Add tutorials on UDEs with neural network rates#1489
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Updated the prob_func to remove an unused parameter.
sebapersson
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Jul 9, 2026
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Thanks for adding, I think it looks good! Left a few minor comments
| Lux.Dense(3 => 1, Lux.softplus, use_bias = false), | ||
| ) | ||
| @SymbolicNeuralNetwork U, θ = nn_arch | ||
| A(z) = U(z, θ)[1] |
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Maybe use U([z, ]) syntax, makes it easier to understand how to have more than a single input to the neural network
| ``` | ||
| Here, `U` represents the neural network structure, and `θ` represents its parameters. Additional options for using the `@SymbolicNeuralNetwork` macro are described [here](https://sciml.github.io/ModelingToolkitNeuralNets.jl/stable/api/#ModelingToolkitNeuralNets.@SymbolicNeuralNetwork) and [here](https://sciml.github.io/ModelingToolkitNeuralNets.jl/stable/symbolic_ude_tutorial/). Next, using the following syntax, we can [interpolate](@ref dsl_advanced_options_symbolics_and_DSL_interpolation) this function approximator as a Catalyst model rate. | ||
| ```@example ude_rate_based | ||
| A(z) = U(z, θ)[1] |
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| The UDE model can now be fitted to the data. Here, we use the Adam implementation from the | ||
| [Optimisers.jl](https://github.com/FluxML/Optimisers.jl) package, running 5 independent starts | ||
| with 10,000 iterations each. |
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| with 10,000 iterations each. | |
| with 10,000 iterations/epochs each. |
| ### [Learning parameters or observables using neural networks](@id udes_parameters_n_observables) | ||
| Throughout this tutorial, we have shown how neural networks can be incorporated into | ||
| Catalyst models to learn unknown functions of system variables within the main model | ||
| system. PEtab, however, also supports two additional ways to incorporate neural networks |
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| system. PEtab, however, also supports two additional ways to incorporate neural networks | |
| system. PEtab.jl, however, also supports two additional ways to incorporate neural networks |
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Merging will likely require #1488 to be finished first (which in turn is waiting for the next OrdinaryDiffEq release).