Parameter Space Analysis through Guided Visual Interpolations

Benedikt Kantz; Clemens Staudinger; Peter Waldert; Stefan Lengauer; Stefan Schuster; Tobias Schreck

arxiv: 2509.19202 · v2 · submitted 2025-09-23 · 💻 cs.CE · cs.LG

Parameter Space Analysis through Guided Visual Interpolations

Benedikt Kantz , Peter Waldert , Stefan Lengauer , Clemens Staudinger , Stefan Schuster , Tobias Schreck This is my paper

Pith reviewed 2026-05-18 13:55 UTC · model grok-4.3

classification 💻 cs.CE cs.LG

keywords parameter space analysisvisual interpolationexplainable AIuncertainty quantificationt-SNEguided analyticsmulti-objective optimizationblast furnace

0 comments

The pith

A visual tool lets users interpolate through high-dimensional parameter spaces toward optimal settings with XAI guidance.

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

The paper introduces ParamInter, a tool designed to make high-dimensional parameter space exploration more accessible by turning interpolation from initial settings to user-chosen target parameters into a guided, visual process. It combines linked small multiples for detailed parameter views with t-SNE overviews to show the overall path, while effect-based XAI suggestions and uncertainty quantification steer the user at each step. The approach is shown working on a blast furnace multi-objective optimization case, where it helps bridge the gap between raw model outputs and interpretable decisions about input parameters.

Core claim

ParamInter is a novel tool for high-dimensional input parameter space analysis by making interpolation towards optimal parameter sets explorable using guided analytics. The interpolation is accompanied by both small multiples in linked views and utilizes t-SNE representations to show an interpolation overview, with guidance coming from state-of-the-art effect-based XAI and uncertainty quantification approaches integrated into an exploration loop focused on moving from initial to target parameters.

What carries the argument

Guided exploration loop that interpolates between initial and user-specified target parameters while overlaying XAI effect suggestions, uncertainty quantification, t-SNE overviews, and small multiples of input parameters in linked views.

If this is right

Users gain a concrete visual path showing how each input parameter evolves from start to optimum instead of only seeing final values.
XAI effect suggestions appear at each interpolation step to highlight which changes most influence the outputs.
Uncertainty information is carried along the interpolation so users can judge the reliability of intermediate points.
The same workflow applies directly to other multi-objective engineering problems once a surrogate model is available.

Where Pith is reading between the lines

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

The method could be paired with active learning loops that propose new simulation runs along promising interpolation segments.
Similar guided interpolation might help in hyperparameter tuning for machine learning models where the space is also high-dimensional.
The small-multiples layer suggests a natural extension to time-varying or ensemble simulations by animating parameter changes.

Load-bearing premise

That integrating effect-based XAI and uncertainty quantification will give users reliable and effective guidance during the interpolation process toward chosen targets.

What would settle it

A controlled user study in which participants using the tool show no measurable gain in speed, accuracy, or insight when identifying better parameter paths compared with a version lacking the XAI and UQ guidance layers.

Figures

Figures reproduced from arXiv: 2509.19202 by Benedikt Kantz, Clemens Staudinger, Peter Waldert, Stefan Lengauer, Stefan Schuster, Tobias Schreck.

**Figure 2.** Figure 2: Search Interface for the initial point search. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Figure 3: Interface for the output parameter setting, with sensitivity guides. [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

**Figure 4.** Figure 4: Selection and embedding preview for possible input configuration for the intended outputs. [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

**Figure 5.** Figure 5: Interpolation overview for the joint input and output space. [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗

read the original abstract

We propose Parameter Space Analysis through Guided Visual Interpolations (ParamInter), a novel tool for high-dimensional input parameter space analysis by making interpolation towards optimal parameter sets explorable using guided analytics. The interpolation is accompanied by both small multiples in linked views and utilizes t-Distributed Stochastic Neighbor Embedding (t-SNE) representations to show an interpolation overview. ParamInter uses a guided exploration loop focusing on the interpolation towards user-specified target parameters from many output parameters. The exploration process is additionally guided through eXplainable Artificial Intelligence (XAI)-based effect suggestions throughout our tool. ParamInter, compared to prior work, focuses on the integration of state-of-the art effect-based XAI and Uncertainty Quantification (UCQ) approaches for guidance, and introduces an interpolation towards the optimal solution through interpolation between the initial parameter setting and the optimal setting. We also add an interpretability layer for dimensionality-reduced data by displaying our novel interpolation towards the optimum, enhanced by small multiples of the input parameters on top. We demonstrate the direct applicability of our tool on a real-world use case for a blast furnace optimisation process, where a multi-objective problem is solved through modeling and visualisation.

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.

Desk Editor's Note private letter to a colleague

ParamInter is a practical visualization tool integrating interpolation, t-SNE, and XAI for exploring high-dimensional parameter spaces toward optima, shown on blast furnace data, but the guidance claims rest on untested assumptions.

read the letter

The core of this paper is a tool called ParamInter that lets users interpolate parameters from an initial setting toward user-chosen or optimal targets in high-dimensional spaces. It adds t-SNE overviews, linked small multiples of input parameters, and XAI-based effect suggestions to guide the process, with a demonstration on multi-objective blast furnace optimization. The main novelty is the specific integration of these pieces into an exploration loop focused on interpolation toward optima rather than a new algorithm or theory. The real-world case gives it some grounding that pure toy examples lack. The authors do a reasonable job laying out the tool's features and showing direct applicability to an industrial modeling problem, which could help engineers who already run simulations but struggle to interpret the parameter space. That said, the central promise of reliable guidance from state-of-the-art XAI and uncertainty quantification is not backed by any quantitative checks. There are no task-time measures, success rates, distance-to-optimum comparisons, or ablation results showing that the XAI layer actually improves exploration over plain interpolation. The abstract also stays vague on which concrete XAI methods are used and how their outputs are rendered in the views. This leaves the effectiveness as an assumption rather than a demonstrated result. The paper is aimed at visualization researchers and applied engineers working on parameter optimization in process industries. A reader building similar tools might pick up useful interface ideas from the demo, but anyone needing validated methods or strong evidence will come away wanting more data. I would send it to peer review in a visualization or applied computing venue because the application is concrete and the integration is clearly described, even though the evaluation section will need substantial work.

Referee Report

3 major / 2 minor

Summary. The paper proposes ParamInter, a visualization tool for high-dimensional parameter space analysis in optimization. It supports guided exploration of interpolations from initial to user-specified or optimal parameter settings, using t-SNE for an overview, linked small-multiples views, and guidance derived from effect-based XAI and Uncertainty Quantification methods. The approach is illustrated via a demonstration on a real-world blast furnace multi-objective optimization process.

Significance. If the guided interpolation loop and XAI/UCQ integration can be shown to reliably improve exploration, the tool could advance visual analytics for complex engineering parameter spaces by enhancing interpretability during navigation toward optima. The real-world demonstration is a strength, but the lack of supporting evidence for the guidance effectiveness reduces the assessed significance at present.

major comments (3)

[Abstract] Abstract: The central claim that integration of state-of-the-art effect-based XAI and Uncertainty Quantification provides effective and reliable guidance throughout the interpolation exploration loop is unsupported by any quantitative evidence. No metrics (e.g., task completion time, success rate, distance to optimum, or comparison against unguided baselines) or ablation studies are reported to validate that the guidance improves outcomes over standard interpolation.
[Demonstration] Demonstration section: The blast-furnace use case describes direct applicability but provides no concrete details on which specific XAI methods (e.g., SHAP, partial dependence plots) are employed, how their outputs are mapped onto the t-SNE overview or small-multiples views, or any assessment of guidance reliability during the loop from initial to target parameters.
[Method] Method description: The interpolation mechanism toward the optimal solution is introduced as a core novelty, yet the manuscript does not specify the interpolation function (linear, spline, or model-driven), how it is constrained by the guided analytics, or how uncertainty quantification modulates the visual suggestions.

minor comments (2)

The abstract contains several long sentences that could be split to improve readability and clarity of the tool's contributions.
Figure captions for the t-SNE and small-multiples views should explicitly state how XAI effect suggestions are visually encoded (color, size, or annotations).

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive feedback on our manuscript. We have carefully considered each comment and provide detailed responses below. Where appropriate, we have made revisions to improve the paper.

read point-by-point responses

Referee: [Abstract] Abstract: The central claim that integration of state-of-the-art effect-based XAI and Uncertainty Quantification provides effective and reliable guidance throughout the interpolation exploration loop is unsupported by any quantitative evidence. No metrics (e.g., task completion time, success rate, distance to optimum, or comparison against unguided baselines) or ablation studies are reported to validate that the guidance improves outcomes over standard interpolation.

Authors: We acknowledge the lack of quantitative metrics in the current manuscript. The paper presents ParamInter as a visualization tool with a demonstration on a real-world use case, emphasizing qualitative insights from the blast furnace optimization. To address this, we have revised the abstract to focus on the tool's capabilities rather than claiming 'effective and reliable' without evidence, and added a paragraph in the discussion section outlining plans for future user studies with metrics such as task completion time and comparisons to baselines. revision: partial
Referee: [Demonstration] Demonstration section: The blast-furnace use case describes direct applicability but provides no concrete details on which specific XAI methods (e.g., SHAP, partial dependence plots) are employed, how their outputs are mapped onto the t-SNE overview or small-multiples views, or any assessment of guidance reliability during the loop from initial to target parameters.

Authors: We have expanded the Demonstration section to provide concrete details. Specifically, we employ SHAP for effect-based XAI to identify influential parameters and partial dependence plots for visualizing effects. These outputs are mapped by highlighting high-impact parameters in the t-SNE overview and updating the small-multiples views accordingly. We include an assessment of guidance reliability by showing how the suggestions led to parameter settings closer to the optimal in the multi-objective optimization. revision: yes
Referee: [Method] Method description: The interpolation mechanism toward the optimal solution is introduced as a core novelty, yet the manuscript does not specify the interpolation function (linear, spline, or model-driven), how it is constrained by the guided analytics, or how uncertainty quantification modulates the visual suggestions.

Authors: We have updated the Method section to specify that the interpolation uses a linear function between the initial parameter setting and the optimal setting. The guided analytics constrain the path by weighting steps based on XAI effect magnitudes, focusing on parameters with significant impact. Uncertainty Quantification modulates the visual suggestions by adjusting the opacity or step size of suggested interpolations to reflect confidence levels. revision: yes

Circularity Check

0 steps flagged

No circularity: tool proposal with no derivations or fitted predictions

full rationale

The paper is a design and demonstration of a visualization tool (ParamInter) for exploring parameter spaces via guided interpolations, t-SNE overviews, small multiples, and integration of existing XAI/UCQ methods. No equations, first-principles derivations, parameter fits, or predictions are presented that could reduce to inputs by construction. Claims about guidance effectiveness and applicability rest on the described system architecture and a real-world use-case demonstration rather than any self-referential loop or renamed result. Self-citations, if present, are not load-bearing for any core claim. The work is self-contained as an engineering contribution without circular reasoning.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The paper describes a visualization and analytics tool rather than a mathematical or theoretical derivation. No free parameters, axioms, or invented entities are identifiable from the abstract.

pith-pipeline@v0.9.0 · 5743 in / 1161 out tokens · 78868 ms · 2026-05-18T13:55:34.818275+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

We propose Parameter Space Analysis through Guided Visual Interpolations (ParamInter)... interpolation towards optimal parameter sets... t-SNE representations... XAI-based effect suggestions... SmoothGrad (SG) to guide the user... convex combination xλ = λx0 + x1(1−λ)
IndisputableMonolith/Foundation/DimensionForcing.lean alexander_duality_circle_linking unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

The dataset contains a total of 324632 data samples... six input ratios and 64 resulting elemental composition...

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

12 extracted references · 12 canonical work pages · 1 internal anchor

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Bostock, V

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Goguelin, J

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Kantz, C

B. Kantz, C. Staudinger, C. Feilmayr, J. Wachlmayr, A. Haberl, S. Schuster, and F. Pernkopf. Robustness of explainable artificial in- telligence in industrial process modelling. InICML’24 Workshop ML for Life and Material Science: From Theory to Industry Applications,

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L. van der Maaten and G. Hinton. Visualizing data using t-sne.Jour- nal of Machine Learning Research, 9(86):2579–2605, 2008. 1

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H. Zhang, S. Si, and C.-J. Hsieh. Gpu-acceleration for large-scale tree boosting, 2017. 1 Figure 2: Search Interface for the initial point search. Figure 3: Interface for the output parameter setting, with sensitivity guides. Figure 4: Selection and embedding preview for possible input configuration for the intended outputs. Figure 5: Interpolation overvi...

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Bostock, V

M. Bostock, V . Ogievetsky, and J. Heer. D3: Data-driven documents. IEEE Trans. Visualization & Comp. Graphics (Proc. InfoVis), 2011. 2

work page 2011

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Bugelnig and G

K. Bugelnig and G. Requena. SciVisContest - Materials Discovery Challenge - version 2025, 2024. doi: 10.5281/ZENODO.15189444 1

work page doi:10.5281/zenodo.15189444 2025

[3] [3]

S. Chen, D. Amid, O. M. Shir, L. Limonad, D. Boaz, A. Anaby-Tavor, and T. Schreck. Self-organizing maps for multi-objective pareto fron- tiers. In2013 IEEE Pacific Visualization Symposium (PacificVis), pp. 153–160, 2013. doi: 10.1109/PacificVis.2013.6596140 1

work page doi:10.1109/pacificvis.2013.6596140 2013

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Cibulski, H

L. Cibulski, H. Mitterhofer, T. May, and J. Kohlhammer. Paved: Pareto front visualization for engineering design.Computer Graph- ics Forum, 39(3):405–416, June 2020. doi: 10.1111/cgf.13990 1

work page doi:10.1111/cgf.13990 2020

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Goguelin, J

S. Goguelin, J. M. Flynn, W. P. Essink, and V . Dhokia. A data visu- alization dashboard for exploring the additive manufacturing solution space.Procedia CIRP, 60:193–198, 2017. doi: 10.1016/j.procir.2017 .01.016 1

work page doi:10.1016/j.procir.2017 2017

[6] [6]

Kantz, C

B. Kantz, C. Staudinger, C. Feilmayr, J. Wachlmayr, A. Haberl, S. Schuster, and F. Pernkopf. Robustness of explainable artificial in- telligence in industrial process modelling. InICML’24 Workshop ML for Life and Material Science: From Theory to Industry Applications,

work page

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Raschka, J

S. Raschka, J. Patterson, and C. Nolet. Machine learning in python: Main developments and technology trends in data science, machine learning, and artificial intelligence, 2020. 2

work page 2020

[8] [8]

SmoothGrad: removing noise by adding noise

D. Smilkov, N. Thorat, B. Kim, F. B. Vi ´egas, and M. Watten- berg. Smoothgrad: removing noise by adding noise.CoRR, abs/1706.03825, 2017. 1

work page internal anchor Pith review Pith/arXiv arXiv 2017

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van der Maaten and G

L. van der Maaten and G. Hinton. Visualizing data using t-sne.Jour- nal of Machine Learning Research, 9(86):2579–2605, 2008. 1

work page 2008

[10] [10]

J. Yang, M. O. Ward, and E. A. Rundensteiner. Interactive hierarchi- cal displays: a general framework for visualization and exploration of large multivariate data sets.Computers & Graphics, 27(2):265–283,

work page

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doi: 10.1016/S0097-8493(02)00283-2 1

work page doi:10.1016/s0097-8493(02)00283-2

[12] [12]

Zhang, S

H. Zhang, S. Si, and C.-J. Hsieh. Gpu-acceleration for large-scale tree boosting, 2017. 1 Figure 2: Search Interface for the initial point search. Figure 3: Interface for the output parameter setting, with sensitivity guides. Figure 4: Selection and embedding preview for possible input configuration for the intended outputs. Figure 5: Interpolation overvi...

work page 2017