and datasets.
  • The criterion serves as an effective query function inside active learning loops.
  • The approach applies across modeling problems in power systems, underwater acoustics, and material science.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Experimental costs could drop in domains where each measurement is expensive.
  • The same logic might apply to other domains that rely on sloppy models, such as chemical kinetics.
  • Integration into large-scale machine-learning pipelines could reduce the data volume needed for downstream tasks.

Load-bearing premise

Models often contain many unidentifiable sloppy parameters while quantities of interest depend on a relatively small number of parameter combinations.

What would settle it

A controlled test in which data chosen by the information-matching criterion produce worse QoI prediction accuracy than randomly chosen data of equal size, when both are used to train the same model.

Figures

Figures reproduced from arXiv: 2411.02740 by 2, (2) Achilles Heel Technologies, 3) ((1) Brigham Young University, (3) SLAC National Accelerator Laboratory, (4) University of Electronic Science, (5) University of Minnesota, (6) Lawrence Livermore National Laboratory), Alex M. Stankovic (3), Benjamin L. Francis (2), CA, Chengdu, China, Ellad B. Tadmor (5), Ilia Nikiforov (5), Mark K. Transtrum (1, Menlo Park, Mingjian Wen (4), Minneapolis, MN, Orem, Provo, Technology of China, Tracianne B. Neilsen (1), USA, UT, Vasily V. Bulatov (6), Vincenzo Lordi (6), Yonatan Kurniawan (1).

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: as buses are highlighted in different colors based on their respective areas. Notably, there are overlaps (double-highlighted buses) between optimal PMU place￾ments for full and (the union of) three subnetworks, while non-overlapping locations are a consequence of enforcing observability for each of the subnetworks separately. Next, we consider an optimal sensor placement prob￾lem in passive acoustic sourc… view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p013_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p016_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p017_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p018_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p021_5.png] view at source ↗
read the original abstract

The efficacy of mathematical models heavily depends on the quality of the training data, yet collecting sufficient data is often expensive and challenging. Many modeling applications require inferring parameters only as a means to predict other quantities of interest (QoI). Because models often contain many unidentifiable (sloppy) parameters, QoIs often depend on a relatively small number of parameter combinations. Therefore, we introduce an information-matching criterion based on the Fisher Information Matrix to select the most informative training data from a candidate pool. This method ensures that the selected data contain sufficient information to learn only those parameters that are needed to constrain downstream QoIs. It is formulated as a convex optimization problem, making it scalable to large models and datasets. We demonstrate the effectiveness of this approach across various modeling problems in diverse scientific fields, including power systems and underwater acoustics. Finally, we use information-matching as a query function within an Active Learning loop for material science applications. In all these applications, we find that a relatively small set of optimal training data can provide the necessary information for achieving precise predictions. These results are encouraging for diverse future applications, particularly active learning in large machine learning models.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 4 minor

Summary. The manuscript proposes an information-matching criterion derived from the Fisher Information Matrix to select training data for optimal experimental design and active learning. The approach exploits model sloppiness by ensuring selected data constrain only the low-dimensional parameter combinations needed to predict downstream quantities of interest (QoIs), rather than all parameters. It is formulated as a convex optimization problem and demonstrated on applications in power systems, underwater acoustics, and active learning for materials science, where small optimal datasets suffice for precise QoI predictions.

Significance. If the central claims hold, the work provides a scalable, QoI-focused alternative to standard OED that can reduce data collection costs in sloppy models common across scientific domains. The convex formulation and cross-field demonstrations (power systems, acoustics, materials) are strengths that support potential adoption in active learning pipelines for large models. The emphasis on matching information content to QoI sensitivity rather than full identifiability is a clear conceptual advance over conventional D-optimal or A-optimal designs.

minor comments (4)
  1. Abstract: the statement that 'a relatively small set of optimal training data can provide the necessary information for achieving precise predictions' should be supported by explicit quantitative metrics (e.g., QoI error reduction factors or confidence interval widths) rather than qualitative description.
  2. The integration of the information-matching query function into the active learning loop (final application) would benefit from a pseudocode listing or explicit comparison against standard uncertainty-sampling baselines to clarify the incremental benefit.
  3. Notation: the distinction between the full Fisher Information Matrix and the projected QoI-relevant submatrix should be introduced with consistent symbols early in the methods section to avoid reader confusion when moving between the convex program and the application results.
  4. Figure captions for the application results should include the size of the candidate pool and the fraction of data selected, to allow direct assessment of data efficiency claims.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive summary and significance assessment of our manuscript, as well as for recommending minor revision. We appreciate the recognition that our information-matching approach provides a scalable, QoI-focused alternative to standard OED for sloppy models.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper proposes an information-matching criterion based on the Fisher Information Matrix, formulated as a convex optimization problem to select training data that constrains only the parameter combinations relevant to downstream QoIs. This builds directly on the standard observation of sloppy models and low-dimensional QoI dependence, which is an external premise from the literature rather than a self-derived input. No equations or steps in the provided abstract reduce by construction to fitted parameters or self-citations; the method is presented as a scalable formulation with demonstrations across independent applications (power systems, acoustics, materials) serving as external checks. The derivation chain remains self-contained against established optimal experimental design benchmarks without load-bearing self-referential reductions.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Approach rests on standard statistical assumptions about the Fisher Information Matrix and the premise of sloppy models; no free parameters, invented entities, or ad-hoc axioms are identifiable from the abstract.

axioms (2)
  • domain assumption The Fisher Information Matrix captures the relevant information content of data for model parameters.
    Core premise of the proposed criterion, standard in statistics.
  • domain assumption Quantities of interest depend on a relatively small number of parameter combinations in models with many unidentifiable parameters.
    Explicitly stated in the abstract as the motivation for the method.

pith-pipeline@v0.9.0 · 5897 in / 936 out tokens · 39169 ms · 2026-05-23T18:11:05.624951+00:00 · methodology

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