Selinda

Selinda is a self-inductive AI for advancing network resilience theories. Contributors to this project are from the Future Intelligence Lab at Tsinghua University.

Featuring a symbolized reinforcement learning framework, Selinda learns from how AI solves a complicated network dismantling problem and symbolizes its network attack strategies into theoretical formulas. This framework establishes a comprehensive set of network resilience theories, including the first-ever resilience theory that accounts for both network topology and dynamics in non-linear and heterogeneous systems, as well as two new resilience theories that refine existing well-established ones regarding pure topology and homogeneous dynamics.

Installation

Environment

• Tested OS: Linux (Ubuntu 22.04.1 LTS, training and testing)
• Python: 3.11.0
• Pytorch: 2.0.0
• CUDA: 11.7
• Julia: 1.9.3

Package Dependencies

pip install -r requirements.txt

Usage

Search with reinforcement learning (RL)

bash app_rl.sh

Distill with explainable artificial intelligence (XAI)

bash app_explain.sh

Discover with symbolic regression (SR)

Generate the dataset for SR:

bash app_sr_data.sh

Run SR:

export PATH=$PATH:path/to/julia
bash app_sr.sh

Baselines

Note

For the following two baselines (FINDER and GDM), you will need to change to another Python 3.7 environment to run them (tested on Linux only). We recommend using Anaconda or Virtualenv to manage multiple Python environments.

FINDER

You will need to change to another Python 3.7 environment to run FINDER, with the following packages installed:

cython==0.29.13
networkx==2.3
pandas==0.25.2
scipy==1.3.1
tensorflow==1.14.0

Then, make all the files:

cd thirdparty/FINDER/code/FINDER_ND/
python setup.py build_ext -i

GDM

You will need to change to another Python 3.7 environment to run GDM, with the following packages installed:

torch==1.0.1
torch-cluster==1.2.4
torch-scatter==1.1.2
torch-sparse==0.2.4
torch-spline-conv==1.0.6
torch-geometric==1.1.2

Note

For the following four baselines (GND, EI, CI, and CoreHD), you will need to first install a C++ compiler and dependencies (tested on Linux only):

sudo apt install build-essential gcc-12 g++-12 cmake libboost-all-dev libomp-dev

GND

You will need to compile the C++ code:

cd thirdparty/GND/
make

EI

You will need to compile the C code:

cd thirdparty/EI/
make -C Library

CI

You will need to compile the C code:

cd thirdparty/CI/
make

CoreHD

You will need to compile the C++ code:

cd thirdparty/CoreHD/
make

Topological resilience

We apply the framework to discover pure topological resilience theories for networks without running system dynamics.

First, train a DRL agent to identify critical nodes for network topology dismantling

bash app_rl_topology.sh

Then, distill the important node features in the RL agent

bash app_explain_topology.sh

Finally, discover the hidden mathematical connections between important features and critical nodes

bash app_sr_data_topology.sh
bash app_sr_topology.sh

Reproducing and refining classical physical metrics

We apply the self-inductive framework to re-discover or refine the following classical physical metrics in a fully data-driven manner, while their original proposals are based on physical intuitions and heavy derivations:

• β (Nature, 2016)
• resilience centrality (Physical Review E, 2020)

The first search process is shared between the two metrics. We train a DRL agent to identify critical nodes in dynamical homogenous scenarios:

bash app_rl_homo.sh

For resilience centrality, we distill knowledge from the policy network which selects nodes for removal, similar to the above workflow.

bash app_explain_homo_policy.sh # utilize XAI to identify important node features for the policy network
bash app_sr_data_homo_policy.sh # generate training data for SR
bash app_sr_homo_policy.sh # utilize SR to derive a physical metric that mimics the policy network

As for β, it describes the current resilience state of the network, which is achieved by the value network in our DRL agent estimating how far a network is to losing its resilience. Meanwhile, β is a network-level index rather than a node-level one, the primitives for SR also become network-level features. Therefore, we distill the value network instead.

bash app_explain_homo_value.sh # utilize XAI to identify important node features for the value network
bash app_sr_data_homo_value.sh # generate training data for SR
bash app_sr_homo_value.sh # utilize SR to derive a physical metric that mimics the value network

License

Please see the license for further details.