Efficient Global Multi Parameter Calibration for Complex System Models Using Machine-Learning Surrogates - Efficient global optimization pipeline

Aug 3, 2026

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Multi-parameter calibration of complex, high-computation Modelica system models is addressed by replacing an expensive parameter-space screening stage with a computationally efficient machine-learning surrogate. The approach trains a Physics Enhanced Latent Space Variational Autoencoder (PELS-VAE) using data generated by the Modelica model, guided by sensitivity analysis with Sobol indices to focus on influential parameters. The surrogate provides strong initial values for a subsequent gradient-based polishing step using the original physical model, reducing reliance on extensive model calls while improving robustness over common optimization strategies.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages14

Reading Time35 min

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Introduction

Multi-parameter calibration challenges in Modelica models

Combined surrogate screening and local polishing approach

Background and theory

Variational autoencoders

Global sensitivity analysis with Sobol indices

Method overview

PELS-VAE surrogate training with limited data

Global optimization screening and gradient-based polishing

Efficient Global Multi Parameter Calibration for Complex System Models Using Machine-Learning Surrogates Julius Aka 1,2 Johannes Brunnemann 1 Svenne Freund2 Arne Speerforck2 1 XRG Simulation GmbH, {aka,[brunnemann}@xrg-simulation.de](brunnemann}@xrg-simulation.de) 2 Hamburg University of Technology, {julius.aka,svenne .freund,[arne.speerforck}@tuhh.de](arne.speerforck}@tuhh.de) Abstract In this work, we address challenges associated with multi parameter calibration of complex system models of high computational expense. We propose to replace the Modelica Model for screening of parameter space by a computational effective Machine-Learning Surrogate, followed by polishing with a gradientbased optimizer coupled to the Modelica Model. Our results show the advantage of this approach compared to common-used optimization strategies. We can resign on determining initial optimization values while using a small number of Modelica model calls, paving the path towards efficient global optimization. The Machine Learning Surrogate, namely a Physics Enhanced Latent Space Variational Autoencoder (PELS-VAE), is able to capture the impact of most influential parameters on small training sets and delivers sufficiently good starting values to the gradient-based optimizer. In order to make this paper self-contained, we give a sound overview to the necessary theory, namely Variational Autoencoders and Global Sensitivity Analysis with Sobol Indices. Keywords: Sensitivity Analysis, Sobol-Indices, Variational Autoencoders, VAE, Physics-Enhanced Latent Space Variational Autoencoder, PELS-VAE, Model Calibration, Global Optimization, Machine Learning Surrogate 1 Introduction To enable model based investigation of ”real world”technical systems the underlying Modelica system models can quickly grow in size and computational expense. When they are applied in extensive parameter studies, in particular for model calibration or model based optimization, computation becomes a resource intensive task: if the objective function cannot be decomposed into submodel dependencies but depends on the model as a ’whole’, then also the whole model needs to be simulated. In practice optimization based on such models is limited to a few varied parameters and to local, gradient based optimization algorithms. If the modeller has sufficient knowledge on the model, reason- able choices of relevant parameters as well as starting points for the local optimization algorithm can be made from experience. But for complex models this empirical approach may suffer from overlooking parameters and the optimization algorithm running into local minima of the objective function due to the chosen starting points in parameter space. In this paper we address these issues with a combined approach: A Machine Learning Model, namely a Physics Enhanced Latent Space Variational Autoencoder (PELS-VAE) (Martínez-Palomera, Bloom, and Abrahams 2020; Zhang and Mikelsons 2022) is trained on data generated by the Modelica model. It captures the dependencies of model output to the most influential parameters, determined by a preceding sensitivity analysis (Sobol 1993), while requiring a limited set of training data. This surrogate is computationally cheap, and can be used to apply a global optimization algorithm that relies on a large number of model runs. After this global screening, a subsequent local optimization based on the original physical model (polishing) is performed. Figure 1 . Schematic of standard single office, taken from (Freund and Schmitz 2021) We choose to test our approach on a computational inexpensive, thermal Modelica model of a single office (Figure 1) with measurement data available for calibration (Freund and Schmitz 2021) . Like this, data generation for the machine learning models is fast and we are able to focus on the application of the PELS- DOI Proceedings of the Modelica Conference 2023 107 10.3384/ecp204107 October 9-11, 2023, Aachen, Germany

FAQs

What problem does the paper address in multi-parameter calibration?

It targets calibration of complex Modelica system models where evaluating the whole model is computationally expensive, making global and robust optimization difficult.

How does the proposed method reduce computational cost?

It replaces the parameter-space screening with a Physics Enhanced Latent Space Variational Autoencoder (PELS-VAE) surrogate trained on limited data, then uses the physical model only for local polishing.

What role do Sobol indices and sensitivity analysis play?

Sensitivity analysis with Sobol indices determines the most influential parameters, so the surrogate captures dominant effects even with small training sets.

Aug 3, 2026

Upload by Asher