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
https://arxiv.org/pdf/2303.04877.pdf

#DifferentialEquations #OptimizationandControl

@univienna @stem_univie

(for the video click at https://twitter.com/ESIVienna/status/1678690316377833472)
@PoliTOnews

Beautiful PDE visualization tool!

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

https://visualpde.com/sim/?preset=Alan

#Mathematics #DifferentialEquations #PDEs #ODEs

Top Math Prize Awarded for Describing the Dynamics of the Flow of Rivers and the Melting of Ice - Scientific American
https://www.scientificamerican.com/article/top-math-prize-awarded-for-describing-the-dynamics-of-the-flow-of-rivers-and-the-melting-of-ice/#

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

#mathematics #differentialEquations

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

The same #DifferentialEquations program as before, but this time in #OtusLisp or #Scheme:

Euler method - Rosetta Code https://rosettacode.org/wiki/Euler_method#Ol

#FunctionalProgramming #Lisp

A new entry for #ObjectIcon --

Euler method - Rosetta Code https://rosettacode.org/wiki/Euler_method#ObjectIcon

#Icon #ObjectOriented #GoalDirected #EulerMethod #DifferentialEquations

A new paper, Machine Learning Methods for Autonomous Ordinary Differential Equations
by M Bouchereau, P Chartier, M Lemou, F Méhats, https://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

#SabineHossenfelder - What are #DifferentialEquations and how do they work?

https://www.youtube.com/watch?v=Em339AlejIs&ab_channel=SabineHossenfelder

#Math #Maths #Mathematics #Equations #Physics #Prediction

@xameer

Cf. #DifferentialLogic • Discussion 3
• https://inquiryintoinquiry.com/2020/06/17/differential-logic-discussion-3/

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

#arxivfeed :

"Langevin algorithms for Markovian Neural Networks and Deep Stochastic control"
https://arxiv.org/abs/2212.12018

#MachineLearning #DeepLearning #ControlTheory #Optimization #DifferentialEquations

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.

http://scihi.org/sofia-kovalevskaya-mathematician-writer/

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

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!
#Hamiltonian #classicalmechanics #field #quantumfield #fieldequations #functional #theoreticalphysics #differentialequations

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!
#Hamiltonian #classicalmechanics #field #quantumfield #fieldequations #functional #theoreticalphysics #differentialequations

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

I really enjoyed the paper

Oteo & Ros, Why Magnus expansion?, URL: https://doi.org/10.1080/00207160.2021.1938011 (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)

#MagnusExpansion #DifferentialEquations #MatrixExponential #QuantumMechanics #LieGroups #NumericalAnalysis #GeometricNumericalIntegration

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!

https://docs.sciml.ai/SciMLWorkshop/stable/

#julialang #sciml #differentialequations #machinelearning

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!

https://docs.sciml.ai/SciMLWorkshop/stable/

#julialang #sciml #differentialequations #machinelearning

My #introduction: 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: #symboliccomputation #Maplesoft #differentialequations #math-communication, and more.

#DifferentialLogic and #DynamicSystems • Overview
• https://inquiryintoinquiry.com/2019/09/10/differential-logic-and-dynamic-systems-overview/

In modeling #IntelligentSystems, natural or artificial, there is a tension between #DynamicParadigms & #SymbolicParadigms.

#DynamicModels afford a system #QuantitativeDescription, charting its #TimeEvolution via #DifferentialEquations.

#SymbolicModels afford a system #QualitativeDescription, deducing its #LogicalConsequences. So far these tend to be static models, awaiting a logical analogue of #DifferentialCalculus.

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