#odes — Public Fediverse posts

RE: https://mathstodon.xyz/@DurstewitzLab/116549716016889895

🧠 New preprint by Brändle et al./ @DurstewitzLab: Continuous-Time Piecewise-Linear #RecurrentNeuralNetworks introduces continuous-time #PLRNNs for #DynamicalSystems reconstruction.

The model combines interpretability and analytical tractability of pw-linear #RNN with cont.-time dynamics, allowing semi-analytic analysis of equilibria and limit cycles while handling irregularly sampled data better than standard Neural #ODEs.

#NeuralDynamics #Neuroscience #NeuralODE

RE: https://mathstodon.xyz/@DurstewitzLab/116549716016889895

🧠 New preprint by Brändle et al./ @DurstewitzLab: Continuous-Time Piecewise-Linear #RecurrentNeuralNetworks introduces continuous-time #PLRNNs for #DynamicalSystems reconstruction.

The model combines interpretability and analytical tractability of pw-linear #RNN with cont.-time dynamics, allowing semi-analytic analysis of equilibria and limit cycles while handling irregularly sampled data better than standard Neural #ODEs.

#NeuralDynamics #Neuroscience #NeuralODE

RE: https://mathstodon.xyz/@DurstewitzLab/116549716016889895

🧠 New preprint by Brändle et al./ @DurstewitzLab: Continuous-Time Piecewise-Linear #RecurrentNeuralNetworks introduces continuous-time #PLRNNs for #DynamicalSystems reconstruction.

The model combines interpretability and analytical tractability of pw-linear #RNN with cont.-time dynamics, allowing semi-analytic analysis of equilibria and limit cycles while handling irregularly sampled data better than standard Neural #ODEs.

#NeuralDynamics #Neuroscience #NeuralODE

RE: https://mathstodon.xyz/@DurstewitzLab/116549716016889895

🧠 New preprint by Brändle et al./ @DurstewitzLab: Continuous-Time Piecewise-Linear #RecurrentNeuralNetworks introduces continuous-time #PLRNNs for #DynamicalSystems reconstruction.

The model combines interpretability and analytical tractability of pw-linear #RNN with cont.-time dynamics, allowing semi-analytic analysis of equilibria and limit cycles while handling irregularly sampled data better than standard Neural #ODEs.

#NeuralDynamics #Neuroscience #NeuralODE

RE: https://mathstodon.xyz/@DurstewitzLab/116549716016889895

🧠 New preprint by Brändle et al./ @DurstewitzLab: Continuous-Time Piecewise-Linear #RecurrentNeuralNetworks introduces continuous-time #PLRNNs for #DynamicalSystems reconstruction.

The model combines interpretability and analytical tractability of pw-linear #RNN with cont.-time dynamics, allowing semi-analytic analysis of equilibria and limit cycles while handling irregularly sampled data better than standard Neural #ODEs.

#NeuralDynamics #Neuroscience #NeuralODE

Alright, future engineers!
**Euler's Method:** Approximates solutions to differential equations by taking small linear steps.
Formula: `y_n+1 = y_n + h * f(x_n, y_n)`
Pro-Tip: Smaller step size (h) improves accuracy but increases computational cost!

#NumericalMethods #ODEs #STEM #StudyNotes

Alright, future engineers!

**Euler's Method:** Approximates solutions to ODEs by taking small linear steps. Ex: `y_new = y_old + h * f(x_old, y_old)`. Pro-Tip: Accuracy depends heavily on step size `h`. Smaller `h` is better for precision!
#ODEs #NumericalMethods #STEM #StudyNotes

Alright, future engineers!

Euler's Method: Approximates solutions to Ordinary Differential Equations (ODEs) by taking small steps along the tangent. Ex: `y_new = y_old + h * f(x_old, y_old)`. Pro-Tip: Simple, but smaller 'h' improves accuracy (at cost of computation)!
#ODEs #NumericalAnalysis #STEM #StudyNotes

Euler's Method approximates ODE solutions by stepping along tangent lines. Formula: `y_n+1 = y_n + h * f(x_n, y_n)`. Pro-Tip: A smaller step size `h` means more accuracy but more computation. Balance wisely!
#NumericalMethods #ODEs #STEM #StudyNotes

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

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

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

I wrote a blog post about a lecture introducing stability in ODE models and their numerical solution. The lecture transcript and code for figures are included.

https://nadiah.org/2025/12/04/mxb261

#mathematicalEcology #ODEs #stability #mathematics #lectureNotes #populationDynamics

I wrote a blog post about a lecture introducing stability in ODE models and their numerical solution. The lecture transcript and code for figures are included.

https://nadiah.org/2025/12/04/mxb261

#mathematicalEcology #ODEs #stability #mathematics #lectureNotes #populationDynamics

I wrote a blog post about a lecture introducing stability in ODE models and their numerical solution. The lecture transcript and code for figures are included.

https://nadiah.org/2025/12/04/mxb261

#mathematicalEcology #ODEs #stability #mathematics #lectureNotes #populationDynamics

I wrote a blog post about a lecture introducing stability in ODE models and their numerical solution. The lecture transcript and code for figures are included.

https://nadiah.org/2025/12/04/mxb261

#mathematicalEcology #ODEs #stability #mathematics #lectureNotes #populationDynamics

I wrote a blog post about a lecture introducing stability in ODE models and their numerical solution. The lecture transcript and code for figures are included.

https://nadiah.org/2025/12/04/mxb261

#mathematicalEcology #ODEs #stability #mathematics #lectureNotes

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

All the better to see you …
#odes #ocelli #optics #norfolk

Odes and garden wildlife ...

https://1001species.substack.com/p/odes-and-garden-wildlife

#dragonflies #wildlife #wildlifegardening #odes #rain #nature #biodiversity #montreal #canada

'Identifiability and Asymptotics in Learning Homogeneous Linear ODE Systems from Discrete Observations', by Yuanyuan Wang, Wei Huang, Mingming Gong, Xi Geng, Tongliang Liu, Kun Zhang, Dacheng Tao.

http://jmlr.org/papers/v25/22-1159.html

#estimation #estimator #odes

'Stable Implementation of Probabilistic ODE Solvers', by Nicholas Krämer, Philipp Hennig.

http://jmlr.org/papers/v25/20-1423.html

#numerical #solvers #odes

Faster Training of Neural ODEs Using Gauß–Legendre Quadrature

Alexander Luke Ian Norcliffe, Marc Peter Deisenroth

Action editor: Kevin Swersky.

https://openreview.net/forum?id=f0FSDAy1bU

#odes #models #quadrature

Reposting! Welcoming any thoughts about teaching diff eqs/coding and scientific computing in general #math #ODEs #Python

I asked #ChatGPT to write an ode to ODEs.

#math #mathematics #odes #ODEs

We build these using data collected from clinical trials (e.g. blood samples, clinical observations, scores, X-rays and suchlike - multiple samples, over time, from many subjects), which we use to build compartmental models which approximate what is happening over time using ordinary differential equations (#ODEs).

https://www.europesays.com/ie/159862/ I Still Want to Kiss Josh Hutcherson #boyfriends #comedy #culture #Éire #Entertainment #hbo #IE #Ireland #odes #simping #TV

Odes of Solomon, Lost Psalms of Early Christianity Discovered - PODCAST @
https://podcasts.apple.com/us/podcast/spiritual-awakening-radio/id1477577384

https://open.spotify.com/show/5kqOaSDrj630h5ou65JSjE

https://podcasts.google.com/feed/aHR0cHM6Ly9mZWVkcy5saWJzeW4uY29tLzIwNzIzNi9yc3M

https://santmatradhasoami.blogspot.com/2022/09/odes-of-solomon-lost-psalms-of-early.html

#SpiritualAwakeningRadio #SantMatSatsangPodcasts #Satsang #Hymns #Psalms #OdesofSolomon #NewTestament #BookoftheOdes #ODES #NewTestamentPsalms #ExtraCanonicalScriptures #LostBooksoftheBible #Bible #Apocrypha #Pseudepigrapha #EarlyChristianity #JesusMovement #EarlyChurch #Christianity #Gnosticism #SpiritualPodcasts

in many ways, #mathematical #physics is based on the #smoothing properties of the #integral

#integrableSystems #mathematicalPhysics #complexAnalysis #spectralTheory #harmonicAnalysis #functionalAnalysis #mathematicalAnalysis #differentialEquations #ODEs #PDEs #SDEs #DEs #equations #BrownianMotion #LangevinDynamics #dynamics #Langevin #StochasticDifferentialEquations #StochasticProcesses #WienerProcess #OrnsteinUhlenbeck #HarmonicOscillator #WaveEquation #Newton #Newtonian #Maxwell #Einstein

in many ways, #mathematical #physics is based on the #smoothing properties of the #integral

#integrableSystems #mathematicalPhysics #complexAnalysis #spectralTheory #harmonicAnalysis #functionalAnalysis #mathematicalAnalysis #differentialEquations #ODEs #PDEs #SDEs #DEs #equations #BrownianMotion #LangevinDynamics #dynamics #Langevin #StochasticDifferentialEquations #StochasticProcesses #WienerProcess #OrnsteinUhlenbeck #HarmonicOscillator #WaveEquation #Newton #Newtonian #Maxwell #Einstein

in many ways, #mathematical #physics is based on the #smoothing properties of the #integral

#integrableSystems #mathematicalPhysics #complexAnalysis #spectralTheory #harmonicAnalysis #functionalAnalysis #mathematicalAnalysis #differentialEquations #ODEs #PDEs #SDEs #DEs #equations #BrownianMotion #LangevinDynamics #dynamics #Langevin #StochasticDifferentialEquations #StochasticProcesses #WienerProcess #OrnsteinUhlenbeck #HarmonicOscillator #WaveEquation #Newton #Newtonian #Maxwell #Einstein

in many ways, #mathematical #physics is based on the #smoothing properties of the #integral

#integrableSystems #mathematicalPhysics #complexAnalysis #spectralTheory #harmonicAnalysis #functionalAnalysis #mathematicalAnalysis #differentialEquations #ODEs #PDEs #SDEs #DEs #equations #BrownianMotion #LangevinDynamics #dynamics #Langevin #StochasticDifferentialEquations #StochasticProcesses #WienerProcess #OrnsteinUhlenbeck #HarmonicOscillator #WaveEquation #Newton #Newtonian #Maxwell #Einstein

'Identifiability and Asymptotics in Learning Homogeneous Linear ODE Systems from Discrete Observations', by Yuanyuan Wang, Wei Huang, Mingming Gong, Xi Geng, Tongliang Liu, Kun Zhang, Dacheng Tao.

http://jmlr.org/papers/v25/22-1159.html

#estimation #estimator #odes

'Identifiability and Asymptotics in Learning Homogeneous Linear ODE Systems from Discrete Observations', by Yuanyuan Wang, Wei Huang, Mingming Gong, Xi Geng, Tongliang Liu, Kun Zhang, Dacheng Tao.

http://jmlr.org/papers/v25/22-1159.html

#estimation #estimator #odes

'Identifiability and Asymptotics in Learning Homogeneous Linear ODE Systems from Discrete Observations', by Yuanyuan Wang, Wei Huang, Mingming Gong, Xi Geng, Tongliang Liu, Kun Zhang, Dacheng Tao.

http://jmlr.org/papers/v25/22-1159.html

#estimation #estimator #odes

'Identifiability and Asymptotics in Learning Homogeneous Linear ODE Systems from Discrete Observations', by Yuanyuan Wang, Wei Huang, Mingming Gong, Xi Geng, Tongliang Liu, Kun Zhang, Dacheng Tao.

http://jmlr.org/papers/v25/22-1159.html

#estimation #estimator #odes