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Machine-learning (ML) based discretization has been developed to simulate complex partial differential equations (PDEs) with tremendous success across various fields. These learned PDE solvers can effectively resolve the underlying solution structures of interest and achieve a level of accuracy which often requires an order-of-magnitude finer grid for a conventional numerical method using polynomial-based approximations. In a previous work [13], we introduced a learned finite volume discretization that further incorporates the semi-Lagrangian (SL) mechanism, enabling larger CFL numbers for stability. However, the efficiency and effectiveness of such a methodology heavily rely on the availability of abundant high-resolution training data, which can be prohibitively expensive to obtain. To address this challenge, in this paper, we propose a novel multifidelity MLbased SL method for transport equations. This method leverages a combination of a small amount of high-fidelity data and sufficient but cheaper low-fidelity data. The approach is designed based on a composite convolutional neural network architecture that explores the inherent correlation between high-fidelity and low-fidelity data. The proposed method demonstrates the capability to achieve a reasonable level of accuracy, particularly in scenarios where a single-fidelity model fails to generalize effectively. We further extend the method to the nonlinear Vlasov--Poisson system by employing high-order Runge--Kutta exponential integrators. A collection of numerical tests are provided to validate the efficiency and accuracy of the proposed method. 

Per- and polyfluoroalkyl substances (PFASs) have recently garnered considerable concerns regarding their impacts on human and ecological health. Despite the important roles of polyamide membranes in remediating PFASs contaminated water, the governing factors influencing PFAS transport across these membranes remain elusive. In this study, we investigate PFAS rejection by polyamide membranes using two machine learning (ML) models, namely XGBoost and multimodal transformer models. Utilizing the Shapley additive explanation method for XGBoost model interpretation unveils the impacts of both PFAS characteristics and membrane properties on model predictions. The examination of the impacts of chemical structure involves interpreting the multimodal transformer model incorporated with simplified molecular input line entry system strings through heatmaps, providing a visual representation of the attention score assigned to each atom of PFAS molecules. Both ML interpretation methods highlight the dominance of electrostatic interaction in governing PFAS transport across polyamide membranes. The roles of functional groups in altering PFAS transport across membranes are further revealed by molecular simulations. The combination of ML with computer simulations not only advances our knowledge of PFAS removal by polyamide membranes, but also provides an innovative approach to facilitate data-driven feature selection for the development of high-performance membranes with improved PFAS removal efficiency. 

Abstract Delivery of proteins in plant cells can facilitate the design of desired functions by modulation of biological processes and plant traits but is currently limited by narrow host range, tissue damage, and poor scalability. Physical barriers in plants, including cell walls and membranes, limit protein delivery to desired plant tissues. Herein, a cationic high aspect ratio polymeric nanocarriers (PNCs) platform is developed to enable efficient protein delivery to plants. The cationic nature of PNCs binds proteins through electrostatic. The ability to precisely design PNCs’ size and aspect ratio allowed us to find a cutoff of ≈14 nm in the cell wall, below which cationic PNCs can autonomously overcome the barrier and carry their cargo into plant cells. To exploit these findings, a reduction‐oxidation sensitive green fluorescent protein (roGFP) is deployed as a stress sensor protein cargo in a model plantNicotiana benthamianaand common crop plants, including tomato and maize. In vivo imaging of PNC‐roGFP enabled optical monitoring of plant response to wounding, biotic, and heat stressors. These results show that PNCs can be precisely designed below the size exclusion limit of cell walls to overcome current limitations in protein delivery to plants and facilitate species‐independent plant engineering.