Unsupervised Machine Learning Based on Non-Negative Tensor Factorization for Analyzing Reactive-Mixing

Abstract Analysis of reactive-diffusion simulations representing complex mixing processes requires a large number of independent model runs. For each high-fidelity model simulation, the model inputs are varied and the predicted mixing behavior is represented by temporal and spatial changes in species concentration. It is then required to discern how the model inputs (such as diffusivity, dispersion, anisotropy, and velocity field properties) impact the mixing process. This task is challenging and typically involves interpretation of large model outputs representing temporal and spatial changes of species concentration within the model domain. However, the task can be automated and substantially simplified by applying Machine Learning (ML) methods. In this paper, we present an application of an unsupervised ML method (called NTF k ) using Non-negative Tensor Factorization (NTF) coupled with a custom clustering procedure based on k -means to reveal the temporal and spatial features in product concentrations. An attractive and unique aspect of the proposed ML method is that it ensures the extracted features are non-negative, which is important to obtain a meaningful deconstruction of the mixing processes. The ML methodology is applied to a large set of high-resolution finite-element model simulations representing anisotropic reaction-diffusion processes in perturbed vortex-based velocity fields. The applied finite-element method ensures that spatial and temporal species concentration are always non-negative, even in the case of high anisotropic contrasts. The simulated reaction is a fast irreversible bimolecular reaction A + B → C , where species A and B react to form species C . The reactive-diffusion model input parameters that control mixing include properties of the velocity field (such as vortex structures), anisotropic dispersion, and molecular diffusion. We demonstrate the applicability of the ML feature extraction method to produce a meaningful deconstruction of model outputs to discriminate between different physical processes impacting the reactants, their mixing, and the spatial distribution of the product C . The presented ML analysis allowed us to identify additive temporal and spatial features that characterize mixing behavior. The application of the proposed NTF k approach is not limited to reactive-mixing. NTF k can be readily applied to any observed or simulated datasets that can be represented as tensors (multi-dimensional arrays) and have separable latent signatures or features.