All Categories (1-9 of 9)

1. A Hands-on Introduction to Physics-Informed Neural Networks

   Online Presentations | 16 Jun 2021 | Contributor(s):: Ilias Bilionis, Atharva Hans

   Can you make a neural network satisfy a physical law? There are two main types of these laws: symmetries and ordinary/partial differential equations. I will focus on differential equations in this short presentation. The simplest way to bake information about a differential equation with neural...

2. A Hands-on Introduction to Physics-Informed Neural Networks

   Tools | 21 May 2021 | Contributor(s):: Atharva Hans, Ilias Bilionis

   A Hands-on Introduction to Physics-Informed Neural Networks

3. Uncertainty Quantification and Scientific Machine Learning for Complex Engineering Systems

   Online Presentations | 17 Aug 2020 | Contributor(s):: Guang Lin

   In this talk, I will first present a review of the novel UQ techniques I developed to conduct stochastic simulations for very large-scale complex systems.

4. Range Decomposition: A Low Communication Algorithm for Solving PDEs on Massively Parallel Machines

   Online Presentations | 07 Feb 2016 | Contributor(s):: Tom Manteuffel

   The Range Decomposition (RD) algorithm uses nested iteration and adaptive mesh refinement locally before performing a global communication step. Only several such steps are observed to be necessary before reaching a solution within a small multiple of discretization error. The target application...

5. Space-time constrained FOSLS with AMGe upscaling

   Online Presentations | 04 Feb 2016 | Contributor(s):: Panayot Vassilevski

   We consider time-dependent PDEs discretized in combined space-time domains. We first reduce the PDE to a first order system. Very often in practice, one of the equations of the reduced system involves the divergence operator (in space-time). The popular FOSLS (first order system least-squares)...

6. Numerical Methods for Partial Differential Equations

   Online Presentations | 25 Jan 2016 | Contributor(s):: Sandip Mazumder

   A Youtube channel that presents numerous high-quality lectures on methods for solving Partial Differential Equations (PDEs). Topics include (1) Finite Difference Method: Cartesian and Curvilinear Mesh (2) Finite Volume Method: Cartesian, Curvilinear and Unstructured Mesh (3) Iterative solvers:...

7. IMA 2013 UQ: Bayesian Approaches for Spatial- Stochastic Basis Selection: Applications to Fuel Cell Predictive Modeling

   Online Presentations | 28 May 2014 | Contributor(s):: Guang Lin

   In this talk, two fully Bayesian methods (Bayesian uncertainty method and Bayesian mixture procedure) will be introduced that can evaluate generalized Polynomial Chaos (gPC) expansions in both stochastic and spatial domains when the number of the available basis functions is significantly larger...

8. Padre

   Tools | 12 Jan 2006 | Contributor(s):: Mark R. Pinto, kent smith, Muhammad A. Alam, Steven Clark, Xufeng Wang, Gerhard Klimeck, Dragica Vasileska

   2D/3D devices under steady state, transient conditions or AC small-signal analysis

9. Numerical Methods for Partial Differential Equations

   Courses|' 26 Jan 2016

   This course focuses on two popular deterministic methods for solving partial differential equations (PDEs), namely finite difference and finite volume methods. The lectures are intended to...

   https://nanohub.org/courses/npde