Characterizing the Neural Network Method of Solving Differential Equations on Low-Dimensional Parametrized Problems from Biophysics
The neural network method (NNM) is a relatively new way of solving mathematical problems called partial differential equations (PDEs). PDEs are used as mathematical models for a wide range of phenomena in science, engineering, finance, and elsewhere. Recently, the NNM is receiving attention because several studies have shown that it can solve certain PDE problems that are impossible to solve using most traditional methods. Paradigm AI Incorporated, a start-up specializing in the use of neural network techniques to solve engineering problems, is interested in leveraging these advantages of the NNM to develop next-generation simulation algorithms. Unfortunately, the basic NNM implementations presented in those proof-of-concept studies are slower than traditional techniques for many practical problems, such as those commonly arising in engineering. The proposed research project will attempt to accelerate the NNM using a variety of well-established techniques that have already been applied successfully in machine vision and natural language processing.