Hybrid Modelling by Machine Learning Corrections of Analytical Model Predictions towards High-Fidelity Simulation Solutions

Abstract

Within the fields of materials mechanics, the consideration of physical laws in machine learning predictions besides the use of data can enable low prediction errors and robustness as opposed to predictions only based on data. On the one hand, exclusive utilization of fundamental physical relationships might show significant deviations in their predictions compared to reality, due to simplifications and assumptions. On the other hand, using only data and neglecting well-established physical laws can create the need for unreasonably large data sets that are required to exhibit low bias and are usually expensive to collect. However, fundamental but simplified physics in combination with a corrective model that compensates for possible deviations, e.g., to experimental data, can lead to physics-based predictions with low prediction errors, also despite scarce data. In this article, it is demonstrated that a hybrid model approach consisting of a physics-based model that is corrected via an artificial neural network represents an efficient prediction tool as opposed to a purely data-driven model. In particular, a semi-analytical model serves as an efficient low-fidelity model with noticeable prediction errors outside its calibration domain. An artificial neural network is used to correct the semi-analytical solution towards a desired reference solution provided by high-fidelity finite element simulations, while the efficiency of the semi-analytical model is maintained and the applicability range enhanced. We utilize residual stresses that are induced by laser shock peening as a use-case example. In addition, it is shown that non-unique relationships between model inputs and outputs lead to high prediction errors and the identification of salient input features via dimensionality analysis is highly beneficial to achieve low prediction errors. In a generalization task, predictions are also outside the process parameter space of the training region while remaining in the trained range of corrections. The corrective model predictions show substantially smaller errors than purely data-driven model predictions, which illustrates one of the benefits of the hybrid modelling approach. Ultimately, when the amount of samples in the data set is reduced, the generalization of the physics-related corrective model outperforms the purely data-driven model, which also demonstrates efficient applicability of the proposed hybrid modelling approach to problems where data is scarce.

Machine Learning Driven Prediction of Residual Stresses for the Shot Peening Process Using a Finite Element Based Grey-Box Model Approach

“…Based on this combination, the number of practical experiments for the calibration of the algorithm can be further reduced. Recent work from Bock et al [62] can additionally serve as a basis for the training of a physical data-driven artificial neural network.…”

Deformation by design: data-driven approach to predict and modify deformation in thin Ti-6Al-4V sheets using laser peen forming

“…After defining these inputs and outputs for the LPF process, one can proceed with developing an ANN model; however, this technique is not particularly an efficient approach because the correlations between the processing parameters, material constants, and other derived parameters are not taken into account. This is clearly evident from the work of Bock et al (2021). Based on the physical quantities and material constants, a dimensional analysis is performed with the corresponding input-output parameters to create dimensionless inputs and outputs.…”

Machine Learning Aided Multiscale Magnetostatics

“…This motivates the development of computationally feasible approaches in this realm. A recently emerging third alternative in literature to this end is employing data-driven surrogate models devising machine learning, see, e.g., [12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33] and the references therein. Deploying the training costs offline materializing simulation or experimental data, these models surpass conventional rule-based approaches by drastically reducing the computational cost required during the prediction phase [34,35,36].…”