Tags: algorithms

More tags

Description

Whether you're simulating the electronic structure of a carbon nanotube or the strain within an automobile part, the calculations usually boil down to a simple matrix equation, Ax = f. The faster you can fill the matrix A with the coefficients for your partial differential equation (PDE), and the faster you can solve for the vector x given a forcing function f, the faster you have your overall solution. Things get interesting when the matrix A is too large to fit in the memory available on one machine, or when the coefficients in A cause the matrix to be ill-conditioned.

Many different algorithms have been developed to map a PDE onto a matrix, to pre-condition the matrix to a better form, and to solve the matrix with blinding speed. Different algorithms usually exploit some property of the matrix, such as symmetry, to reduce either memory requirements or solution speed or both.

Learn more about algorithms from the many resources on this site, listed below.

Online Presentations (1-20 of 115)

  1. Machine Learning with MATLAB

    Online Presentations | 11 Mar 2022 | Contributor(s):: Gaby Arellano Bello

    In this session, we explore the fundamentals of machine learning using MATLAB. We introduce machine learning techniques available in MATLAB to quickly explore your data, evaluate machine learning algorithms, compare the results and apply the best technique to your problem.

  2. Data Analysis with MATLAB

    Online Presentations | 04 Mar 2022 | Contributor(s):: Gen Sasaki

    Learn how MATLAB can be used to visualize and analyze data, perform numerical computations, and develop algorithms. Through live demonstrations and examples, you will see how MATLAB can help you become more effective in your coursework as well as in research.

  3. Simulating Field Theory in the Light-Front Formulation

    Online Presentations | 08 Jan 2021 | Contributor(s):: Peter J. Love

    I will talk about quantum simulation algorithms based on the light-front formulation of quantum field theory. They will range from ab initio simulations with nearly optimal resource scalings to VQE-inspired methods available for existing devices.

  4. Designing a NISQ Reservoir with Maximal Memory Capacity for Volatility Forecasting

    Online Presentations | 28 Oct 2020 | Contributor(s):: Samudra Dasgupta

    In this talk, we lay out the systematic design considerations for using a NISQ reservoir as a computing engine. We then show how to experimentally evaluate the memory capacity of various reservoir topologies  (using IBM-Q’s Rochester device) to identify the configuration with maximum...

  5. ECE 595ML Lecture 1.2: Linear Regression - Geometry

    Online Presentations | 28 May 2020 | Contributor(s):: Stanley H. Chan

  6. PennyLane - Automatic Differentiation and Machine Learning of Quantum Computations

    Online Presentations | 29 Apr 2020 | Contributor(s):: Nathan Killoran

    PennyLane is a Python-based software framework for optimization and machine learning of quantum and hybrid quantum-classical computations.

  7. ECE 595ML Lecture 1.1: Linear Regression

    Online Presentations | 21 Jan 2020 | Contributor(s):: Stanley H. Chan

  8. ECE 595ML Lecture 2.1: Regularized Linear Regression

    Online Presentations | 21 Jan 2020 | Contributor(s):: Stanley H. Chan

  9. Universal Variational Quantum Computation

    Online Presentations | 28 Oct 2019 | Contributor(s):: Jacob Biamonte

    We show that the variational approach to quantum enhanced algorithms admits a universal model of quantum computation.

  10. Quantum Algorithmic Breakeven: on Scaling Up with Noisy Qubits

    Online Presentations | 21 Aug 2019 | Contributor(s):: Daniel Lidar

    In this talk I will argue in favor of a different criterion I call "quantum algorithmic breakeven," which focuses on demonstrating an algorithmic scaling improvement in an error-corrected setting over the uncorrected setting. I will present evidence that current experiments with...

  11. Overview of Computational Methods and Machine Learning: Panel Talks

    Online Presentations | 14 Jun 2019 | Contributor(s):: Brett Matthew Savoie, Pradeep Kumar Gurunathan, Peilin Liao, Xiulin Ruan, Guang Lin

    The Panel Discussion which follows these individual presentations can be found here.Individucal Presentations:Theory and Machine Learning in the Chemical Sciences, Brett Matthew Savoie;Divide and Conquer with QM/MM Methods, Pradeep Kumar Gurunathan;Computational Chemistry/Materials, Peilin...

  12. Overview of Computational Methods and Machine Learning: Panel Discussion

    Online Presentations | 14 Jun 2019 | Contributor(s):: Brett Matthew Savoie, Pradeep Kumar Gurunathan, Peilin Liao, Xiulin Ruan, Guang Lin

    The individual Panel Talks which accompanies this discussion can be found here.Why do we need experiments?Are your methods “descriptive” or “predictive”?Do you work with any other theory/simulation groups?On the 5 year timescale: is machine-learning hype or a real...

  13. Big Data in Reliability and Security: Some Basics

    Online Presentations | 30 May 2019 | Contributor(s):: Saurabh Bagchi

  14. Big Data in Reliability and Security: Applications

    Online Presentations | 30 May 2019 | Contributor(s):: Saurabh Bagchi

  15. Human-Interpretable Concept Learning via Information Lattices

    Online Presentations | 23 May 2019 | Contributor(s):: Lav R. Varshney

    The basic idea is an iterative discovery algorithm that has a student-teacher architecture and that operates on a generalization of Shannon’s information lattice, which itself encodes a hierarchy of abstractions and is algorithmically constructed from group-theoretic foundations.

  16. Networked Dynamical Systems for Function and Learning: Paradigms for Data-Driven Control and Learning in Neurosensory Systems

    Online Presentations | 16 Jan 2019 | Contributor(s):: J. Nathan Kutz

    Our objective is to use emerging data-driven methods to extract the underlying engineering principles of cognitive capability, namely those that allow complex networks to learn and enact control and functionality in the robust manner observed in neurosensory systems. Mathematically, the...

  17. Data-Driven Discovery of Governing Equations of Physical Systems

    Online Presentations | 16 Jan 2019 | Contributor(s):: J. Nathan Kutz

    We introduce a number of data-driven strategies for discovering nonlinear multiscale dynamical systems and their embeddings from data. We consider two canonical cases: (i) systems for which we have full measurements of the governing variables, and (ii) systems for which we have incomplete...

  18. Quantifying Uncertainties in Physical Models

    Online Presentations | 28 Aug 2017 | Contributor(s):: Ilias Bilionis

    Increasing modeling detail is not necessarily correlated with increasing predictive ability. Setting modeling and numerical discretization errors aside, the more detailed a model gets, the larger the number of parameters required to accurately specify its initial/boundary conditions, constitutive...

  19. A Distributed Algorithm for Computing a Common Fixed Point of a Family of Paracontractions

    Online Presentations | 21 Jun 2017 | Contributor(s):: A. Stephen Morse

    In this talk a distributed algorithm is described for finding a common fixed point of a family of m paracontractions assuming that such a common fixed point exists. The common fixed point is simultaneously computed by m agents assuming each agent knows only paracontraction, the current estimates...

  20. ECE 695NS Lecture 3: Practical Assessment of Code Performance

    Online Presentations | 25 Jan 2017 | Contributor(s):: Peter Bermel

    Outline:Time ScalingExamplesGeneral performance strategiesComputer architecturesMeasuring code speedReduce strengthMinimize array writesProfiling