Dynamic cellular automata control using multiple recurrent neural nets and unsupervised learning

Background “Structurally dynamic” cellular automata (Ilachinski, Halpern 1987) have been shown to simulate biological functions with emergent behavior “Agent-based” models show how complex macro behavior in a population emerges from simple individual rules My model is not structurally dynamic, just dynamic I used neural nets because they allow for a broad search space of cellular behavior, given some fixed environmental challenges.

Cellular automata Written in Typescript, a JavaScript superset with types Uses JavaScript library of neuron nets, Synaptic. Allows for arbitrary “projecting of layers” Composable

Demo Jamiesonwarner.com/plants

Setting The cellular automata is an M by N grid of cells. Each cell is a “fluid vector” {f1, …, fn}, each fi is a scalar. The “plant” is the set of living cells in the automata. Some dynamic systems simulated: diffusion, osmosis, and biological functions: photosynthesis, active transport, cell metabolism, cell death, and cell reproduction

Control model A set of m actions is defined. Each tick, every cell executes one of the m actions. Each living cell is assigned a cell type Each cell type x action pair is assigned a neural net: n inputs, where n is the number of fluids 1 output, representing the decision weight for this action Every tick, the decision weight for every action is computed on every cell, and the action chosen is result of the softmax function over the decision weights

Action directionality I wanted action choices to be symmetric left and right To accomplish this, whenever a “directional” action is performed, First the fluid gradient is computed at the performing cell (2 x n-dimensional) Then the direction computed is a constant matrix times the fluid gradient

Problem encountered: balancing Some early environmental challenges made it “too hard” for plant growth. For instance early plants would die of dehydration immediately upon reaching the air because the air had lower humidity levels => death by passive transport As a solution I decreased passive transport into the plant, and gave plants the ability to regulate water pressure by pumping fluid from cell to cell.

Training Random search over all weights of the neural nets (BIG search space) Fitness is defined as the number of living cells after G=100 ticks

Extensions Relax adjacency constraints to make a “structurally dynamic” cellular automata (Ilachinski, Halpern 1987) Get rid of cell types in favor of finer control over the fluid vector Every dimension of the fluid vector (past dimension K) gets its own neural net The value fi , i >K, is the sum of its current value and the output of the neural net Use simulated annealing search

Project url: https://github.com/jamiesonwarner/springfever