Compact Neural Network Solutions to Laplace's Equation in a Nanofluidic Device

Martin Magill, Faisal Z. Qureshi, Hendrick W. de Haan

Abstract: We explore the use of neural networks to solve the Laplace equation in a two-dimensional geometry. Specifically, we study a PDE problem that models the electric potential inside the slit-well nanofluidic device. Such devices are typically used to separate polymer mixtures by molecular size. Processes like these are commonly studied using GPU-accelerated coarse-grained particle simulations, for which GPU memory is a bottleneck. We compare the memory required to represent the field using neural networks to that needed to store solutions obtained using the finite element method. We find that even simple fully-connected neural networks can achieve accuracy to memory consumption ratios comparable to the good finite element solutions. These preliminary results demonstrate an industrial application that would benefit greatly from compact neural network representation techniques.

Keywords: neural network, compact representation, partial differential equation, nanofluidic