mlsanityData to 7 Oct 2026

Local approximate Gaussian process regression for data-driven constitutive laws: Development and comparison with neural networks

arXiv 2105.04554 ↗First posted 7 May 2021cs.CE cs.AI stat.MLcited by 17

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Abstract (arXiv)

Hierarchical computational methods for multiscale mechanics such as the FE2 and FE-FFT methods are generally accompanied by high computational costs. Data-driven approaches are able to speed the process up significantly by enabling to incorporate the effective micromechanical response in macroscale simulations without the need of performing additional computations at each Gauss point explicitly. Traditionally artificial neural networks (ANNs) have been the surrogate modeling technique of choice in the solid mechanics community. However they suffer from severe drawbacks due to their parametric nature and suboptimal training and inference properties for the investigated datasets in a three dimensional setting. These problems can be avoided using local approximate Gaussian process regression (laGPR). This method can allow the prediction of stress outputs at particular strain space locations by training local regression models based on Gaussian processes, using only a subset of the data for each local model, offering better and more reliable accuracy than ANNs. A modified Newton-Raphson approach is proposed to accommodate for the local nature of the laGPR approximation when solving the global structural problem in a FE setting. Hence, the presented work offers a complete and general framework enabling multiscale calculations combining a data-driven constitutive prediction using laGPR, and macroscopic calculations using an FE scheme that we test for finite-strain three-dimensional hyperelastic problems.

Key facts. Cited by 17 papers in the map (data through 7 Oct 2026). Builds on 17 of its 59 references that are in the map. First posted on arXiv 7 May 2021.

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17 of 59 references.

References · 17

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5 more
  1. 2020On-the-fly construction of surrogate constitutive models for concurrent multiscale mechanical analysis through probabilistic machine learningcited by 14
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 2; 2022: 3; 2023: 4; 2024: 2; 2025: 3; 2026: 3.

17 papers.

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  1. 2024A review on data-driven constitutive laws for solidscited by 35
  2. 2022NN-EUCLID: deep-learning hyperelasticity without stress datacited by 30
  3. 2023GPLaSDI: Gaussian Process-based Interpretable Latent Space Dynamics Identification through Deep Autoencodercited by 29
  4. 2022Modular machine learning-based elastoplasticity: generalization in the context of limited datacited by 16
  5. 2023Extreme sparsification of physics-augmented neural networks for interpretable model discovery in mechanicscited by 16
  6. 2025Can KAN CANs? Input-convex Kolmogorov-Arnold Networks (KANs) as hyperelastic constitutive artificial neural networks (CANs)cited by 12
  7. 2022Geometric deep learning for computational mechanics Part II: Graph embedding for interpretable multiscale plasticitycited by 11
  8. 2021Interval and fuzzy physics-informed neural networks for uncertain fieldscited by 9
  9. 2023Stress representations for tensor basis neural networks: alternative formulations to Finger-Rivlin-Ericksencited by 9
  10. 2023Learning thermodynamically constrained equations of state with uncertaintycited by 5
  11. 2024Machine Learning Aided Modeling of Granular Materials: A Reviewcited by 2
  12. 2021MD-inferred neural network monoclinic finite-strain hyperelasticity models for β-HMX: Sobolev training and validation against physical constraintscited by 1
5 more
  1. 2025Towards scientific machine learning for granular material simulations -- challenges and opportunitiescited by 1
  2. 2025A Comparison of Surrogate Constitutive Models for Viscoplastic Creep Simulation of HT-9 Steelcited by 0
  3. 2026Physics-Informed Gaussian Process Regression for the Constitutive Modeling of Concrete: A Data-Driven Improvement to Phenomenological Modelscited by 0
  4. 2026Benchmarking data-driven material models on the classic Treloar datasetcited by 0
  5. 2026Adaptive multi-resolution Gaussian processes: Scalable exact inference with naturally data-sparse covariance matricescited by 0