Erwin Schrödinger Institute · @ESIVienna
128 followers · 69 posts · Server mathstodon.xyz

Have you already taken a look at the newest paper of our workshop participants?🤠

Stefano Almi, Marco Morandotti, Francesco Solombrino: Optimal control problems in transport dynamics with additive noise
arxiv.org/pdf/2303.04877.pdf

@univienna @stem_univie

(for the video click at twitter.com/ESIVienna/status/1)
@PoliTOnews

#optimizationandcontrol #differentialequations

Last updated 1 year ago

Yohan John 🤖🧠 · @DrYohanJohn
1337 followers · 1173 posts · Server fediscience.org

Beautiful PDE visualization tool!

Here's a reaction-diffusion system with a pic of Turing himself as the initial condition.

visualpde.com/sim/?preset=Alan

#ODEs #PDEs #differentialequations #mathematics

Last updated 1 year ago

Mark Crocker · @mcrocker
46 followers · 410 posts · Server indieweb.social

Top Math Prize Awarded for Describing the Dynamics of the Flow of Rivers and the Melting of Ice - Scientific American
scientificamerican.com/article

I hated diff-EQ at University, because I found the topic unapproachably difficult. So I have to admire someone brave enough too take on the field professionally and make significant enough progress to win the Abel Prize

#differentialequations #mathematics

Last updated 1 year ago

The same conscious mind that detested math in high school obviously didn’t get the memo from the part of my mind that handles such astoundingly complex computations instantaneously, spontaneously, on a daily, minute by minute, second by second basis.

#transhumanism #gnosticism #differentialequations

Last updated 2 years ago

Barry Schwartz 🫖 · @chemoelectric
501 followers · 7684 posts · Server masto.ai
Barry Schwartz 🫖 · @chemoelectric
501 followers · 7683 posts · Server masto.ai
empet :julia: · @empet
16 followers · 57 posts · Server fosstodon.org

A new paper, Machine Learning Methods for Autonomous Ordinary Differential Equations
by M Bouchereau, P Chartier, M Lemou, F Méhats, arxiv.org/abs/2304.09036gives ,
presents a method that uses neural networks to modify the original vector field defining the ODE,
to get a computationally cheap numerical solution. , ,

#ml #differentialequations #neuralnetwork

Last updated 2 years ago

Jim Donegan ✅ · @jimdonegan
1467 followers · 4317 posts · Server mastodon.scot
Jon Awbrey · @Inquiry
182 followers · 1112 posts · Server mathstodon.xyz

@xameer

Cf. • Discussion 3
inquiryintoinquiry.com/2020/06

once had a ( of ) long before did but physics learned to reduce complexity through the use of and (combined in ). One of the promising features of is their relationship to . So I’ve been looking into that. Here’s a link, a bit in medias res, but what I’ve got for now.

#ai #dynamicupdating #complexity #physics #differentialoperators #MinimalNegationOperators #liegroups #groupsymmetries #differentialequations #frameproblem #DifferentialLogic

Last updated 2 years ago

Dominic Boutet · @dominic_boutet
565 followers · 76 posts · Server neuromatch.social
SciHi Blog · @scihiblog
244 followers · 122 posts · Server fedihum.org

On January 15, 1850, Russian mathematician Sofia Kovalevskaya was born. Kovalevskaya was responsible for important original contributions to analysis, partial differential equations and mechanics, and the first woman appointed to a full professorship in Northern Europe.

scihi.org/sofia-kovalevskaya-m

#maths #mathematics #analysis #differentialequations #historyofscience #WomenInScience #womeninstem #otd

Last updated 2 years ago

Hamiltonian field equations:
\[\boxed{\boxed{\dot\phi_i=+\dfrac{\delta\mathcal{H}}{\delta\pi_i},\ \dot\pi_i=-\dfrac{\delta\mathcal{H}}{\delta\phi_i}}}\]
The field analogue of the Hamiltonian formulation of classical mechanics!

#differentialequations #theoreticalphysics #functional #fieldequations #quantumfield #field #classicalmechanics #hamiltonian

Last updated 2 years ago

Hamiltonian field equations:
\[\dot\phi_i=+\dfrac{\delta\mathcal{H}}{\delta\pi_i},\ \dot\pi_i=-\dfrac{\delta\mathcal{H}}{\delta\phi_i}\]
The field analogue of the Hamiltonian formulation of classical mechanics!

#differentialequations #theoreticalphysics #functional #fieldequations #quantumfield #field #classicalmechanics #hamiltonian

Last updated 2 years ago

Geodesic equation using Einstein summation convention:
\[\boxed{\ddot{\gamma}^\mu+\Gamma^\mu_{\alpha\beta}\dot\gamma^\alpha\dot\gamma^\beta=0}\]
which are the Euler-Lagrange equations of motion for the energy functional, and \(\Gamma^\mu_{\alpha\beta}\) are the Christoffel symbols. In general relativity, a geodesic generalizes the notion of a "straight line" to curved spacetime.

#differentialequations #physics #differentialgeometry #geodesic #mathematicalphysics #spacetime #generalrelativity

Last updated 2 years ago

Jitse Niesen · @jitseniesen
48 followers · 67 posts · Server mathstodon.xyz

I really enjoyed the paper

Oteo & Ros, Why Magnus expansion?, URL: doi.org/10.1080/00207160.2021. (paywall)

and not just because it cites a paper of mine (though it does help!)

It's a historical/personal reflection on the Magnus expansion, a series solution to the differential equation \( x'(t) = A(t) x(t) \) which I describe below the fold. (1/n, n≈7)

#geometricnumericalintegration #numericalanalysis #liegroups #quantummechanics #matrixexponential #differentialequations #magnusexpansion

Last updated 2 years ago

The new SciML documentation is almost out now. One big piece just came online: the SciML workshop, pre-built exercises for running workshops (and courses) with SciML! Some of the exercises have answers and hints, some do not... so use them as HW problems!

docs.sciml.ai/SciMLWorkshop/st

#julialang #SciML #differentialequations #machinelearning

Last updated 2 years ago

The new SciML documentation is almost out now. One big piece just came online: the SciML workshop, pre-built exercises for running workshops (and courses) with SciML! Some of the exercises have answers and hints, some do not... so use them as HW problems!

docs.sciml.ai/SciMLWorkshop/st

#julialang #SciML #differentialequations #machinelearning

Last updated 2 years ago

Michelle Hatzel · @mlhatzel
1 followers · 2 posts · Server mathstodon.xyz

My : currently powering through undergrad PDEs and stochastic processes. These are the last weeks of the last semester of my math degree; am considering grad studies since it is now getting interesting, and don’t want to stop. Interests: -communication, and more.

#math #differentialequations #Maplesoft #symboliccomputation #introduction

Last updated 2 years ago

Jon Awbrey · @Inquiry
57 followers · 186 posts · Server mathstodon.xyz
Sarah Kavassalis · @sc_k
377 followers · 60 posts · Server climatejustice.social

For my introduction, I’m an who builds models of the with lots of different tools (finite state machines, many flavours of , and ). I also work on cool collaboration with computer scientists and psychologists to try and understand what makes some research more effective at changing than others. A lot of my energy goes into undergraduate and trying to figure out how we should best climate science (and the modern computational tools behind it) for societal good. Career wise, I’ll be starting as an Assistant of and at Harvey Mudd College next summer.

#atmospheric #chemist #atmosphere #computational #differentialequations #machinelearning #environmental #regulations #education #teach #professor #climate #chemistry

Last updated 2 years ago