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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.

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  1. Machine Learning with MATLAB

    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

    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. Recursive algorithm for NEGF in Python GPU version

    02 Feb 2021 | | Contributor(s):: Ning Yang, Tong Wu, Jing Guo

    This folder contains two Python functions for GPU-accelerated simulation, which implements the recursive algorithm in the non-equilibrium Green’s function (NEGF) formalism. Compared to the matlab implementation [1], the GPU version allows massive parallel running over many cores on GPU...

  4. Simulating Field Theory in the Light-Front Formulation

    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.

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

    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...

  6. Samudra Dasgupta

    Samudra Dasgupta obtained his B.Tech in Electronics and Electrical Engineering from IIT-Kharagpur 2006, followed by M.S. in Engineering and Applied Sciences from Harvard 2008 and an M.B.A. from...

    https://nanohub.org/members/305162

  7. Interactive Learning Tools for Scientific Computing and Data Analysis Using R

    29 Jul 2020 | | Contributor(s):: Cindy Nguyen, Rei Sanchez-Arias

    Root-finding methods and numerical optimization techniques with applications in science, engineering, and data analysis

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

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

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

    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.

  10. Advances in Computational and Quantum Imaging Workshop

    28 Jan 2020 |

    The purpose of the workshop is to bring different communities together, review recent theoretical and experimental advances and explore synergetic collaborations. The workshop aligns well with the significant investments in quantum technologies through the National Quantum Initiative in the...

  11. ECE 595ML Lecture 1.1: Linear Regression

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

  12. ECE 595ML Lecture 2.1: Regularized Linear Regression

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

  13. ECE 595ML: Machine Learning I

    17 Jan 2020 | | Contributor(s):: Stanley H. Chan

    Spring 2020 - This course is in productionCourse Website: https://engineering.purdue.edu/ChanGroup/ECE595/index.htmlCourse Outline:Part 1: Mathematical BackgroundLinear Regression and OptimizationPart 2: ClassificationMethods to train linear classifiersFeature analysis, Geometry, Bayesian...

  14. Universal Variational Quantum Computation

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

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

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

    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...

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

    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...

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

    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...

  18. Big Data in Reliability and Security: Some Basics

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

  19. Big Data in Reliability and Security: Applications

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

  20. Peter Shor

    Peter Shor is Morss Professor of Applied Mathematics since 2003, and Chair of the Applied Mathematics Committee since 2015. He received the B.A. in mathematics from Caltech in 1981, and the Ph.D....

    https://nanohub.org/members/230531