# \#ode

**URL:** https://discourse.julialang.org/tag/ode/175.md

[Latest](https://discourse.julialang.org/latest.md) · [Categories](https://discourse.julialang.org/categories.md) · [Tags](https://discourse.julialang.org/tags.md)

---

## [AD using Enzyme in ODE problem with DataInterpolations](https://discourse.julialang.org/t/ad-using-enzyme-in-ode-problem-with-datainterpolations/137771)

<div class="topic-metadata">

**Author:** [@imre](https://discourse.julialang.org/u/imre)\
**Replies:** 3\
**Last updated:** [June 29, 2026, 7:47am UTC](https://discourse.julialang.org/t/ad-using-enzyme-in-ode-problem-with-datainterpolations/137771 "2026-06-29T07:47:07Z")

</div>

Hello, I have an ODE problem which uses DataInterpolations.jl to obtain input values for the system at specific timepoints in order to compute dx. I want to use Enzyme.jl to compute the gradients with respect to paramete…

---

## [Making a Universal Differential Equation Faster](https://discourse.julialang.org/t/making-a-universal-differential-equation-faster/137829)

<div class="topic-metadata">

**Author:** [@Ashima\_Kalathingal](https://discourse.julialang.org/u/Ashima_Kalathingal)\
**Replies:** 1\
**Last updated:** [June 28, 2026, 1:57am UTC](https://discourse.julialang.org/t/making-a-universal-differential-equation-faster/137829 "2026-06-28T01:57:32Z")

</div>

I have a two-state ODE, one of which is embedded in a neural network, making it a UDE. I am using 9 datasets for training, resulting in 9 distinct ODEs. prob1 = ODEProblem(UDE\_model1!,\[SOC0\_1, T∞1\],(time1\[1\],time1\[end\])…

---

## [Sensitivity Analysis on ODE system](https://discourse.julialang.org/t/sensitivity-analysis-on-ode-system/137757)

<div class="topic-metadata">

**Author:** [@violabini](https://discourse.julialang.org/u/violabini)\
**Replies:** 4\
**Last updated:** [June 25, 2026, 9:40am UTC](https://discourse.julialang.org/t/sensitivity-analysis-on-ode-system/137757 "2026-06-25T09:40:40Z")

</div>

Hi everyone, I am trying to use automatic differentiation in julia to compute the Jacobian of my outputs wrt my design variables for local sensitivity, but my ODEs are nearly coupled as for example du\[3\]=A\*du\[2\]+B u\[1\].…

---

## [Finding mutations that Zygote complains about](https://discourse.julialang.org/t/finding-mutations-that-zygote-complains-about/135864)

<div class="topic-metadata">

**Author:** [@Neodym](https://discourse.julialang.org/u/Neodym)\
**Replies:** 19\
**Last updated:** [March 1, 2026, 6:47pm UTC](https://discourse.julialang.org/t/finding-mutations-that-zygote-complains-about/135864 "2026-03-01T18:47:53Z")

</div>

Hey, Apparently, I have some hidden mutations in my code that I cannot find. Unfortunately, Zygote easily finds them and complains about it. I get call stacks 40+ layers deep, the last of my own functions being near th…

---

## [Force MTK to generate explicit ODEs?](https://discourse.julialang.org/t/force-mtk-to-generate-explicit-odes/135245)

<div class="topic-metadata">

**Author:** [@benjamin](https://discourse.julialang.org/u/benjamin)\
**Replies:** 9\
**Last updated:** [January 29, 2026, 1:30pm UTC](https://discourse.julialang.org/t/force-mtk-to-generate-explicit-odes/135245 "2026-01-29T13:30:05Z")

</div>

Hi! I am using ModelingToolkit.jl to model a physical system. The compiler generates an index-1 DAE, which works great for simulation. However, I need to use a standard Kalman Filter, which requires a minimal state-spa…

---

## [Large ODE Solver for Metal.jl](https://discourse.julialang.org/t/large-ode-solver-for-metal-jl/134769)

<div class="topic-metadata">

**Author:** [@Gavin-Rockwood](https://discourse.julialang.org/u/Gavin-Rockwood)\
**Replies:** 11\
**Last updated:** [December 29, 2025, 2:49am UTC](https://discourse.julialang.org/t/large-ode-solver-for-metal-jl/134769 "2025-12-29T02:49:29Z")

</div>

Is there any implementation for ODE solving using Metal.jl backends? I know there is DiffEqGPU, but the metal support is only for ensemble problems. I cannot for instance do f(u,p,t) = A\*u tspan = (0.0f0, 1.0f0) prob = …

---

## [Learning a mapping from an image to an ODE](https://discourse.julialang.org/t/learning-a-mapping-from-an-image-to-an-ode/134456)

<div class="topic-metadata">

**Author:** [@csvance](https://discourse.julialang.org/u/csvance)\
**Replies:** 4\
**Last updated:** [December 10, 2025, 6:00pm UTC](https://discourse.julialang.org/t/learning-a-mapping-from-an-image-to-an-ode/134456 "2025-12-10T18:00:06Z")

</div>

I have trained a CNN to map an image to a sequence of feature vectors f\_v and I want to learn a function du(u, f\_v) that maps the feature vectors to an ODE. For each image I know how to compute both the function and firs…

---

## [Compositional Methods in GeometricIntegrators.jl](https://discourse.julialang.org/t/compositional-methods-in-geometricintegrators-jl/133595)

<div class="topic-metadata">

**Author:** [@leespen1](https://discourse.julialang.org/u/leespen1)\
**Replies:** 0\
**Last updated:** [November 1, 2025, 6:23pm UTC](https://discourse.julialang.org/t/compositional-methods-in-geometricintegrators-jl/133595 "2025-11-01T18:23:05Z")

</div>

How can I use a compositional method, based on the implicit midpoint rule, in GeometricIntegrators.jl? My idea of a compositional method is based on Chapter V.3 Symmetric Composition Methods of Hairer et al.'s Geometric…

---

## [Fitting neural ODE to periodic time series](https://discourse.julialang.org/t/fitting-neural-ode-to-periodic-time-series/42263)

<div class="topic-metadata">

**Author:** [@SebastianCallh](https://discourse.julialang.org/u/SebastianCallh)\
**Replies:** 18\
**Last updated:** [October 13, 2025, 6:31pm UTC](https://discourse.julialang.org/t/fitting-neural-ode-to-periodic-time-series/42263 "2025-10-13T18:31:03Z")

</div>

Hello, I am trying to fit a neural ODE adapted from an example in the docs to the Mauna Loa dataset. but am running in to some problems. Fitting the model to too many time steps at once causes it to underfit dramatical…

---

## [\[ANN\] New release of OptimalControl.jl](https://discourse.julialang.org/t/ann-new-release-of-optimalcontrol-jl/132764)

<div class="topic-metadata">

**Author:** [@control-toolbox](https://discourse.julialang.org/u/control-toolbox)\
**Replies:** 5\
**Last updated:** [October 6, 2025, 10:55am UTC](https://discourse.julialang.org/t/ann-new-release-of-optimalcontrol-jl/132764 "2025-10-06T10:55:49Z")

</div>

It is a pleasure to announce the new release of OptimalControl.jl (v1.1). Intended to solve optimal control problems on ODEs, the package features: a friendly DSL both direct (optimisation) and indirect (aka. shooting)…

---

## [Choosing suitable options for solver ODE](https://discourse.julialang.org/t/choosing-suitable-options-for-solver-ode/77843)

<div class="topic-metadata">

**Author:** [@Camilo\_Chaparro](https://discourse.julialang.org/u/Camilo_Chaparro)\
**Replies:** 2\
**Last updated:** [August 6, 2025, 1:28pm UTC](https://discourse.julialang.org/t/choosing-suitable-options-for-solver-ode/77843 "2025-08-06T13:28:41Z")

</div>

Hello everyone, I want about the most suitable ODE solver for the following problem: using DifferentialEquations using Plots; plotly() #Parameters omega\_m = 1.6e6 N = 1 Delta\_mw = -0.7 …

---

## [Setting \`abstol\` and \`reltol\` when solving the Schrödinger equation with OrdinaryDiffEq](https://discourse.julialang.org/t/setting-abstol-and-reltol-when-solving-the-schrodinger-equation-with-ordinarydiffeq/125534)

<div class="topic-metadata">

**Author:** [@goerz](https://discourse.julialang.org/u/goerz)\
**Replies:** 27\
**Last updated:** [August 5, 2025, 9:10pm UTC](https://discourse.julialang.org/t/setting-abstol-and-reltol-when-solving-the-schrodinger-equation-with-ordinarydiffeq/125534 "2025-08-05T21:10:57Z")

</div>

Note: This topic was originally title “DiffEqOrdinaryDiffEq fails to preserve norm in simple Schrödinger equation”, which was solved by setting reltol. The more interesting part of the discussion is how to set abstol and…

---

## [Solving a large sparse ODE using Exponential methods](https://discourse.julialang.org/t/solving-a-large-sparse-ode-using-exponential-methods/125159)

<div class="topic-metadata">

**Author:** [@albertomercurio](https://discourse.julialang.org/u/albertomercurio)\
**Replies:** 8\
**Last updated:** [June 25, 2025, 7:49pm UTC](https://discourse.julialang.org/t/solving-a-large-sparse-ode-using-exponential-methods/125159 "2025-06-25T19:49:29Z")

</div>

Hello, I need to integrate a differential equation of the form \\dot{u} = L(t) u \\, , where u is a vector, L(t) = L\_0 + c(t) \* L\_1 \\, , L\_0 and L\_1 large sparse matrices, and c(t) a time dependent coefficient. I k…

---

## [Discrepancy of ODE Sensitivity Analysis paper results with benchmarks](https://discourse.julialang.org/t/discrepancy-of-ode-sensitivity-analysis-paper-results-with-benchmarks/129853)

<div class="topic-metadata">

**Author:** [@mra](https://discourse.julialang.org/u/mra)\
**Replies:** 31\
**Last updated:** [June 18, 2025, 2:01pm UTC](https://discourse.julialang.org/t/discrepancy-of-ode-sensitivity-analysis-paper-results-with-benchmarks/129853 "2025-06-18T14:01:19Z")

</div>

I have tried to reproduce results from the paper “A Comparison of Automatic Differentiation and Continuous Sensitivity Analysis for Derivatives of Differential Equation Solutions” (https://arxiv.org/pdf/1812.01892, Fig. …

---

## [Integrators with analytic derivatives w/r/t initial conditions (especially the independent variable)](https://discourse.julialang.org/t/integrators-with-analytic-derivatives-w-r-t-initial-conditions-especially-the-independent-variable/129832)

<div class="topic-metadata">

**Author:** [@stevenhughes](https://discourse.julialang.org/u/stevenhughes)\
**Replies:** 2\
**Last updated:** [June 13, 2025, 12:43pm UTC](https://discourse.julialang.org/t/integrators-with-analytic-derivatives-w-r-t-initial-conditions-especially-the-independent-variable/129832 "2025-06-13T12:43:37Z")

</div>

Hello, I am working on an application that requires derivatives odes to compute partials for solvers. The approach I am taking is to prefer analytic partials (for performance, which is key), and fallback to AD or finit…

---

## [Help training a NN that's used as a parameter in an ODE](https://discourse.julialang.org/t/help-training-a-nn-thats-used-as-a-parameter-in-an-ode/129231)

<div class="topic-metadata">

**Author:** [@alexl123](https://discourse.julialang.org/u/alexl123)\
**Replies:** 1\
**Last updated:** [May 22, 2025, 2:01am UTC](https://discourse.julialang.org/t/help-training-a-nn-thats-used-as-a-parameter-in-an-ode/129231 "2025-05-22T02:01:42Z")

</div>

Hello! I’ve been pulling my hair out trying to implement an ODE where one of the parameters is the output of a NN net. ChatGPT has me going in circles. Depending on what fixes I try I either get a: Error in epoch 1: Me…

---

## [Run only the algebraic part of the solver](https://discourse.julialang.org/t/run-only-the-algebraic-part-of-the-solver/128803)

<div class="topic-metadata">

**Author:** [@Bart\_van\_de\_Lint](https://discourse.julialang.org/u/Bart_van_de_Lint)\
**Replies:** 27\
**Last updated:** [May 20, 2025, 11:39am UTC](https://discourse.julialang.org/t/run-only-the-algebraic-part-of-the-solver/128803 "2025-05-20T11:39:55Z")

</div>

I’m working with a DAE system in ModelingToolkit.jl, and I’d like to run only the algebraic part of the integrator-that is, solve the algebraic constraints for given differential states, without advancing the differentia…

---

## [Conditional exact integration in ODE solving](https://discourse.julialang.org/t/conditional-exact-integration-in-ode-solving/127267)

<div class="topic-metadata">

**Author:** [@BdeKoning](https://discourse.julialang.org/u/BdeKoning)\
**Replies:** 2\
**Last updated:** [March 22, 2025, 6:57pm UTC](https://discourse.julialang.org/t/conditional-exact-integration-in-ode-solving/127267 "2025-03-22T18:57:53Z")

</div>

Say in my ODE problem I have an equation like this: \\frac{\\text{d}u\_i}{\\text{d}t} = r(\\mathbf{u})A(t) Here A(t) is a known non-negative interpolation function and r(\\mathbf{u}) is what we call a ‘reduction factor’; it…

---

## [Help with misbehaving ODE simulation](https://discourse.julialang.org/t/help-with-misbehaving-ode-simulation/126936)

<div class="topic-metadata">

**Author:** [@JonathanH](https://discourse.julialang.org/u/JonathanH)\
**Replies:** 1\
**Last updated:** [March 14, 2025, 12:43am UTC](https://discourse.julialang.org/t/help-with-misbehaving-ode-simulation/126936 "2025-03-14T00:43:24Z")

</div>

Hi all, I am having some issues with a set of ODEs I am simulating with DifferentialEquations.jl and am wondering if anyone can help. Basically, the code is simulating populations of bacteria and their viruses (phage) t…

---

## [Strang Splitting with SplitODEProblem](https://discourse.julialang.org/t/strang-splitting-with-splitodeproblem/126255)

<div class="topic-metadata">

**Author:** [@svretina](https://discourse.julialang.org/u/svretina)\
**Replies:** 2\
**Last updated:** [February 25, 2025, 3:27pm UTC](https://discourse.julialang.org/t/strang-splitting-with-splitodeproblem/126255 "2025-02-25T15:27:46Z")

</div>

Hi all, I am interested in implementing a split ODE problem, I am solving the wave equation with a Finite Volume scheme such as MUSCL with a discontinuous source term. I want to implement a fractional step method and …

---

## [Errors when running a Universal Differential Equation (UDE)](https://discourse.julialang.org/t/errors-when-running-a-universal-differential-equation-ude/125273)

<div class="topic-metadata">

**Author:** [@Ashima\_Kalathingal](https://discourse.julialang.org/u/Ashima_Kalathingal)\
**Replies:** 8\
**Last updated:** [February 8, 2025, 12:50pm UTC](https://discourse.julialang.org/t/errors-when-running-a-universal-differential-equation-ude/125273 "2025-02-08T12:50:58Z")

</div>

Hello, I am building a UDE as a part of my work in Julia. I am using the following example as reference https://docs.sciml.ai/Overview/stable/showcase/missing\_physics/ Unfortunately I am getting a warning message and …

---

## [Trouble with Optimization.jl errors](https://discourse.julialang.org/t/trouble-with-optimization-jl-errors/125410)

<div class="topic-metadata">

**Author:** [@Bill\_Holmes](https://discourse.julialang.org/u/Bill_Holmes)\
**Replies:** 2\
**Last updated:** [February 6, 2025, 3:46am UTC](https://discourse.julialang.org/t/trouble-with-optimization-jl-errors/125410 "2025-02-06T03:46:24Z")

</div>

Hello all. I’m running into an issue with Optimization.jl when trying to estimate parameters of ODEs. The specific issue is that some optimizers work while others don’t. Furthermore, different optimizers throw different …

---

## [Solving 2D PDE similar to advection-diffusion on unstructured mesh with Trixi](https://discourse.julialang.org/t/solving-2d-pde-similar-to-advection-diffusion-on-unstructured-mesh-with-trixi/125462)

<div class="topic-metadata">

**Author:** [@Liris](https://discourse.julialang.org/u/Liris)\
**Replies:** 6\
**Last updated:** [February 5, 2025, 5:41pm UTC](https://discourse.julialang.org/t/solving-2d-pde-similar-to-advection-diffusion-on-unstructured-mesh-with-trixi/125462 "2025-02-05T17:41:52Z")

</div>

Dear all, I am trying to solve the following equation: \\frac{\\partial \\phi}{\\partial t} + \\nabla\\cdot(\\phi \\boldsymbol{u}) - \\frac{\\partial}{\\partial z} \\left\[\\mathcal{F} \\phi(1-\\phi)\\right\] = \\nabla \\cdot (\\mathcal{D}…

---

## [Computing ODE sensitivities with sparse Jacobians in solver](https://discourse.julialang.org/t/computing-ode-sensitivities-with-sparse-jacobians-in-solver/125536)

<div class="topic-metadata">

**Author:** [@Neodym](https://discourse.julialang.org/u/Neodym)\
**Replies:** 3\
**Last updated:** [February 4, 2025, 6:31pm UTC](https://discourse.julialang.org/t/computing-ode-sensitivities-with-sparse-jacobians-in-solver/125536 "2025-02-04T18:31:17Z")

</div>

Hey there, I’m trying to compute the derivatives of a function involving an ODE solution. This works if I use dense Jacobians in the ODE solver. However, the Jacobian is actually sparse (PDE discretization, stiff) and …

---

## [Can remake be used with specific ODEProblem types?](https://discourse.julialang.org/t/can-remake-be-used-with-specific-odeproblem-types/110135)

<div class="topic-metadata">

**Author:** [@homocomputeris](https://discourse.julialang.org/u/homocomputeris)\
**Replies:** 3\
**Last updated:** [January 29, 2025, 10:36am UTC](https://discourse.julialang.org/t/can-remake-be-used-with-specific-odeproblem-types/110135 "2025-01-29T10:36:43Z")

</div>

When I try to remake a SecondOrderODEProblem with remake(secondorderprob; u0 = x\[1\], du0 = x\[2\]) I get Unrecognized keyword arguments found. The only allowed keyword arguments to \`solve\` are: (:dense, :saveat, …

---

## [Modifying time in sol after solve() function using DifferentialEquations.jl](https://discourse.julialang.org/t/modifying-time-in-sol-after-solve-function-using-differentialequations-jl/124647)

<div class="topic-metadata">

**Author:** [@Iddingsite](https://discourse.julialang.org/u/Iddingsite)\
**Replies:** 4\
**Last updated:** [January 10, 2025, 10:24pm UTC](https://discourse.julialang.org/t/modifying-time-in-sol-after-solve-function-using-differentialequations-jl/124647 "2025-01-10T22:24:49Z")

</div>

Hi, I was wondering, using DifferentialEquations.jl (and co), if there is an easy way to modify the t in sol object after it is output and to synchronise it with the interpolation? I have tried to simply modify it with…

---

## [Specify analytic exponential and pseudoinverse of linear part of a SplitODEProblem](https://discourse.julialang.org/t/specify-analytic-exponential-and-pseudoinverse-of-linear-part-of-a-splitodeproblem/124596)

<div class="topic-metadata">

**Author:** [@Gregstrq](https://discourse.julialang.org/u/Gregstrq)\
**Replies:** 1\
**Last updated:** [January 10, 2025, 3:14pm UTC](https://discourse.julialang.org/t/specify-analytic-exponential-and-pseudoinverse-of-linear-part-of-a-splitodeproblem/124596 "2025-01-10T15:14:54Z")

</div>

I have a system of ODE of the form du/dt = A(t)\*u + f(u) The linear part corresponds to fast dynamics, in comparison to the slow dynamics of the non-linear part. A(t) is actually so simple, that I can provide an analy…

---

## [Forecast Time series using Neural ODE for supervised learning](https://discourse.julialang.org/t/forecast-time-series-using-neural-ode-for-supervised-learning/124268)

<div class="topic-metadata">

**Author:** [@roilsed0903](https://discourse.julialang.org/u/roilsed0903)\
**Replies:** 0\
**Last updated:** [December 30, 2024, 5:59am UTC](https://discourse.julialang.org/t/forecast-time-series-using-neural-ode-for-supervised-learning/124268 "2024-12-30T05:59:43Z")

</div>

I’m aiming for time series prediction. I’ve seen a good prediction of time series through the post forcast weather NODE(“Forecasting the weather with neural ODEs” taked Sebastian Callh personal blog and “Forcasting time …

---

## [LegendreBasis from DiffEqFlux is not present in current version?](https://discourse.julialang.org/t/legendrebasis-from-diffeqflux-is-not-present-in-current-version/123568)

<div class="topic-metadata">

**Author:** [@Luis\_Reig\_Quilis](https://discourse.julialang.org/u/Luis_Reig_Quilis)\
**Replies:** 3\
**Last updated:** [December 7, 2024, 5:51pm UTC](https://discourse.julialang.org/t/legendrebasis-from-diffeqflux-is-not-present-in-current-version/123568 "2024-12-07T17:51:41Z")

</div>

Good day, everyone. I am trying to follow this tutorial from DiffEqFlux. During the second step of the tutorial, we have to create a TensorLayer to perform 10th order expansions in a Legendre Basis using the following …

---

## [Periodic solution to a forced oscillator ODE](https://discourse.julialang.org/t/periodic-solution-to-a-forced-oscillator-ode/123080)

<div class="topic-metadata">

**Author:** [@xor0110](https://discourse.julialang.org/u/xor0110)\
**Replies:** 10\
**Last updated:** [November 27, 2024, 5:32pm UTC](https://discourse.julialang.org/t/periodic-solution-to-a-forced-oscillator-ode/123080 "2024-11-27T17:32:22Z")

</div>

I’m working with an ODE model. I’m looking for the periodic solution to a forced, non-conservative, non-linear and time-invariant oscillator. For example, something like x''(t) = - k (x(t) + 0.1 x^3(t)) - a x'(t) + A si…

[Next page](https://discourse.julialang.org/tag/ode/175.md?match_all_tags=true&page=1&tags%5B%5D=ode)