Memory reduction for numerical solution of differential equations using compressive sensing

  title={Memory reduction for numerical solution of differential equations using compressive sensing},
  author={Midhun P Unni and M. Girish Chandra and A. Anil Kumar},
  journal={2017 IEEE 13th International Colloquium on Signal Processing \& its Applications (CSPA)},
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… 

Figures and Tables from this paper

Enhanced Model Predictive Control-Based STATCOM Implementation for Mitigation of Unbalance in Line Voltages

The proposed enhanced MPC state-space model presented in this paper is adapted for mitigating unbalanced voltages at nominated buses by injecting suitable unbalanced currents and reactive powers by STATCOM and a proposed MPC objective function is developed and implemented to predict output current according to line voltages of adjacent buses.



A computational analysis of the long-term regulation of arterial pressure.

The developed model reveals: long-term control of arterial blood pressure is primarily through the baroreflex arc and the renin-angiotensin system; and arterial stiffening provides a sufficient explanation for the etiology of primary hypertension associated with ageing.

Deterministic nonperiodic flow

Finite systems of deterministic ordinary nonlinear differential equations may be designed to represent forced dissipative hydrodynamic flow. Solutions of these equations can be identified with

Sequential Compressed Sensing

This paper proposes a method to estimate the reconstruction error directly from the samples themselves, for every candidate in this sequence of candidate reconstructions, which provides a way to obtain run-time guarantees for recovery methods that otherwise lack a priori performance bounds.

Sketching Sparse Matrices

This paper considers the problem of recovering an unknown sparse p⇥ p matrix X from an m ⇥ m matrix Y = AXB T, and shows that there exist constructions of the “sketching” matrices A and B so that even if X has O(p) non-zeros, it can be recovered exactly and eciently using a convex program.

Compressive sensing

This paper overviews the recent work on compressive sensing, a new approach to data acquisition in which analog signals are digitized for processing not via uniform sampling but via measurements

An Introduction To Compressive Sampling

The theory of compressive sampling, also known as compressed sensing or CS, is surveyed, a novel sensing/sampling paradigm that goes against the common wisdom in data acquisition.

Nonlinear Model Predictive Control with Constraint Satisfactions for a Quadcopter

This paper presents a nonlinear model predictive control (NMPC) strategy combined with constraint satisfactions for a quadcopter. The full dynamics of the quadcopter describing the attitude and

The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods

The Euler Method and its Generalizations Analysis of Runge-Kutta Methods General Linear Methods Bibliography.

A Reversible Sketch Based on Chinese Remainder Theorem: Scheme and Performance Study

This paper presents a scheme based on Chinese Remainder Theorem, which involves the usage of two sketches based on two different prime-number sets for reducing the false positives.

Compressive Sensing [Lecture Notes]

This lecture note presents a new method to capture and represent compressible signals at a rate significantly below the Nyquist rate. This method, called compressive sensing, employs nonadaptive