Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Fine Tuning a Simulation-Driven Estimator

Braghadeesh Lakshminarayanan, Margarita A. Guerrero, Cristian R. Rojas

TL;DR

This paper tackles the calibration of high-fidelity simulators (digital twins) when the true parameters fall outside the training range, causing out-of-distribution errors in simulation-driven estimators. It proposes a transfer-learning style fine-tuning approach that preserves the first-stage feature extractor of the Two-Stage estimator while updating only the final layers, triggered by a feature-space OOD detector. The method combines a Gauss–Newton update to refine the estimate, a confidence ellipsoid plus sensitivity-based sampling to generate a targeted synthetic dataset, and a final-layer retraining to improve accuracy in OOD scenarios. Numerical studies on the Van der Pol oscillator and cascaded water tanks demonstrate substantial gains over pretrained TS and competitive performance with baseline methods, at the cost of additional computational overhead for data generation and fine-tuning.

Abstract

Many industries now deploy high-fidelity simulators (digital twins) to represent physical systems, yet their parameters must be calibrated to match the true system. This motivated the construction of simulation-driven parameter estimators, built by generating synthetic observations for sampled parameter values and learning a supervised mapping from observations to parameters. However, when the true parameters lie outside the sampled range, predictions suffer from an out-of-distribution (OOD) error. This paper introduces a fine-tuning approach for the Two-Stage estimator that mitigates OOD effects and improves accuracy. The effectiveness of the proposed method is verified through numerical simulations.

Fine Tuning a Simulation-Driven Estimator

TL;DR

This paper tackles the calibration of high-fidelity simulators (digital twins) when the true parameters fall outside the training range, causing out-of-distribution errors in simulation-driven estimators. It proposes a transfer-learning style fine-tuning approach that preserves the first-stage feature extractor of the Two-Stage estimator while updating only the final layers, triggered by a feature-space OOD detector. The method combines a Gauss–Newton update to refine the estimate, a confidence ellipsoid plus sensitivity-based sampling to generate a targeted synthetic dataset, and a final-layer retraining to improve accuracy in OOD scenarios. Numerical studies on the Van der Pol oscillator and cascaded water tanks demonstrate substantial gains over pretrained TS and competitive performance with baseline methods, at the cost of additional computational overhead for data generation and fine-tuning.

Abstract

Many industries now deploy high-fidelity simulators (digital twins) to represent physical systems, yet their parameters must be calibrated to match the true system. This motivated the construction of simulation-driven parameter estimators, built by generating synthetic observations for sampled parameter values and learning a supervised mapping from observations to parameters. However, when the true parameters lie outside the sampled range, predictions suffer from an out-of-distribution (OOD) error. This paper introduces a fine-tuning approach for the Two-Stage estimator that mitigates OOD effects and improves accuracy. The effectiveness of the proposed method is verified through numerical simulations.

Paper Structure

This paper contains 17 sections, 22 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Problem Statement
  3. The Two-Stage (TS) Estimator
  4. Fine-Tuning the TS Estimator
  5. Step 1: Feature–Space OOD Detector
  6. Step 2: Synthetic data generation
  7. Gauss--Newton update
  8. Sampling procedure
  9. Step 3: Final–Layer Transfer on a Targeted Set
  10. Simulation Study
  11. Common settings
  12. Feature compression and stage-2 network.
  13. Van der Pol Oscillator
  14. Remark on choosing $\alpha$
  15. Cascaded Water Tanks
  16. ...and 2 more sections

Figures (4)

  • Figure 1: VDP (OOD $\mu=3.0$): ground-truth vs. mean predictions over $100$ MC runs. The trajectory plots are measurements without noise.
  • Figure 2: VDP (OOD $\mu=5.0$): ground-truth vs. mean predictions over $100$ MC runs. The trajectory plots are measurements without noise.
  • Figure 3: Tanks (OOD 1): average trajectory (ground truth vs. mean predictions over $100$ MC runs. The trajectory plots are measurements without noise.
  • Figure 4: Tanks (OOD 2): average trajectory (ground truth vs. mean predictions over $100$ MC runs. The trajectory plots are measurements without noise.

Theorems & Definitions (1)

  • Remark III.1