𝐶𝑎𝑟𝑎𝑚𝑖𝑧𝑎𝑟𝑢'𝑠 𝐵𝑙𝑜𝑔 feed:2023:12:04

Geometric Numerical Integration

anonymous@undisclosed.example.com (Anonymous) — Sat, 27 Apr 2024 11:48:10 +0000

Geometric Numerical Integration

Abstract:

Many differential equations of interest in the physical sciences and engineering exhibit geometric properties that are preserved by the dynamics. Recently, there has been a trend towards the construction of numerical schemes that preserve as many of these geometric invariants as possible.

Such methods are of particular interest when simulating mechanical systems that arise from Lagrangian or Hamiltonian mechanics, wherein the preservation of physical invariants such as the energy, momentum, and symplectic form can be important when simulating long-time dynamics of such systems.

In applications arising from astrodynamics and robotics, the dynamics evolve on nonlinear manifolds such as Lie groups, and in particular the rotation group, and the special Euclidean group. Numerical schemes that respect the underlying nonlinear manifold structure will also be discussed.

This course will begin with an overview of classical numerical integration schemes, and their analysis, followed by a more in depth discussion of the various geometric properties that are of importance in many practical applications, followed by a survey of the various geometric integration schemes that have been developed in recent years. Issues pertaining to the analysis and implementation of such schemes will also be addressed.

course, math, ODE, numerics, Melvin-Leok, Geometric

How are memories stored in neural networks?

anonymous@undisclosed.example.com (Anonymous) — Mon, 04 Dec 2023 11:24:59 +0000

How are memories stored in neural networks?

neural-networks, Hopfield-Network, memorie

Information Geometry and its Applications

anonymous@undisclosed.example.com (Anonymous) — Sat, 27 Apr 2024 11:49:57 +0000

Information Geometry and its Applications

Playlist Link

Abstract:

Information geometry involves the use of differential geometric tools to describe the manifold of probability density functions, and allows one to investigate the intrinsic properties of statistical models as opposed to their parametric representations. In particular, we will discuss how divergence functions, and their induced geometric structures, like the Riemannian metric, dually flat affine connections, and curvature relate to statistical issues like asymptotic efficiency of maximum likelihood estimators as well as optimization algorithms on the manifold of probability distributions.

course, math, information-geometry, Melvin-Leok

Neural Networks: Zero to Hero

anonymous@undisclosed.example.com (Anonymous) — Mon, 04 Dec 2023 21:16:38 +0000

Neural Networks: Zero to Hero

Playlist Link

ML, DL, neural-networks, course, Andrej-Karpathy

Numerical Methods for Physical Modeling

anonymous@undisclosed.example.com (Anonymous) — Sat, 27 Apr 2024 11:49:27 +0000

Numerical Methods for Physical Modeling

Playlist Link

Abstract:

This course surveys numerical methods for physical modeling, and discusses floating point arithmetic, direct and iterative solution of linear equations, iterative solution of nonlinear equations, optimization, approximation theory, interpolation, quadrature, numerical methods for initial and boundary value problems in ordinary differential equations.

course, math, Melvin-Leok, ODE, numerics

Numerical Ordinary Differential Equations (Graduate)

anonymous@undisclosed.example.com (Anonymous) — Sat, 27 Apr 2024 11:48:33 +0000

Numerical Ordinary Differential Equations (Graduate)

Playlist Link

Abstract:

This graduate course in numerical analysis will focus on the mathematical analysis and derivation of numerical methods for the solution of ordinary differential equations. Issues include order of accuracy, convergence, stability.

course, math, ODE, numerics, Graduate, Melvin-Leok

Numerical Ordinary Differential Equations (Undergraduate)

anonymous@undisclosed.example.com (Anonymous) — Sat, 27 Apr 2024 11:48:49 +0000

Numerical Ordinary Differential Equations (Undergraduate)

Playlist Link

Abstract:

This undergraduate course in numerical analysis will focus on the mathematical analysis and derivation of numerical methods for numerical differentiation and integration, and the solution of ordinary differential equations and boundary-value problems. Issues include order of accuracy, convergence, stability.

course, math, ODE, numerics, Undergraduate, Melvin-Leok

Optimization on Manifolds (course)

anonymous@undisclosed.example.com (Anonymous) — Sat, 27 Apr 2024 11:49:43 +0000

Optimization on Manifolds (course)

Playlist Link

Abstract:

Smooth optimization on manifolds naturally generalizes smooth optimization in Euclidean spaces in a manner that is of interest in a variety of applications, including modal analysis, blind source separation (via independent component analysis), pose estimation in computer vision, and model reduction in dynamical systems. Manifolds of interest include the Stiefel manifolds and Grassmann manifolds.

After presenting a number of motivating applications, we will introduce the basics of differential manifolds and Riemannian geometry, and describe how methods in optimization, like line-search, Newton's method, and trust region methods can be generalized to the case of manifolds. The course will assume only a basic knowledge of matrix algebra and real analysis.

course, math, Melvin-Leok, optimization, Manifolds

ReadTheDocs Sphinx GitHub CI-CD

anonymous@undisclosed.example.com (Anonymous) — Mon, 04 Dec 2023 21:14:46 +0000

ReadTheDocs Sphinx GitHub CI-CD

Playlist Link

Read-The-Docs, Sphinx, GitHub, CI-CD

Sănătate mintală în 2023

anonymous@undisclosed.example.com (Anonymous) — Tue, 05 Dec 2023 11:56:17 +0000

Sănătate mintală în 2023

Cătălin-Moise, romanian

The Complete Mathematics of Neural Networks and Deep Learning

anonymous@undisclosed.example.com (Anonymous) — Mon, 04 Dec 2023 13:46:57 +0000

The Complete Mathematics of Neural Networks and Deep Learning

Mathematics, Neural-Networks, Deep-Learning, DL, ML