A novel physics-informed deep learning strategy with local time-updating discrete scheme for multi-dimensional forward and inverse consolidation problems

Hongwei Guo, Zhen Yu Yin

Research output: Journal article publicationJournal articleAcademic researchpeer-review

1 Citation (Scopus)


Physics-informed deep learning (PIDL) offers innovative and powerful ways for spatio-temporal soil consolidation analysis. However, status quo applications employ physics-informed deep learning with the continuous-time scheme that necessitates sampling massive collocation points across the entire spatio-temporal domain, which can be computationally expensive in time-evolution simulation and high-dimensional models. In this paper, a physics-informed deep learning (PIDL) framework with a local time-updating discrete scheme for forward and inverse consolidation analysis is proposed and formulated by combining the local time-updating strategy and the Runge–Kutta time discretization methods with the PIDL. Furthermore, the total and local time-updating discrete time schemes fitted to PIDL to solve the time-dependent partial differential equations are investigated. The proposed model was validated across various soil consolidation cases spanning 1D to 3D single and double drainage, exponentially time-growing drainage boundary conditions, and inverse analysis to retrieve the material and model parameters. A comprehensive evaluation of PIDL with the continuous and discrete time schemes in time-dependent multi-dimensional consolidation analysis, which is of significant reference value, is performed. Numerical results manifested that PIDL with the discrete time scheme outperforms the continuous time scheme in consolidation analysis, particularly in high dimensions. The PIDL using the local time-updating strategy yielded more accurate results than the total time-updating strategy and can facilitate training with time evolution. A transfer learning model in time domain fitted to PIDL with the discrete time scheme was developed to enhance model generality and reduce the computation cost. In addition, PIDL with the discrete time scheme can unify forward simulation and inverse analysis in a unified framework requiring less training data, which can be a promising candidate to serve as a versatile surrogate modeling tool in geotechnical engineering.

Original languageEnglish
Article number116819
JournalComputer Methods in Applied Mechanics and Engineering
Publication statusPublished - 1 Mar 2024


  • Consolidation
  • Deep learning
  • Discrete time scheme
  • Inverse analysis
  • Physics-informed
  • Self-supervised

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • General Physics and Astronomy
  • Computer Science Applications


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