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Stream-Based Active Learning with Cooperative Neural Networks for Data-Efficient Partial Inverse Design: An Automotive Glass Run Channel Case Study

Agung Nugraha, Hyerin Kwon, Heungjun Im, Gian Antariksa, Jihwan Lee

arXiv:2610.09848v1cs.LGcs.AI

TL;DR

Partial inverse design must infer unspecified variables under fixed constraints, while costly labels limit data acquisition. CoNN-AL adds stream-based active learning to cooperative neural networks, and on an automotive glass run channel dataset, 20,000 actively selected samples reach near-upper-bound performance with a potential 98% reduction in simulation effort versus exhaustive labeling.

  • Problem

    Partial inverse design with predetermined variables lacks an integrated stream-based acquisition approach that reduces labeling costs under realistic engineering constraints.

    Source: §1 · pp. 1–2

  • Method

    CoNN-AL uses Monte Carlo dropout uncertainty in a cooperative surrogate to decide in real time whether to query or discard each incoming candidate.

    Source: §1 · p. 3

  • Results

    With 20,000 actively selected samples, CoNN-AL reaches near-upper-bound performance, corresponding to a potential reduction of approximately 98% in simulation effort relative to exhaustive labeling.

    Source: §5 · p. 18

  • Takeaways & Limitations

    The GRC dataset is publicly released as a large-scale benchmark to support reproducibility and future research on data-driven inverse design.

    Source: §5 · p. 18

    The study evaluates only the deterministic CoNN-DAE variant and uses MC-Dropout as its sole uncertainty estimator, which may misrepresent predictive uncertainty.

    Source: §5 · p. 18

Abstract

from arXiv · show

Inverse design in engineering often runs into a simple problem. Each labeled training sample must be produced through expensive simulation, so building a large dataset is slow and costly. This study addresses that problem for partial inverse design, where only some design variables are specified and the rest must be inferred to reach a target performance value. We propose CoNN-AL, a framework for data-efficient partial inverse design that adds stream-based active learning to the Cooperative Neural Network with Denoising Autoencoder (CoNN-DAE). The model estimates predictive uncertainty through Monte Carlo dropout and uses it to decide, in real time, which incoming candidate samples are worth labeling, so the limited labeling budget is spent on the most informative designs. We validate the framework on a real-world automotive glass run channel dataset of more than 900,000 unique simulated designs. With only 20,000 actively selected labels, about 2.3% of the training pool, CoNN-AL reaches R-squared values of 0.967 to 0.982 across all missing-variable levels, approaching the upper-bound models trained on far more data. It reaches R-squared of at least 0.95 with 30 to 40% fewer labels than random sampling at the more difficult missing-variable levels and, at the most challenging level, is the only strategy in this study to reach R-squared of 0.98. Together with this work, we publicly release the dataset to support future research on data-driven design.

1 Introduction

Engineering inverse design relies on costly forward simulation, and partial inverse design must infer unspecified variables while respecting preset constraints. This study addresses the gap between constrained partial inverse design and stream-based, uncertainty-guided label acquisition with CoNN-AL.

1 Introduction

  • Repeated finite element analyses make conventional engineering design computationally intensive and time-consuming, particularly across large, nonlinear, high-dimensional design spaces.Data-driven models have been investigated as lower-cost approximations of simulation outcomes.Source: §1 · p. 1
  • Partial inverse design must infer unspecified variables while honoring those fixed by manufacturing, operational, material, or regulatory constraints.Prior work introduced a cooperative surrogate-imputation framework for this problem, while Bayesian approaches can be computationally demanding for complex, high-dimensional, or large-data settings.Source: §1 · pp. 1–2
  • Prior partial inverse design assumes a sufficiently large labeled dataset, while prior active-learning inverse design is predominantly pool-based and assumes freely selectable design variables.The paper identifies their intersection—stream-based acquisition for constrained partial inverse design—as unaddressed by prior work.Source: §1 · pp. 2–3
  • CoNN-AL integrates stream-based active learning with CoNN, using Monte Carlo dropout uncertainty to decide in real time whether to query or discard incoming candidates.The framework is evaluated on a real-world automotive glass run channel dataset with more than 900,000 samples, and the dataset is publicly released.Source: §1 · p. 3

2 Methodology

The methodology combines CoNN-DAE, which reconstructs missing design variables while predicting target performance, with stream-based active learning that selects incoming samples for labeling using predictive uncertainty.

2 Methodology

  • CoNN-AL pairs CoNN-DAE with stream-based active learning, using predictive uncertainty to select informative samples for labeling.The architecture and acquisition loop are illustrated in Figures 1 and 2.Source: §2 · p. 3

2.1 Cooperative Neural Network (CoNN-DAE)

  • CoNN-DAE jointly trains a surrogate and imputation network, balancing reconstruction accuracy against performance fidelity.The surrogate's performance-loss gradients guide imputations toward designs whose predicted output matches the target.Source: §2.1 · pp. 3–4, Figure 1 · p. 5
  • The imputer combines corrupted designs with a missingness mask, decodes full designs within observed feature bounds, and restores the known entries.The mask distinguishes genuinely zero-valued features from variables that were masked.Source: §2.1 · p. 4

2.2 Stream-Based Active Learning

  • Incoming designs arrive sequentially, and MC-Dropout estimates predictive uncertainty for each sample in real time.Figure 2 depicts the stream-based acquisition loop.Source: §2.2 · p. 6, Figure 2 · p. 6
  • High-variance samples are queried from the FEA oracle, while low-uncertainty samples are discarded; newly labeled samples join the pool for fine-tuning over repeated rounds.This focuses labeling on informative regions rather than redundant samples in well-understood regions.Source: §2.2 · p. 6

3 Experiment Setup

Experiments use a shared model, preprocessing, and evaluation pipeline to support fair comparisons across training strategies.

3 Experiment Setup

  • All experiments share the same model, preprocessing, and evaluation pipeline for fair comparison across training strategies.The section covers the dataset, problem formulation, model architecture, experimental protocol, and evaluation metrics.Source: §3 · p. 7

3.1 Dataset

The GRC dataset combines more than 900,000 simulated designs with 12 grouped design variables and sealing force as the output. The section also describes how the data are partitioned and standardized for evaluation.

3.1 Dataset

  • The combined dataset contains 906,215 unique designs: 885,735 original records plus 20,480 newly simulated samples.The dataset is publicly available under a CC BY-NC-SA 4.0 license; shared design variables are standardized, while sealing force remains in N/dm.Source: §3.1 · p. 7
  • Each record has 12 design variables in Lip, Notch, and Design groups, with sealing force (N/dm) as the output.The output represents GRC sealing effectiveness under the specified finite element analysis conditions.Source: §3.1 · p. 7
  • The data are split into 886,215 training samples and a fixed, non-overlapping test set of 20,000 samples.Input and output standardization statistics are computed from the training pool; the shared standardized inputs are rounded to three decimals.Source: §3.1 · p. 7
  • The dataset’s scale supports upper-bound benchmarking and evaluation of active learning across different levels of missing-variable difficulty.The design variables are standardized in the shared dataset, while the sealing-force output remains in its original unit.Source: §3.1 · pp. 7–8

3.2 Problem Formulation

Partial inverse design infers unspecified design variables so a completed design meets a target sealing force. The formulation varies both how many variables are missing and which variables are missing.

3.2 Problem Formulation

  • Partial inverse design reconstructs unspecified variables so a completed design achieves the desired sealing force.Some parameters may be fixed by engineering constraints, manufacturing requirements, or regulatory standards.Source: §3.2 · p. 8
  • A binary mask marks known variables as 1 and variables to infer as 0; each sample has a randomly selected missing-variable count and pattern.MM sets the maximum number missing, from MM=1 to MM=6 out of 12 variables; higher levels increase task difficulty.Source: §3.2 · p. 8

3.3 Evaluation Configuration

The evaluation uses CoNN-DAE throughout and compares upper-bound, random-sampling, and stream-based active-learning protocols. The comparisons examine performance and label efficiency across missing-variable levels.

3.3.1 Upper-Bound Benchmark

  • Upper-bound benchmarks train CoNN-DAE for 100 epochs on subsets of 100,000 samples and the full 886,215-sample training pool.These models provide reference performance at each MM level.Source: §3.3.1 · p. 8

3.3.2 Random Sampling Baseline

  • Random-sampling learning curves use subsets from 10,000 to 100,000 labels in 10,000-sample increments, trained for 100 epochs at each MM level.This passive acquisition baseline measures performance as randomly selected training data increase.Source: §3.3.2 · p. 9

3.3.3 Stream-Based Active Learning

  • Stream-based active learning starts with 3,000 labeled samples and adds 1,000 labels per round from each 3,000-candidate batch.It queries the 750 most uncertain candidates and 250 random candidates, using MC-Dropout with T=20; the remaining 2,000 are discarded. Models are fine-tuned for 10 epochs per round, and 100 rounds yield about 103,000 labels.Source: §3.3.3 · p. 9

3.3.4 Label Efficiency Analysis

  • Label-efficiency comparisons use matched budgets of 20,000 labels and about 76,000 labels, with threshold-based label counts assessed at MM=6.The approximately 76,000-label checkpoint is compared with the best random-sampling result and upper-bound models.Source: §3.3.4 · p. 9

3.4 Evaluation Metrics

The study evaluates performance with five complementary metrics on a held-out test set, reporting results separately for each missing-variable level.

3.4 Evaluation Metrics

  • Five complementary metrics are computed on the 20,000-sample held-out test set and reported separately for MM=1 through MM=6.Table 2 summarizes the evaluation metrics and their definitions.Source: §3.4 · p. 9, Table 2 · p. 9

4 Results and Discussion

CoNN-DAE approaches its performance ceiling with 100,000 labels, while stream-based active learning reaches near-upper-bound performance with substantially fewer labels. Across the reported comparisons, active learning improves label efficiency and remains effective as the number of missing variables increases.

4.1 Upper-Bound Benchmark Performance

  • R2 values of 0.97–0.99 at both training sizes indicate performance saturation at 100,000 labels, nearly an order of magnitude below the full dataset.The radar chart compares MSE, MAE, sMAPE, and R2 for 100,000 and 886,215 labels across MM levels.Source: §4.1 · p. 10, Figure 4 · p. 11

4.2 Random Sampling Baseline

  • Random-sampling curves plateaued around 40,000 samples, with R2 values from 0.968 (MM=5) to 0.985 (MM=1) at that checkpoint.Random sampling required 20,000 labels to reach R2 ≥0.95 at MM=2–6, compared with 10,000 at MM=1.Source: §4.2 · pp. 10–11, Figure 7 · p. 13

4.3 Stream-Based Active Learning

  • Active learning reached R2 ≥0.95 with 30–40% fewer labels than random sampling at MM=2–6, while the strategies were comparable at MM=1.Across all MM levels, round 18 produced R2 values of 0.967–0.982 using 20,000 labels.Source: §4.3 · pp. 13–14, Figure 8 · p. 14
  • R2 values of 0.967–0.982 across MM levels were achieved with 20,000 active-learning labels, about 2.3% of the full pool, approaching upper-bound performance.The round-18 scatter plots show predictions close to the identity line across MM=1–6.Source: §4.3 · p. 14, Figure 9 · p. 15
  • Round 74 (76,000 labels) was an efficient stopping point: later acquisition brought no further improvement and MM=6 R2 declined about 1.3 percentage points.This checkpoint reduced labeling by approximately 91% versus the full pool and 24% versus the 100,000-sample upper-bound budget, without sacrificing predictive quality.Source: §4.3 · pp. 14–15, Figure 10 · p. 15

4.4 Label Efficiency and Comparative Analysis

  • At MM=6 and 20,000 labels, active learning reached R2 0.970 versus random sampling’s 0.958, approaching the 0.974 and 0.976 upper-bound results.Active-learning MSE was 0.030 versus 0.042 for random sampling.Source: Figure 11 · p. 16, §4.4 · p. 16
  • At MM=6, active learning reached R2 = 0.98 with 76,000 labels, while random sampling did not reach that threshold within 100,000 labels.At R2 = 0.96 and 0.97, active learning required 15,000 and 20,000 labels, respectively, versus 30,000 and 40,000 for random sampling.Source: §4.4 · pp. 16–17, Table 3 · p. 17

R2 Threshold Random Sampling Active Learning Efficiency Ratio

CoNN-AL reaches strong performance with a small actively selected label set and reduces the labels needed to meet R2 thresholds in harder missing-mask settings. At MM=6, it also reaches a level no other strategy in the study attained.

R2 Threshold Random Sampling Active Learning Efficiency Ratio

  • 20,000 actively selected labels (2.3% of the training pool) achieved R2 values of 0.967–0.982 across all MM levels, approaching upper-bound performance.At the harder MM levels, 11,000–14,000 labels reached R2 ≥0.95, 30–40% fewer than random sampling.Source: R2 Threshold Random Sampling Active… · p. 17
  • At MM=6, CoNN-AL was the only strategy in this study to reach R2 = 0.98.At 76,000 labels it achieved R2 = 0.9838 and MSE = 0.0164, with slightly higher R2 and substantially lower MSE than random sampling at 60,000 and upper-bound models at 100,000 and 886,215.Source: R2 Threshold Random Sampling Active… · p. 17
  • In the GRC engineering context, integrating active learning with CoNN-DAE is the only approach in the study to reach R2 = 0.98, highlighting its potential value for efficient data-driven partial inverse design.Assuming simulation cost scales approximately with labeled-sample count, potential cost reductions are about 91% at 76,000 labels and about 98% at 20,000 labels relative to the full training pool of 886,215 samples.Source: R2 Threshold Random Sampling Active… · p. 17

5 Conclusion

The study combines stream-based active learning with CoNN-DAE for partial inverse design and evaluates it on a large automotive glass run channel dataset. CoNN-AL performs strongly with few labels, while the study identifies limits in its uncertainty estimation and single-output scope.

5 Conclusion

  • CoNN-AL applies Monte Carlo dropout to CoNN-DAE to estimate uncertainty and guide real-time query-or-discard decisions as unlabeled candidates arrive in a stream.The evaluation used a real-world glass run channel dataset of more than 900,000 CATIA-designed and MSC Marc-simulated samples.Source: §5 · p. 18
  • 20,000 labels (2.3% of the pool) achieved R2 values of 0.967–0.982 across MM levels; 11,000–14,000 labels reached R2 ≥0.95, 30–40% fewer than random sampling at harder levels.At MM=6, CoNN-AL alone reached R2 = 0.98, a level random sampling did not reach within 100,000 labels.Source: §5 · p. 18
  • At MM=6, 76,000 active labels achieved MSE 0.0164, about 37% below the best random result at 60,000 labels, although MAE remained slightly higher than in compared models.The active-learning result also surpassed upper-bound models trained on 100,000 and 886,215 samples in MSE.Source: §5 · p. 18
  • The study estimates that 20,000 actively selected samples could reduce simulation effort by approximately 98% versus exhaustive labeling, and releases the GRC dataset as a benchmark for future research.The cost estimate is specific to the glass run channel context, where each labeled sample requires CATIA modeling and MSC Marc evaluation.Source: §5 · p. 18
  • The evaluation is limited to CoNN-DAE with a deterministic autoencoder, MC-Dropout as its sole uncertainty estimator, and a single scalar sealing-force output.The authors note that generative variants, deep ensembles, multi-output objectives, and other engineering domains remain directions for future work.Source: §5 · pp. 18–19
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