#pde — Public Fediverse posts

📢 MOSS Season 2 continues next week Thursday!

🎙️ Speaker: Claudia García (Universidad de Granada, Spain)

🗣️ Talk title: Patterns and equilibria in incompressible fluids

🗓️ Thursday, 9 April 2026 • 🕓 16:00 CEST • Online

A talk on 2D Euler/Navier–Stokes, relative equilibria, and coherent vortex patterns through bifurcation theory.

👉 Scan the QR code in the image to join the mailing list and receive the online access link.

#Mathematics #FluidDynamics #NavierStokes #EulerEquations #PDE

This year, Simon Prince, Professor of Computer Science at UCL, published a series of tutorials on ordinary differential equations (ODEs) and stochastic differential equations (SDEs) in machine learning for RBC Borealis. These are intended for readers with no background in these areas and require only basic calculus.

Article 1 describes what ODEs and SDEs are and their applications in machine learning.

https://rbcborealis.com/research-blogs/odes-and-sdes-for-machine-learning

Article 2 describes ODEs, vector ODEs and PDEs and defines associated terminology. They develop several categories of ODE and discuss how their solutions are related to one another. They discuss the necessary conditions for an ODE to have a solution.

https://rbcborealis.com/research-blogs/introduction-ordinary-differential-equations

Article 3 describes methods for solving first-order ODEs in closed form. They categorise ODEs into distinct families and develop a method to solve each family.

https://rbcborealis.com/research-blogs/closed-form-solutions-for-odes

For many ODEs, there is no known closed-form solution.

Article 4 considers numerical methods, which can be used to approximate the solution of any ODE regardless of its tractability.

https://rbcborealis.com/research-blogs/numerical-methods-for-odes

This concludes their treatment of ODEs. In the coming weeks, we will focus on SDEs. They will describe stochastic processes and SDEs, and show how to solve SDEs using either direct stochastic integration or Ito's lemma. They will introduce the Fokker-Planck equation, which transforms a stochastic differential equation into the PDE governing the evolving probability density of the solution. They also consider Andersen's theorem, which allows us to reverse the direction of SDEs.

#ODEs #PDEs #SDEs #ODE #PDE #SDE #Calculus #ML #DL #VectorCalculus #LectureSeries #Tutorials

Belle collaboration avec le Pôle Projets : Modélisation #Mathématique des Systèmes Complexes de #centralesupelec Université #parissaclay.
J'ai proposé un problème appliqué de modélisation par #PDE et de résolution numérique d'un processus de diffusion d'insectes avec piègeage, issu de mes travaux de recherche.
J'ai eu le plaisir d'accompagner le travail de Aya Chaieb, Baptiste Petiot, Louis Mudarra et de Lucas Bourret. Utile et enrichissant pour toutes les parties.
https://hal.inrae.fr/hal-05084285v1

[Перевод] 79% научных публикаций об AI завышают результат

Применение AI в науке растет, но результаты его внедрения часто переоценены. Исследования показывают, что 79% публикаций, заявляющих о превосходстве AI, используют некорректные бенчмарки. Это искажает представление о реальном потенциале AI в научном прогрессе.

https://habr.com/ru/articles/911800/

#ии #наука #исследование #машинное+обучение #физика #pde #оптимизация #методология #хайп #deepmind

I'm wondering: #physics makes a lot of use of #periodic functions, in particular it is very useful to solve space-dependent equations in representative volumes with #periodicBoundaryConditions.

However I've only seen it done with periodicity along orthogonal directions, aligned with a Cartesian frame.

Do you know of work, e.g. #PDE resolution, in nonrectangular #periodicDomains? E.g., in a #tiled hexagon? (but with a sufficiently generic setting, not exploiting regular hexagon symmetries) Even better if the periodicity parameters themselves are among the unknowns.

(Maybe I'm completely missing something obvious there, I'm in my first steps towards defining what I want - any random thought on the topic highly welcome!)

#tiling people?

I have arrived, and given my talk, at the tri-section #MAA meeting
#PDE #MathConference

Can anyone recommend a writeup on 1st order linear PDEs which is not written for engineering majors, but for working mathematicians? #PDE #math

Wir freuen uns bei der diesjährigen Zyklenvorstellung insbesondere auf folgende Vortragende und Vorträge:

- Prof. Dr. Russell Luke, Variational #Analysis and #Optimization
- Prof. Dr. Ingo Witt, Analysis of partial differential equations (#PDE)
- Prof. Dr. Anja Sturm, Stochastische Prozesse
- Prof. Dr. Axel Munk, Statistical Foundations of #DataScience

Just found this little helper for #neovim, #lazyvim that lets you manage your node dependencies from within your editor.
I have already seen this in VSCode but never missed it until I installed it in my #pde

https://github.com/vuki656/package-info.nvim

We've been working on a massive riddle tying together #self-organization, #carbonate #diagenesis, reactive transport, #paleoclimate and #Milankovich cycles, and very stiff PDE systems.

If you've missed the poster at #egu24, you can still find it attached to the abstract in the conference program (https://meetingorganizer.copernicus.org/EGU24/EGU24-16400.html) and on Zenodo https://zenodo.org/records/10943274 If you're into numerical methods, tricky PDEs or other aspects of #modeling, please see if you have any advice to us 😄 #solvers #PDE

LINEAR TRANSPORT EQUATION
The linear transport equation (LTE) models the variation of the concentration of a substance flowing at constant speed and direction. It's one of the simplest partial differential equations (PDEs) and one of the few that admits an analytic solution.

Given \(\mathbf{c}\in\mathbb{R}^n\) and \(g:\mathbb{R}^n\to\mathbb{R}\), the following Cauchy problem models a substance flowing at constant speed in the direction \(\mathbf{c}\).
\[\begin{cases}
u_t+\mathbf{c}\cdot\nabla u=0,\ \mathbf{x}\in\mathbb{R}^n,\ t\in\mathbb{R}\\
u(\mathbf{x},0)=g(\mathbf{x}),\ \mathbf{x}\in\mathbb{R}^n
\end{cases}\]
If \(g\) is continuously differentiable, then \(\exists u:\mathbb{R}^n\times\mathbb{R}\to\mathbb{R}\) solution of the Cauchy problem, and it is given by
\[u(\mathbf{x},t)=g(\mathbf{x}-\mathbf{c}t)\]

#LinearTransportEquation #LinearTransport #Cauchy #CauchyProblem #PDE #PDEs #CauchyModel #Math #Maths #Mathematics #Linear #LinearPDE #TransportEquation #DifferentialEquations

VisualPDE: an interactive, lightning-fast browser-based solver for models in #physics, #chemistry, or #biology. #PDE https://visualpde.com/

'Neural Q-learning for solving PDEs', by Samuel N. Cohen, Deqing Jiang, Justin Sirignano.

http://jmlr.org/papers/v24/22-1075.html

#pdes #pde #nonlinear

Just published a story with some background-informations on the simulation for nonlinear force-displacement curves of rubber-metal parts related to our scientific article from 2021.

https://medium.com/@adtzlr/nonlinear-force-displacement-curves-of-rubber-metal-parts-ab7c48448e96

#python #computationalmechanics #scientificcomputing #opensource #rubber #hyperelasticity #finiteelements #fea #pde

FElupe - A Python package for Finite Element Analysis, Version 7.8.0 is available on PyPI. Now with mesh-generators for the elementary shapes line, rectangle, cube, triangle and circle.

https://github.com/adtzlr/felupe

#computationalmechanics #scientificcomputing #python #opensource #finiteelements #fea #pde

@book

There is also scikit-fem (more general approach to pde) and FElupe (more focussed on solid mechanics, hyperelasticity).

#python #fea #pde

https://github.com/kinnala/scikit-fem

https://github.com/adtzlr/felupe

Reminded of this because I talk about #blowups as an operation in algebraic geometry but this is not the same as #blowup in #PDE theory …

"A revisão do Plano Diretor de São Paulo será sancionada nesta sexta-feira (7) e publicada no Diário Oficial no sábado (8). Segundo Nunes, o projeto terá, ao menos, dez vetos". Etiquetas: #SãoPaulo #PlanoDiretor #PDE #urbanismo #regulação #direitourbanístico #RicardoNunes #PrefeituraSP. Via: https://orbi.band.uol.com.br/sao-paulo/plano-diretor-deve-ter-ate-10-vetos-diz-prefeito-ricardo-nunes-7259

Ever been irritated that Fast Multipole Methods require lots of special, problem-specific code for efficiency (e.g. specific to the Coulomb potential?) My student Isuru Fernando has fixed that for you: https://arxiv.org/abs/2305.17867 #fmm #paper #fastmultipole #pde #numerics #scicomp

Windows 11 22H2 introduces Personal Data Encryption (PDE), an easy to manage, simple to use, user authenticated data encryption mechanism #PDE #Windows11 #22H2 #WindowsHelloFor #sharegeneratedinpartwithgpt3 https://techcommunity.microsoft.com/t5/security-compliance-and-identity/introducing-personal-data-encryption-securing-user-data-before/ba-p/3691185

More orthogonal trajectories. #pde #math #orthogonal #visualization #orthogonalTrajectories

Hi guys! Is there someone here doing research in #PDE, #LieGroups, #ComplexAnalysis?

#math #mathematics #maths