3D Network Layout Algorithm (ELI and FUEL) Python Simulation Code

Latest version

Software versions used:

• Python: 3.5.2
• TensorFlow: 1.8.0
• current version net3d_3_v11_2.py.

TL;DR: Checkout current-version/3dart-flavor-steps-052718.ipynb (v11.2); or 3dart-test.ipynb for a complete set of examples (using v10.8).

v11.2: Major changes and restructuring. The new version uses space partitioning for nodes, whereas the old version only did so for link segments. This allows networks with thousands of nodes to be simulated in a reasonable amount of time. The downside is, in small systems interactions across partition walls may result in perpetual fluctuations, as partitions are moved around randomly to remove boundary effects. For small networks it is recommended to use net3d_3_v10_8.py instead.

For a complete set of examples

Paper simulation code

The code used to generate the simulations used in the paper "Structural Transition in Physical Networks" (Dehmamy et.al.) can be found in the paper/ directory.
Software versions used:

• Python: 2.7.12
• TensorFlow: 1.6.0

Some examples of how to use the module are given in 3D-TF-auto-1.ipynb (copy module from old-src/net3d_v9_4_4.py). The module net3d_vX_X.py provides a number of classes and functions for laying out networks in 3D. The important layout classes are:

• netRads(pts,edg,**kw): A simple layout algorithm with short and long-range repulsion among nodes and no repulsion among links. When the long-range node repulsion is small and links are thin, netRads produces layouts similar to the full algorithm networkBase. The main purpose of netRads is to run a quick layout algorithm, ignoring link repulsion, to have a good starting point for the full algorithm networkBase. The output is a JSON in a proprietary format described below. Inputs are

  • node positions pts=np.array([x1,y1,z1]... [xN,yN,zN]])
  • edgelist edg=[[n1,n2],...] (or weighted eidgelist edg=[[n1,n2,w]...], together with links={'weighted':True,...} in **kw)

• networkBase(pts=[],edg=[],fixed=False,JSON=None, keep_paths=False,...**kw): The full simulation with elastic, curving links. Either provide:

  • node positions pts=np.array([x1,y1,z1]... [xN,yN,zN]]) and
  • edgelist edg=[[n1,n2],...] (or weighted edgelist edg=[[n1,n2,w]...], together with links={'weighted':True,...} in **kw),
  • Or provide a JSON file created by networkBase or netRads or manually prepared in the format given below, using JSON='file.json'.
  • fixed: Whether to keep nodes fixed (ELI) or allow them to move (FUEL)
  • keep_paths: Whether to keep the link trajectories (only if JSON provided). If False, will start from straight links. The output can be saved in the JSON format given below.
  • See documentation of networkBase, or examples in run_sims8.py or the notebooks for description other parameters.

The function iter_converge(net, max_its, tol... **kw) is a convenience function which iterates net (a netRads or networkBase object), using their net.iter_all method, until it "converges", in the sense that the checks done by check_convergence(net,tol=tol) (related to logarithmic changes in total link length) become smaller than a tolerance tol. It also accepts keywords that passed to net.iter_all (e.g. c0 which adjusts the time step scaling can be passed to iter_converge; see examples in run_sims8.py).

The output of the simulation can be saved in a proprietary format compatible with 3dviz (also accessible here). The json contains the node and link segment positions, as well as some of the simulation parameters (info key).

netJSON = {
    'scale': (size of network. used to shrink down the network to fit in screen.),
    'info': {
            'nodes':{<sim parameters>},
            'links':{<sim parameters>}
            },
    'links':{
            'link1_label': {
                'points': [[xi,yi,zi],...[xf,yf,zf]], //(points along the link 2 minimum)
                'radius': r (thickness of the link),
                    },
            'link2_label': {...},
            ...
            },
     'nodes': {
        'labels':['n0',...,'nN'],
        'positions':[[x1,y1,z1],...[xN,yN,zN]], //(all nodes at once. labels will be supported later.)
        }

Command-line Example

To run a batch of simulations from some base file input-net.json (such as the series of simulations used in the paper for the phase diagram) you can run
$ ./run_all_th5.py input-net.json 1 "{'links':{'k':.01,'segs':10}}" 1

Details of the script are mostly self-explanatory.

Some of the older versions of the simulation code can be found in paper/old-src/.

For analysis of the phase diagram, see 3D-phase-all-032818.ipynb (Warning: some plots near the bottom may involve non-converged simulations and dataset not used for the paper. For more details email Nima Dehmamy).