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Machine learning-based multiscale constitutive modelling: Development and application to dual-porosity mass transfer

In multiscale modelling, multiple models are used simultaneously to describe scale-dependent phenomena in a system of interest. Here we introduce a machine learning (ML)-based multiscale modelling framework for modelling hierarchical multiscale problems. In these problems, closure relations are required for the macroscopic problem in the form of constitutive relations. However, forming explicit closures for nonlinear and hysteretic processes remains challenging. Instead, we provide a framework for learning constitutive mappings given microscale data generated according to micro and macro transitions governed by two-scale homogenisation rules. The resulting data-driven model is then coupled to a macroscale simulator leading to a hybrid ML-physics-based modelling approach. Accordingly, we apply the multiscale framework within the context of transient phenomena in dual-porosity geomaterials. In these materials, the inter-porosity flow is a complex time-dependent function making its adoption within flow simulators challenging. We explore nonlinear feedforward autoregressive ML strategies for the constitutive modelling of this sequential problem. We demonstrate how to inject the resulting surrogate constitutive model into a simulator. We then compare the resulting hybrid approach to traditional dual-porosity and microscale models on a variety of tests. We show the hybrid approach to give high-quality results with respect to explicit microscale simulations without the computational burden of the latter. Lastly, the steps provided by the multiscale framework herein are sufficiently general to be applied to a variety of multiscale settings, using different data generation and learning techniques accordingly.