gabrielfougeron / choreo

Finds periodic solutions to the N-body problem

Hi, My name is Gabriel Fougeron. For the past ten years I've been working at ESI-Group as a research engineer. My work focuses on simulation and optimization topics in continuum mechanics. Lately, I've mainly been working on applications of optimal transport to reduced order modelling of the simulation of manufacturing processes.

I’ve also invested unreasonable amounts of time in small pet projects across the years. The latest of them is an open-source python library for the computation of periodic N-body gravitational orbits. You can experiment with the web-app demo at this address, no installation required!

choreo's Issues

Get rid of animation artifacts while playing solution

While playing at high speed / low framerates, ugly artifacts are displayed at high curvature locations in the loop.

Get rid of those and measure impact on display performance.

Change FFT definition

Check sign in FFT definition.
IS this the correct normalization / sign convention ?

==> performance and availability of drop-in replacements

Fps limiter in GUI

Create user defined FPS limiter in GUI. Off by default.

Merge PlotInfo and the usual *.txt descriptor

use JSON format.

Change floating point precision "on the fly"

small precision at the start of optim, higher precision later

Convergence Issues for complex systems

Some complex systems have trouble converging. By that I mean that sometimes, the system is far away from singular solutions and the discrétisation level is correct (no need for refinement) and yet, convergence is very slow. This is especially the case for Target init states.

I suspect the linear solvers in the Newton Krylov loop to not be robust enough to handle these complex cases.

• Lgmres seems to perform better in these cases, but it is crashing in pyodide. Raise the issue with the pyodide team.

• How can I help the linear solver? How to design a good preconditionner? Where should the preconditionner act (change of variables?)? Can the preconditionner be adaptive?

Weird behavior of async loads

Talk with Ivan of the behavior of the following lines :

		AllPos = new Array(n_init_gallery_orbits);
		AllPlotInfo = new Array(n_init_gallery_orbits);

		// Load all files asynchronously, keeping promises

		for (var i = 0; i < n_init_gallery_orbits; i++) {
			
			let npyjs_obj = new npyjs();
			let finished_npy = 
				npyjs_obj.load(AllPosFilenames[i])
				.then((res) => {
					AllPos[i] = res;
				});

			let finished_json = 
				fetch(AllPlotInfoFilenames[i],Gallery_cache_behavior)
				.then(response => response.text())
				.then(data => {
					AllPlotInfo[i] = JSON.parse(data);
				});

			await Promise.all([finished_npy ,finished_json ])

			if (i==0) {

				// await Promise.all([finished_npy ,finished_json ])

				$('label:first', "#orbitRadio").removeClass('w3-light-grey').addClass('w3-red');
				setOrbit(0);
				
				startAnimation();

			}
		}

Speed and loading from gallery

Problems:

• Switching between different solutions, especially in the gallery gives the impression of VERY different speeds.
• Overall shape of the solution is not given immediately. Especially when the player is in pause.

Planet trail length scales with FPS

Currently, the colored trailed has a "working length" that scales with the update freq of screen.

=> Make it independant.

Check whether a given solution has symmetries

Given a loop's Fourrier coefficients, decide whether the loop has a given symmetry or not.

This would be fairly straightforward if not for the global translation and rotation invariance.

Then, classify and sort already found solutions in terms of their a posteriori symmetries (and not a priori).

Save GUI state as cookie

Opt in feature to save current state as cookie

Load cookie at startup

What are the legal consequeces / requirements ?

Python worker info not reliable

Python worker info are not very reliable. The associated code is scattered and hard to read/maintain.
The functionnality is great, so this is a shame.

Needs increased reliability and code refactoring.

Symmetry detection fails in a particular configuration, with no warning.

Can be reproduced with init file
choreo_config (2).zip

Web version / local version

The web version of the GUI allows to run some python code with pyodide. This comes with a lot of performance drop.

=> Expert GUI to run python natively ? How to connect the two ?
=> Ask Ivan !

Add help section

tedlt

Local gallery creation

• Allow the user to generate multiple solutions, with pictures and movies.

• #52

• Put the found solutions in an interactive gallery

Implement cubic spline interpolation

Goal : better smoothness impression at low speed and low number of interpolation points
Should be rather straightforward, once the formulas are in place

Symmetry Cp and Dp in GUI

They look switched. Investigate.

Target init state

Indépendant spectral solver

• 1st order ODEs
• standard test case (simple pendulum?)
• 2nd order ODEs? =>Newtonian system

Index Theory

Investigate.
What does it have to do with periodic solutions ?
Compute index ?
Reduce indices too large ?
Link with orbits that loop many times ?

GPU acceleration ?

To be investigated.

Rethink default gallery

• Add a tree structure, identical (at least visually) to the workspace gallery.

• Load files lazily ! I.e. only actually fetch when the button is clicked (for the first time ?)

• #75

Now Playing tab

Desing a "Now Playing" tab giving information about currently displayed choreo.

==> What to display during search ?

Implement GUI Rotation

Rotate displayed image at will ?

=> What happens to min/max ? Out of screen ? Safe distance ? User zoom ?

Lagrangien systems: Stability and initial conditions

• do the stability equations of a lagra gien system define a lagrangien system?
• initial conditions embedded in the lagrangien?
• exploration of solution space <=> exploration of unit conditions?

Several UI changes

• Display particle movement during search ?
• Forbid second search to launch
• Divide "Hide" button into two toggles : trail and bodies.

Automatic proof of existence of solution close to computed solution ?

Fairly self explainatory ...

starting page 88 of Gregory Minton's PhD thesis.

GUI speed meaning

Relate the GUI speed slider position with the time it takes for 1 body to go round a loop and display the information.

Implement info output during search

tedlt

More parametrization of linesearch

Correct clearly bugged scipy implementation ? More flexibility for fixed size stepping ?

Linked to scipy/scipy#17511 and scipy/scipy#17510

Large mass difference, Momentu conservation and conditionning

Solver has much trouble converging when masses ratio is > 10

Efficiency of ComputeNewtonError

Should be very easy to improve. To be tested.

Setup Keyboard shortcuts

Stability investigation

Goal : Reliable and efficient computation of monodromy matrix.

• First order symplectic integrator of the nonautonomous tangent linear system
• Second order symplectic integrator of the nonautonomous tangent linear system
• #96
• Error estimator ==> Check error on init state = known eigenvector with eigenvalue 1
• Video of symplectic integration of perturbed system, along "most unstable" directions (SVD V cols)

Python text auto go to end when changing tabs

Solver output txt should auto scroll down every timethe solver output tab is opened

Kill solver when running

How to send a signal to the Python side to kill the current execution ?

"Newton Error too high, discarding solution" Triggers too easily

Create a small gallery for beta

Not too big considering everything is loaded at every time.

Load local multi-folder gallery in GUI

Find a good way to browse/edit solutions.

GUI for problem definition

• random initial state
• symmetries
• i/o ? (on hold depending on what is happening with David)
• solver details
• #22

Viewport impacts all mobile devices

On Ivans' Ipad, wiewport makes it behave as a phone, regardless of it being in landscape or portrait. That sucks.

Check consistency of symmetries

Create an automatic check to answer the question

$$ \nabla_p S = 0 \Rightarrow \nabla_c S = 0 $$

cf lemma 4.2 p 88 of G Minton's thesis.

Test performance of code and report

What is the difference in performance between the in-browser execution and the single-threaded native python?

AdblockPlus blocked page loading

That sucks !
Not sure what to do about it besides ask AdblockPlus not to do it.

restart search without killing worker

As a GUI user, it is sometimes easy to see that the optimizer will not converge (for isntance when a loop escaped).

Add a button to start next optimization attempt without killing worker.

Implement path display during search

Opt-in option to display the current candidate during search => see the evolution etc.

Rewrite some numerical intensive functions in cython

Specifically the following functions:

• Transform_Coeffs_Single_Loop
• Transform_Coeffs
• Compose_Two_Paths

If user selects a Workspace on its computer, enable more features,

Use localStorage instead of cookies to save configuration

Handling save/load/delete configuration is much easier with localStorage than cookies.

For more info on the difference between localStorage and cookies, see https://blog.shahednasser.com/localstorage-vs-cookies-whats-the-difference/