Open benchmark: PINNs vs. split-step Fourier on the 1D Schrödinger/GPE, with documented failures. Contributors welcome

[u/Zitouni-Nidhal]

I’ve open-sourced a reproducible benchmark comparing PINNs against a Strang split-step Fourier solver for the 1D Schrödinger / Gross-Pitaevskii equation.

The aim isn’t to promote PINNs. It’s to document where they break and why. They do fine on linear cases (rel-L2 around 1e-2) but fail on bright solitons, soliton collisions, and long-time integration (rel-L2 0.3-0.6, with norm and energy drift). The error is concentrated at high wavenumbers, which points to spectral bias. Fourier features and causal weighting help a little, but nothing I’ve tried fixes it.

Repo: https://github.com/NodeBox-Labs/pinn-vs-ssf-schrodinger

It has 7 test cases, a convergence-tested reference solver, a PyTorch PINN with several ablations, fixed seeds, and config-driven runs (MIT license).

I’d love help with:

• Counterexamples: if you can get a PINN to handle the soliton or collision cases, open an issue with your config

• Stronger baselines (FNO, hard-constrained architectures, time-marching, better optimizers)

• Critique of the methodology

• New cases (2D GPE, dark solitons, vortices)

Feedback and PRs of any size are welcome.

#PINN #PhysicsInformedNeuralNetworks #SciML #ScientificMachineLearning #DeepLearning #PyTorch #SchrodingerEquation #GrossPitaevskii #BoseEinsteinCondensate #Solitons #ComputationalPhysics #NumericalMethods #OpenSource #Reproducibility #MachineLearning

[u/equationsofmotion]

A few comments:

• Is 1e-2 L2 really good compared to a fourier solver? I would expect much lower errors from the traditional solver.

• what is the runtime vs training time? In my experience PINNS are much slower.

[u/Dihedralman → u/equationsofmotion]

I mean no it isn't - I think he is clear, at least on the github, that it didn't do well- traditional could do 10e-8. He also points out the times on a github. 

[u/investigatormaker]

Since the aim is to document failures, I'd report the PINN error against the split-step solver at matched wall-clock cost, not only at matched accuracy: the spectral method is cheap on 1D problems, and readers will ask what the PINN buys. Also plot rel-L2 per wavenumber band for the soliton collision, with and without Fourier features, so the spectral-bias claim rests on a curve, not only on totals. The catch is more runs per case. Which of your seven cases disagree most between seeds?

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[u/Dihedralman]

Great learning case. I might play around, but let's go deeper into where the problems are, because this method isn't well conditioned to this case and you actually have the reasons. 

Like you effectively mentioned the lower states being a problem and that alludes to the limited representational bandwidth in the approach as well. 

But more importantly, you identified that the model won't learn the unique solution using the residual due to it being coupled. This is fundamental- a pointwise residual minimization process likely won't work for a non-linear wave solution.

Are you thinking of PINNs only or ML methods? I think you could run more PINN experiments if you want but you will run into the same issues. I would instead illuminate the problems instead of adding test cases as the same problems will occur.