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Predicting the structural properties of water and simple fluids confined in nanometer scale pores and channels is essential in, for example, energy storage and biomolecular systems. Classical continuum theories fail to accurately capture the interfacial structure of fluids. In this work, we develop a deep learning-based quasi-continuum theory (DL-QT) to predict the concentration and potential profiles of a Lennard-Jones (LJ) fluid and water confined in a nanochannel. The deep learning model is built based on a convolutional encoder–decoder network (CED) and is applied for high-dimensional surrogate modeling to relate the fluid properties to the fluid–fluid potential. The CED model is then combined with the interatomic potential-based continuum theory to determine the concentration profiles of a confined LJ fluid and confined water. We show that the DL-QT model exhibits robust predictive performance for a confined LJ fluid under various thermodynamic states and for water confined in a nanochannel of different widths. The DL-QT model seamlessly connects molecular physics at the nanoscale with continuum theory by using a deep learning model. 

It has been established that Newton’s law of viscosity fails for fluids under strong confinement as the strain-rate varies significantly over molecular length-scales. We thereby investigate if a nonlocal shear stress accounting for the strain-rate of an adjoining region by a convolution relation with a nonlocal viscosity kernel can be employed to predict the gravity-driven isothermal flow of a Weeks–Chandler–Andersen fluid in a nanochannel. We estimate, using the local average density model, the fluid’s viscosity kernel from isotropic bulk systems of corresponding state points by the sinusoidal transverse force method. A continuum model is proposed to solve the nonlocal hydrodynamics whose solutions capture the key features and agree qualitatively with the results of non-equilibrium molecular dynamics simulations, with deviations observed mostly near the fluid–channel interface.