Memory reduction for numerical solution of differential equations using compressive sensing

Abstract

Mathematical description of our physical world revolves in a great deal around partial and ordinary differential equations (PDES/ODEs). May it be the case of modelling cardiovascular system or quantum electrodynamics, solving a system of PDEs/ODEs, including their coupled forms is indispensable. It is known that many of these system of DEs does not have a closed form solution and need to be solved by a computer. It takes a large amount of memory in saving the state variables as they evolve in a computer program. This paper describes a method of making use of the compressive sensing in reducing the memory requirement for these programs, especially in the case of simulations involving cardiovascular models and chaotic DEs. One set of equations described here simulates arterial blood flow and the other one known as Lorentz equations is used in weather prediction. With the proposed method, the results show that upto 90% and 80% memory saving in case of PDEs and ODEs respectively.