Multi-fidelity surrogate modeling through hybrid machine learning for biomechanical and finite element analysis of soft tissues

Seyed Shayan Sajjadinia, Bruno Carpentieri*, Duraisamy Shriram, Gerhard A. Holzapfel

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Biomechanical simulation enables medical researchers to study complex mechano-biological conditions, although for soft tissue modeling, it may apply highly nonlinear multi-physics theories commonly implemented by expensive finite element (FE) solvers. This is a significantly time-consuming process on a regular computer and completely inefficient in urgent situations. One remedy is to first generate a dataset of the possible inputs and outputs of the solver in order to then train an efficient machine learning (ML) model, i.e., the supervised ML-based surrogate, replacing the expensive solver to speed up the simulation. But it still requires a large number of expensive numerical samples. In this regard, we propose a hybrid ML (HML) method that uses a reduced-order model defined by the simplification of the complex multi-physics equations to produce a dataset of the low-fidelity (LF) results. The surrogate then has this efficient numerical model and an ML model that should increase the fidelity of its outputs to the level of high-fidelity (HF) results. Based on our empirical tests via a group of diverse training and numerical modeling conditions, the proposed method can improve training convergence for very limited training samples. In particular, while considerable time gains comparing to the HF numerical models are observed, training of the HML models is also significantly more efficient than the purely ML-based surrogates. From this, we conclude that this non-destructive HML implementation may increase the accuracy and efficiency of surrogate modeling of soft tissues with complex multi-physics properties in small data regimes.

Original languageEnglish
Article number105699
JournalComputers in Biology and Medicine
Publication statusPublished - Sep 2022


  • Finite element modeling
  • Hybrid machine learning
  • Multi-fidelity surrogate
  • Soft tissue

ASJC Scopus subject areas

  • Computer Science Applications
  • Health Informatics


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