SciML/NeuralPDE.jl

PINNs Lorenz param estim : kink in the output path of the predicted variables

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#284 opened on Apr 5, 2021

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Description

Running the Lorenz param estim example, the estimated parameters are:

3-element Vector{Float64}: 10.000484105285961 27.99897160477475 2.667291549846074

Then in the graphical analysis:

initθ = discretization.init_params acum = [0;accumulate(+, length.(initθ))] sep = [acum[i]+1 : acum[i+1] for i in 1:length(acum)-1] minimizers = [res.minimizer[s] for s in sep] ts = [domain.domain.lower:dt/10:domain.domain.upper for domain in domains][1] u_predict = [[discretization.phii[1] for t in ts] for i in 1:3] plot(sol) plot!(ts, u_predict, label = ["x(t)" "y(t)" "z(t)"])

produces a kink in the x, predicted x variables different from the published graph as follows:

image

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Domain
machine learning
Issue type
bug
DifficultyEstimated implementation difficulty for a new contributor, from 1 for very small changes to 5 for expert-level work.
4
Estimated timeA rough time range for an experienced contributor to investigate, implement, test, and prepare a pull request.
1-2 days
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mostly clear
Prerequisites
Julia programmingPhysics Informed Neural NetworksNeuralPDE.jl usageDifferential equations
Newbie friendlinessA 1-100 score estimating how approachable this issue is for first-time contributors.
25
Research direction
Investigate the kink in the predicted x variable during the Lorenz parameter estimation. The issue shows that the estimated parameters are close to correct but the trajectory has a kink. Check the code in NeuralPDE.jl related to parameter estimation and the phi function. Look at the discretization and how the minimizers are extracted. Compare the plotting code with the published graph. The problem might be in the way the solution is evaluated or in the network architecture. Consult the comments in the issue for any further clues.
PINNs Lorenz param estim : kink in the output path of the predicted variables · SciML/NeuralPDE.jl#284 | Good First Issue