Inverse PINN to takle this problem
Hi everyone, I hope you are doing well.
I am exploring the idea of using a Physics-Informed Neural Network (PINN) on this dataset to perform inverse design for optimal stellarator geometries, and I'm curious if anyone here has tried a similar approach.
My proposed methodology is a two-step pipeline:
Feature Selection & Correlation: Because the parameter space of the boundary Fourier coefficients (r_cos, z_sin) is so massive, my first step is to run an exploratory analysis. Since plasma physics is highly non-linear, I plan to use tree-based feature importance (like SHAP values) alongside standard correlation matrices. The goal is to isolate exactly which geometric inputs act as the primary drivers for the main physics objectives (Quasisymmetry error, Rotational Transform, Aspect Ratio, etc.).
PINN Inverse Design: Once I have isolated the most influential parameters, I plan to encode those relationships directly into the loss function of a PINN as physical constraints, allowing the network to output an optimized geometry.
If anyone has tackled a similar pipeline, I would love to discuss with them.
Good idea
would like to work on that together?
Yes, I’d be interested in discussing this together.
I have actually tried a simple neural-network surrogate on a cleaned and simplified version of the dataset here: https://huggingface.co/datasets/SII-AI4Fusion/SII-Stellarator-Configuration-Dataset
It achieved fairly good accuracy on the validation/test split, but the main issue I observed is poor generalization in unfamiliar or out-of-distribution parameter regions. So I’m also thinking about whether introducing physics-informed constraints, or a PINN-like loss, could help improve the model’s robustness for inverse design.
Maybe we can compare notes on this. I think the key question is how to define the “physics-informed” part properly for this dataset, since the available data are mostly geometry-to-metric mappings rather than direct PDE residuals.
Hi there,
I hope you are doing well. So yesterday i worked on it a bit and submitted my results. It would be great if we can exchange contact and work on that together using the data we have here to get the best result possible.
Best regards,
good luck in finding a sparing partner
in me e.g.: I'm dazzled by a huge amount of Dunning Kruger Effekt thinking: that can't be such a hard problem to tackle and got no idea.
Yes, AI is going to help us out of this mess, but: we need to be very precise in telling AI what to do - otherwise it would allready be done.
So tackle easy to build, use ALM Solver, let your agent compose a hilarious json file and commit.
Any better ideas?
Thanks a lot for the advice, I already tried it yesterday. Well, the results are not that good, but I'm still working on it. My idea from yesterday was to use the W7X from IPP and try to understand those parameters, then apply them to our case study.
This looks actually great (imho).
I still struggle with conversation (do I reply to email directly or otherwise?) and understanding (did not go through the attempt "using W7X data in PINN" yet).
Still I need to understand the structure of nfp params in equotation.
Did you allready look at the currently leading suggestions from competitors? Do you understand the format of the solutions?
What is your reply to
"SII-LWY Owner May 16
Yes, I’d be interested in discussing this together. .... ""
?
We didn't had the time to talk about it
Basically, my strategy was to perform parameter identification using the W7X literature and then apply it to the case study. Also, I did a correlation matrix to see exactly where I should focus, and now I'm running it by tonight. I should have more details, and then I can share my findings. Here
hey @tazzouni !
How are you doing?
I suggest a (not complete PIN NETWORK, but a PIN) Term - or up to 5 of them. (A-E)
Is that close to your mindset, or is this too different?
(I think you could also fokus on 5 distinct sub topics, but I do not know...)
2. Lightweight Physics-Informed Terms (Practical to Implement)
Here are the most important options, ranked by implementation effort:
A. Geometric Consistency (Very Easy, Always Feasible)
Basic geometric quantities are calculated analytically from the Fourier coefficients, and deviations from the surrogate's output are penalized:
\mathcal{L}_{\rm geom} =
\lambda_A \| A_{\rm pred} - A_{\rm Fourier} \|^2 +
\lambda_\kappa \| \kappa_{\rm pred} - \kappa_{\rm Fourier} \|^2 +
\lambda_\delta \| \delta_{\rm pred} - \delta_{\rm Fourier} \|^2
A_{\rm Fourier},\kappa_{\rm Fourier}, and\delta_{\rm Fourier}are calculated directly fromR_{mn}, Z_{mn}(no VMEC calls required).- The surrogate learns to keep its metric predictions consistent with the actual boundary geometry.
B. Fourier Energy / Smoothness Regularization (Easy)
Physically meaningful boundaries have decaying Fourier spectra. Unphysically large contributions from high-order modes are penalized:
\mathcal{L}_{\rm spectrum} = \sum_{m,n} w(m,n) \big( |R_{mn}|^2 + |Z_{mn}|^2 \big)
with weights w(m,n) \propto (m^2 + n^2)^p (typically p = 1 or 2).
This is a pure regularization term applied to the input and is computationally inexpensive.
C. Quasi-Isodynamic-Like Proxy Terms (Moderate Effort)
Using the boundary coefficients and established approximations (such as near-axis expansions or simple Boozer-coordinate proxies), rough estimates can be constructed for:
- Mirror ratio
- Variation in
\|\nabla B\| - Omnigenity residuals
These proxy quantities are used as additional targets or soft constraints:
\mathcal{L}_{\rm QI-proxy} = \| \text{QI}_{\rm pred} - \text{QI}_{\rm proxy}(R_{mn},Z_{mn}) \|^2
The proxy does not need to be highly accurate—it only needs to provide a physically meaningful direction for optimization.
D. Residual-Like Consistency Term (Somewhat More Involved, but Still Lightweight)
If real-space quantities or force-residual norms are stored in the dataset (or in a small supplementary dataset), a second, small neural network can be trained to estimate an approximate residual norm from the boundary. Then:
\mathcal{L}_{\rm residual} = \| r_{\rm pred} - r_{\rm data} \|^2
Alternatively, the residual norm can be used as an additional output of the multi-task surrogate.
E. Monotonicity / Bound Constraints (Very Easy)
Many metrics have physical bounds (aspect ratio > 1, elongation > 1, QI \ge 0, etc.). Soft constraints or barrier terms can be incorporated:
\mathcal{L}_{\rm bounds} = \sum_i \max(0,\; m_i^{\rm min} - m_i^{\rm pred})^2 + \max(0,\; m_i^{\rm pred} - m_i^{\rm max})^2
Hello Martin,
I hope you are doing well, mate. So now this is what i want to implement i will share with you my strategy.
My goal: minimise the plasma boundary’s maximum elongation subject to aspect ratio ≤ 4, triangularity ≤ −0.5 and edge rotational transform ι/nfp ≥ 0.3. Target score: 0.98.
What I built so far is a Stellar-optimisation-Script:
Physics-based starting shapes: near-circular cross-sections around a helical magnetic axis, so the rotational transform comes from the axis twist rather than from elongated cross-sections.
An exact, differentiable copy of the official elongation metric, matching the scored value to 0.02 %.
Gradient-based design steps and a rewritten augmented-Lagrangian optimiser, with every candidate checked by the leaderboard’s own high-fidelity VMEC++ solver before it’s kept.
For now my result so far: 0.8675 → 0.9667, verified with the leaderboard’s own evaluation, and the triangularity is real: the shape itself meets −0.5
Just as you know for now i didn't do any PINN development except at the beginning (its not done yet) but those results comes from :
VMEC++, the augmented-Lagrangian + Nevergrad optimiser (Proxima’s own baseline), trust-region SQP and DESC are all existing tools.
Torsion-driven rotational transform is textbook physics (Mercier, 1964), and helical-axis stellarators exist (heliacs such as TJ-II and H-1).
SHAP and gradient-boosted models are off-the-shelf.
What is new i would say but here people at Proxima will correct me :
Applying the helical-axis tube as a seed family for this benchmark, with a frame-twist estimate of ι checked against VMEC. The physics is known; using it to get round cross-sections here is the new part.
The elongation finding: the gap between low- and high-fidelity elongation is entirely the metric’s sampling. A replica built on VMEC’s axis reproduces the score to 0.02 %.
The triangularity flaw: the metric depends on how θ is labelled. That’s a real finding about the benchmark, unless someone has already reported it.
Two diagnoses others can reuse: box-shaped trust regions cause VMEC failures in high dimensions, and the dataset’s failure flag doesn’t mean VMEC non-convergence.
Beyond the leaderboard, I think the meaningful next step is engineering feasibility: the coils for these shapes have to respect HTS (REBCO) strain and bending limits and other constrains.
The cool is that we can discuss about it and develop something together in our free time.
these are benchmarks I consider to be crucial...
Yours deferre due to other literature (w7), don't they?
I am also going to pause my investigation for 1 week
Hi Martin,
Sorry I didn't have the time to reply to you. I think I used the benchmark at some point, but I will tell you exactly in which run.
Enjoy your week off.
Best regards
Tarek
thx.
on paper this matches strong constraints for QI and Mirror...
so - let's see why this is SLOP anyway. 😃
Still, that's a great start, Martin. I'm taking a break from this right now, and as soon as the new dataset is released, I will start working on it.
All the best, mate
Hey Tarek,
enjoy your break. Tell me about the new dataset, when you are ready.
Meanwhile I am more than happy and proud of my progress!
In MHD_Stable I managed to submit a valid solution and made 20th place in ranking. I also submitted an even more promissing post and am still curious about my rank. (I (quietly) hope for top 10...)
There are issues with hug face (gradio based evaluation pipeline - see https://huggingface.co/spaces/proxima-fusion/constellaration-bench/discussions/11, where santiago - a heroic proxima fusion admin - fights the shortages of infrastructure at that place).
I enjoy this sport very much and hope to hear from you, tazzouni.
best regards
Yes, Martin, I was waiting for this one. I will try to start working on it in the next few days.
And great job for being in the 20th position. Really proud of you, mate.
Best regards
Tarek