finmod

Formulate some examples using ModelingToolkit

2

For better visibility and integration of BifurcationKit with SciML, some examples, in particular DAE and PDE, should be formulated using MTK with its automatic Jc features. Also, BifurcationKit should have...

Benchmark of examples in data driven discovery of forward operators

1

DataDrivenDiffEq should demonstrate the SciML ecosystem tools and solutions to the same examples that are proposed in deepxde [https://github.com/lululxvi/deepxde/tree/master/examples](url) in Python. deepxde has recently reciprocated with the Lotka-Volterra inverse example...

modified-SINDy: AD to SINDy and extract noise probability distributions from data

8

The paper : https://arxiv.org/abs/2009.08810 extends the numerical differentiation methods within an integrated optimization framework. Noise can be separated from signal, resulting in an architecture that is approximately twice as robust...

ContinuousDataDrivenProblem: Difficulty in forming DX with ODEProblem and DAEProblem

7

To run `ContinuousDataDrivenProblem` on the model below that I want to run as an Implicit system discovery, I get : MethodError: objects of type ODESystem are not callable in forming...

Write and read data files for DataDrivenDiffEq inference

2

Can we have in all your tutorials and the README an intermediate step of writing out the synthetic data generated to an external file of your advocacy and then reading...

Dynamic Discovery of PDEs

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@AlCap23 In the docs and tutorials, could you give an example of PDE discoveries as in https://royalsocietypublishing.org/doi/10.1098/rspa.2020.0279 to demonstrate the versatility of DataDrivenDiffEq.

Common methods for numerically approximating derivatives

5

The function "similar" in basis.jl appears to apply the finite difference method which is appropriate for smooth data. Perhaps there should be an option in "similar" as well as in...

@AlCap23 This paper https://cs.nyu.edu/~pogudin/global.pdf is relevant to DataDrivenDiffEq. It comes with the corresponding app https://github.com/pogudingleb/Global_Identifiability/blob/master/GlobalIdentifiability.mpl in Maple that proves to be particularly efficient. @ChrisRackauckas Note Example 2.13 on the Lotka-Volterra...

Data driven discovery of PDEs

3

https://advances.sciencemag.org/content/advances/suppl/2017/04/24/3.4.e1602614.DC1/1602614_SM.pdf All the elementary functions being in place, this is a natural extension of DataDrivenDiffEq

In the print equations and parameters, three improvements are needed: 1. The parameter set should be shrunk to eliminate all duplicates (ill-conditioning of Hessian), as is also the case in...