# Scaling digital models

## TL;DR

This paper presents a new method using machine learning and dimensional analysis to scale digital models across different system sizes, reducing the need for expensive experimental calibration.

## Contribution

A novel methodology and modular computational framework for scaling digital models using ML and DA, enabling calibration transfer between system sizes.

## Key findings

- Calibration on a single system can be scaled to other sizes using the proposed framework.
- The approach resolves issues with distorted scaling factors in traditional dimensional analysis.
- A case study demonstrates successful scaling of a wheel loader model between industrial and lab systems.

## Abstract

The development of accurate digital models (DMs) for physical systems requires virtual representations that faithfully capture the underlying physics of the system or equipment being represented. Physics-based DMs provide reliable predictions only when accurate mathematical models of physical systems exist. When such models are incomplete or uncertain, experimental calibration can significantly improve model fidelity. However, in industries where systems or equipment exist in multiple sizes or configurations, performing experimental calibration for each variant can be prohibitively expensive and time-consuming. To address this challenge, this paper introduces a novel methodology and modular computational framework that leverages machine learning (ML) and dimensional analysis (DA) to enable scaling of DMs. The proposed approach allows calibration to be performed on a single representative system, with results scaled to other system sizes, whether from full-scale to reduced-scale prototypes or vice versa. Traditional applications of DA in this context often encounter difficulties due to distorted scaling factors. This work resolves these challenges by developing a consistent scaling framework tailored for DMs. The methodology is demonstrated by a case study in which a calibrated DM of a wheel loader is scaled between an industrial-size system and a miniaturized laboratory system.

The online version contains supplementary material available at 10.1038/s41598-026-36310-x.