Recent advances and applications of surrogate models for finite element method computations: a review

Review of machine learning-based surrogate models of groundwater contaminant modeling

Heavy computational load inhibits the application of groundwater contaminant numerical model to groundwater pollution source identification, remediation design, and uncertainty analysis, since a large number of model runs are required for these applications. Machine learning-based surrogate models are an effective approach to enhance the efficiency of the numerical models, and have recently attracted considerable attention in the field of groundwater contaminant modeling. Here, we review 120 research articles on machine learning-based surrogate models for groundwater contaminant modeling that were published between 1994 and 2022. We outline the state of the art method, identify the most significant research challenges, and suggest potential future directions. The six major applications of machine learning-based surrogate models are groundwater pollution source identification, groundwater remediation design, coastal aquifer management, uncertainty analysis of groundwater, groundwater monitoring network design, and groundwater transport parameters inversion. Together, these account for more than 90% of the studies we review. Latin hypercube sampling (LHS) is the most widely used sampling method, and artificial neural networks (ANNs) and Kriging are the two most widely used methods for constructing surrogate model. No method is universally superior, the advantages and disadvantages of different methods, as well as the applicability of these methods for different application purposes of groundwater contaminant modeling were analyzed. Some recommendations on the method selection for various application fields are given based on the reviews and experiences. Based on our review of the state-of-the-art, we suggest several future research directions to enhance the feasibility of the machine learning-based surrogate models of groundwater contaminant modeling: the alleviation of the curse of dimensionality, enhancing transferability, practical applications for real case studies, multi-source dada fusion, and real-time monitoring and prediction.

Tendon Stress Estimation from Strain Data of a Bridge Girder Using Machine Learning-Based Surrogate Model

Prestressed girders reduce cracking and allow for long spans, but their construction requires complex equipment and strict quality control. Their accurate design depends on a precise knowledge of tensioning force and stresses, as well as monitoring the tendon force to prevent excessive creep. Estimating tendon stress is challenging due to limited access to prestressing tendons. This study utilizes a strain-based machine learning method to estimate real-time applied tendon stress. A dataset was generated using finite element method (FEM) analysis, varying the tendon stress in a 45 m girder. Network models were trained and tested on various tendon force scenarios, with prediction errors of less than 10%. The model with the lowest RMSE was chosen for stress prediction, accurately estimating the tendon stress, and providing real-time tensioning force adjustment. The research offers insights into optimizing girder locations and strain numbers. The results demonstrate the feasibility of using machine learning with strain data for instant tendon force estimation.

Inaccuracies of deterministic finite-element models of human middle ear revealed by stochastic modelling

For over 40 years, finite-element models of the mechanics of the middle ear have been mostly deterministic in nature. Deterministic models do not take into account the effects of inter-individual variabilities on middle-ear parameters. We present a stochastic finite-element model of the human middle ear that uses variability in the model parameters to investigate the uncertainty in the model outputs (umbo, stapes, and tympanic-membrane displacements). We demonstrate: (1) uncertainties in the model parameters can be magnified by more than three times in the umbo and stapes footplate responses at frequencies above 2 kHz; (2) middle-ear models are biased and they distort the output distributions; and (3) with increased frequency, the highly-uncertain regions spatially spread out on the tympanic membrane surface. Our results assert that we should be mindful when using deterministic finite-element middle-ear models for critical tasks such as novel device developments and diagnosis.