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Multi-Task Deep Learning for Surface Metrology

D. Kucharski, A. Gaska, T. Kowaluk, K. Stepien, M. Repalska, B. Gapinski, M. Wieczorowski, M. Nawotka, P. Sobecki, P. Sosinowski, J. Tomasik, A. Wojtowicz

TL;DR

This work develops a reproducible deep learning framework for surface metrology that jointly predicts surface texture parameters and their reported uncertainties across multiple instruments. It combines deterministic predictors with probabilistic heads (quantile and heteroscedastic) and post-hoc conformal calibration to yield calibrated uncertainty intervals, while addressing negative transfer by favoring single-target models. The approach achieves high fidelity for Ra, Rz, and RONt and robust uncertainty for Ra_uncert and Rz_uncert, with RONt_uncert remaining challenging due to cross-instrument heterogeneity. The results enable calibrated, decision-relevant predictions for instrument selection and acceptance in metrological workflows, and the authors provide a reproducible open bundle for cross-lab deployment.

Abstract

A reproducible deep learning framework is presented for surface metrology to predict surface texture parameters together with their reported standard uncertainties. Using a multi-instrument dataset spanning tactile and optical systems, measurement system type classification is addressed alongside coordinated regression of Ra, Rz, RONt and their uncertainty targets (Ra_uncert, Rz_uncert, RONt_uncert). Uncertainty is modelled via quantile and heteroscedastic heads with post-hoc conformal calibration to yield calibrated intervals. On a held-out set, high fidelity was achieved by single-target regressors (R2: Ra 0.9824, Rz 0.9847, RONt 0.9918), with two uncertainty targets also well modelled (Ra_uncert 0.9899, Rz_uncert 0.9955); RONt_uncert remained difficult (R2 0.4934). The classifier reached 92.85% accuracy and probability calibration was essentially unchanged after temperature scaling (ECE 0.00504 -> 0.00503 on the test split). Negative transfer was observed for naive multi-output trunks, with single-target models performing better. These results provide calibrated predictions suitable to inform instrument selection and acceptance decisions in metrological workflows.

Multi-Task Deep Learning for Surface Metrology

TL;DR

This work develops a reproducible deep learning framework for surface metrology that jointly predicts surface texture parameters and their reported uncertainties across multiple instruments. It combines deterministic predictors with probabilistic heads (quantile and heteroscedastic) and post-hoc conformal calibration to yield calibrated uncertainty intervals, while addressing negative transfer by favoring single-target models. The approach achieves high fidelity for Ra, Rz, and RONt and robust uncertainty for Ra_uncert and Rz_uncert, with RONt_uncert remaining challenging due to cross-instrument heterogeneity. The results enable calibrated, decision-relevant predictions for instrument selection and acceptance in metrological workflows, and the authors provide a reproducible open bundle for cross-lab deployment.

Abstract

A reproducible deep learning framework is presented for surface metrology to predict surface texture parameters together with their reported standard uncertainties. Using a multi-instrument dataset spanning tactile and optical systems, measurement system type classification is addressed alongside coordinated regression of Ra, Rz, RONt and their uncertainty targets (Ra_uncert, Rz_uncert, RONt_uncert). Uncertainty is modelled via quantile and heteroscedastic heads with post-hoc conformal calibration to yield calibrated intervals. On a held-out set, high fidelity was achieved by single-target regressors (R2: Ra 0.9824, Rz 0.9847, RONt 0.9918), with two uncertainty targets also well modelled (Ra_uncert 0.9899, Rz_uncert 0.9955); RONt_uncert remained difficult (R2 0.4934). The classifier reached 92.85% accuracy and probability calibration was essentially unchanged after temperature scaling (ECE 0.00504 -> 0.00503 on the test split). Negative transfer was observed for naive multi-output trunks, with single-target models performing better. These results provide calibrated predictions suitable to inform instrument selection and acceptance decisions in metrological workflows.
Paper Structure (18 sections, 1 equation, 11 figures, 6 tables)

This paper contains 18 sections, 1 equation, 11 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Contributions.
  3. Method
  4. Data set and augmentation
  5. Problem formulation
  6. Baseline deterministic models
  7. Quantile regression
  8. Heteroscedastic Gaussian regression
  9. Conformal prediction
  10. Stacking experiments
  11. Calibration (temperature scaling)
  12. Evaluation metrics
  13. Implementation and reproducibility
  14. Results
  15. Classification performance
  16. ...and 3 more sections

Figures (11)

  • Figure 1: Reference roughness specimen used in constructing the measurement database
  • Figure 2: Mock-up fixture with mounted pyramidal and cylindrical samples (varied materials and machining parameters) used for multi-instrument acquisition
  • Figure 3: Representative network architecture (multi-output trunk with specialised heads or single-target pyramidal narrowing)
  • Figure 4: Classifier network architecture: pyramidal multi-layer perceptron (e.g. 512-256-128-64) with batch normalisation and dropout after dense layers, feeding a softmax output over instrument classes. This schematic complements the regression architecture (Fig. \ref{['fig:arch_multi']}) to provide visual parity across tasks
  • Figure 5: Confusion matrix of the calibrated classification model (system type prediction)
  • ...and 6 more figures