It seems I wrote a distributed Levenberg-Marquardt optimization algorithm. Each time the algorithm needs updated residue or the Hessian matrix it sends request to a worker pool which might be a heterogeneous collection of independent problems.

#numericalmethods

PhD or PostDoc position in numerical simulation of cell membranes
HTW Dresden

PhD or PostDoc position in numerical simulation of nanoplastics entry in cell membranes

See the full job description on jobRxiv: https://jobrxiv.org/job/htw-dresden-27778-phd-or-postdoc-position-in-numerical-simulation-of-cell-membranes/

#numericalmethods #ScienceJobs #hiring #research
https://jobrxiv.org/job/htw-dresden-27778-phd-or-postdoc-position-in-numerical-simulation-of-cell-membranes/?fsp_sid=4540

Các nhà nghiên cứu chỉ ra rằng giải pháp ODE ngầm (implicit) không phải lúc nào cũng bền vững hơn giải pháp ODE rõ ràng (explicit). Không có solver ODE nào là "tốt nhất" cho mọi trường hợp – lựa chọn phụ thuộc vào bài toán cụ thể. Bài viết phân tích chi tiết qua các ví dụ thực tế trong lập trình số học.

#ODE #NumericalMethods #ToanHocTinh #LapTrinh #PhanTichSo #ODEsolvers #PhuongPhapSo

https://www.reddit.com/r/programming/comments/1nirweo/mplicit_ode_solvers_are_not_universally_more/

🌪️ Chaos in Simple Dynamic Systems - Why it Matters in Physics & Simulations

Chaos is one of the most fascinating aspects of nonlinear dynamics. Even in the simplest systems governed by deterministic equations, a tiny change in initial conditions can lead to dramatically different outcomes - a phenomenon popularly known as the “butterfly effect.”

Two toy problems here illustrate how chaos emerges in physical systems:

🔹 Problem 1 - Lorenz Attractor
A set of three nonlinear ODEs originally derived to model atmospheric convection. What starts as a simple flow model quickly evolves into the famous “butterfly” trajectory - showing how sensitive fluid systems are to initial conditions.

🔹 Problem 2 - Chaotic Billiards
Two balls start with nearly identical positions inside a circular boundary. Initially, their paths overlap, but after a few bounces, their trajectories diverge completely - despite following the same physical laws of elastic collisions.

💡 These toy examples highlight a deeper truth:

Chaos is not randomness. It arises from deterministic equations that amplify small differences.

Capturing chaotic dynamics accurately in computational fluid dynamics (CFD) or turbulence simulations is an ongoing challenge in physics, HPC, and AI.
In real-world engineering, this sensitivity influences weather prediction, turbulence modeling, aerodynamics, and even industrial process simulations.

Here are some animations of both systems - the iconic Lorenz attractor and the chaotic motion of bouncing balls - to visualize just how quickly order gives way to apparent disorder:

https://m.youtube.com/watch?v=6z4qRhpBIyA

https://scipython.com/blog/chaotic-balls/

#ChaosTheory #HPC #NumericalMethods #AI #FluidDynamics #ButterflyEffect #Simulation

“How Does A Computer/Calculator Compute Logarithms?”, Zach Artrand (https://zachartrand.github.io/SoME-3-Living/).

Via HN: https://news.ycombinator.com/item?id=40749670 (which provides important addenda)

#Calculator #Mathematics #Maths #Logarithms #TaylorSeries #NumericalMethods #NumericalAnalysis #FastMath

Nice:

“Taming Floating Point Sums”, Orson Peters (https://orlp.net/blog/taming-float-sums/).

Via HN: https://news.ycombinator.com/item?id=40477604

On Lobsters: https://lobste.rs/s/lps7qx/taming_floating_point_sums

#Programming #NumericalMethods #FloatingPoint #Sum #KahanSummation #Rust #AutoVectorization #Speed #Accuracy #RoundingErrors

"Floats Are Weird", Anthony Wang (https://a.exozy.me/posts/floats-weird/).

Via HN: https://news.ycombinator.com/item?id=39426341

On Lobsters: https://lobste.rs/s/2axq6g/floats_are_weird

See also: "The Right Way To Calculate Stuff" [2003], Don Hatch (http://www.plunk.org/~hatch/rightway.html).

#Arithmetic #NumericalMethods #FloatingPoint

Whenever I walk to/from home, I have to walk up/down an inclined street; I noticed that the asphalt floor has different curvatures depending on how near it is of a bend, and I try to find a less steep incline while walking.

This got me inspiration for the few questions below. Any simple explanations, and related links, are welcome.

Given a #differentiable surface within R^3, and two distinct points in it, there are infinitely many differentiable paths from one point to another, remaining on the surface. At each point of the #path, one can find the path's local #curvature. Then:

- Find a path that minimizes the supreme of the curvature. In other words, find the "flattest" path.

- Find a path that minimizes the variation of the curvature. In other words, find a path that "most resembles" a circle arc.

Are these tasks always possible within the given conditions? Are any stronger conditions needed? Are there cases with an #analytic solution, or are they possible only with numerical approximations?

#Analysis #DifferentialGeometry #Calculus #DifferentialEquations #NumericalMethods