Physics-constrained deep learning for data assimilation of subsurface transport

Data assimilation of subsurface transport is important in many energy and environmental applications,but its solution is typically challenging.In this work,we build physics-constrained deep learning models to predict the full-scale hydraulic conductivity,hydraulic head,and concentration fields in porous media from sparse measure-ment of these observables.The model is developed based on convolutional neural networks with the encoding-decoding process.The model is trained by minimizing a loss function that incorporates residuals of governing equations of subsurface transport instead of using labeled data.Once trained,the model predicts the unknown conductivity,hydraulic head,and concentration fields with an average relative error<10%when the data of these observables is available at 12.2%of the grid points in the porous media.The model has a robust predictive performance for porous media with different conductivities and transport under different Péclet number(0.5<Pe<500).We also quantify the predictive uncertainty of the model and evaluate the reliability of its prediction by incorporating a variational parameter into the model.

Learning Invariant Representation of Multiscale Hyperelastic Constitutive Law from Sparse Experimental Data

Constitutive modeling of heterogeneous hyperelastic materials is still a challenge due to their complex and variable microstructures.We propose a multiscale datadriven approach with a hierarchical learning strategy for the discovery of a generic physics-constrained anisotropic constitutive model for the heterogeneous hyperelastic materials.Based on the sparse multiscale experimental data,the constitutive artificial neural networks for hyperelastic component phases containing composite interfaces are established by the particle swarm optimization algorithm.A microscopic finite element coupled constitutive artificial neural networks solver is introduced to obtain the homogenized stress-stretch relation of heterogeneous materials with different microstructures.And a dense stress-stretch relation dataset is generated by training a neural network through the FE results.Further,a generic invariant representation of strain energy function(SEF)is proposed with a parameter set being implicitly expressed by artificial neural networks(SANN),which describes the hyperelastic properties of heterogeneous materials with different microstructures.A convexity constraint is imposed on the SEF to ensure that the multiscale constitutive model is physically relevant,and the ℓ_(1) regularization combined with thresholding is introduced to the loss function of SANN to improve the interpretability of this model.Finally,the multiscale model is hierarchically trained,cross-validated and tested using the experimental data of cord-rubber composite materials with different microstructures.The proposed multiscale model provides a convenient and general methodology for constitutive modeling of heterogeneous hyperelastic materials.