In this project a Machine Learning model is trained for learning a simulator for Material-Flow systems, where the Machine Learning model is based on Graph Neural Networks. The data for training the model is generated using an accurate physicbased simulator.
Based on DeepMind's Graph Nets (Library for building graph networks in Tensorflow and Sonnet https://github.com/deepmind/graph_nets) and their project Learning to Simulate Complex Physics with Graph Networks (https://github.com/deepmind/deepmind-research/tree/master/learning_to_simulate)
The commissioning of modern production plants is an important phase in the development process, as it becomes visible whether the developed plant with its software and control technology meets all requirements. In order to reduce time-consuming and cost-intensive iterative adjustments during planning and commissioning, virtual commissioning with its simulation models has become established. The simulation of virtual commissioning has high requirements in terms of computing time, so that communication with the control system is possible in real time. Modern production plants often consist of multiple sub-stations between which goods are transported by Material-Flow systems. It is important to ensure reliable Material-Flow between the stations so that the plant can run efficiently. In order to be able to detect error cases during the Material-Flow within the simulation, such as jamming or tipping over of goods, high-resolution process models that take physical effects into account are required. These physics-based Simulators are not solvable within the required real-time, especially for material flow scenes with many goods. An alternative is to use Deep Learning to train the Simulator based on recorded training data. In recent years, Deep Learning has successfully solved many Machine Learning tasks such as image classification and speech recognition. In many Deep Learning tasks, the data can be represented as a graph with complex relationships and dependencies between objects. Scientific work of recent years shows that the complex and computationally intensive relationships of graph data can be modelled and learned using Graph Neural Networks.
In the simulation of physical systems, it is assumed that describes the state of the system at time
. By calculating the dynamics of the system over
time steps, a trajectory of system states
is obtained. A simulator models the dynamics of the system by iterating each state
is iteratively mapped to a subsequent state
. Thus, a simulated trajectory is given by
.
The learned simulator predicts future states of the piece goods starting from an initial configuration using the learned function
and a specified updating procedure. Therefore the learnable simulator
uses the computed dynamics of the current state to predict the subsequent state. For this purpose, the dynamics of the system are computed as accelerations of the particles
using the parameterized function
, where the parameters
are optimized during the training phase. Finally, a numerical integration method is used to predict the subsequent state
from the current state
and the accelerations calculated by
. The learning function
of the simulator, whose parameters
are optimized during the training phase, consists of encoder, processor and decoder.
The encoder constructs an initial graph by assigning a node to each object and adding edges between the node and all other objects within a constant radius of connectivity
. The edges reflect the local connectivity of the object. The edges reflect the local interactions of the objects. The embeddings of the nodes are learned based on the states of the objects
, that represent the positions and the velocities of the past
time steps of the objects.
The processor forwards messages between nodes via the edges. It computes the interactions between nodes over
steps, where
. Here
is a Graph Net Block and uses Artificial Neural Networks as internal edge and node update functions. The processor returns the final graph
. In physics, these interactions correspond to the exchange of energy and momentum between particles.
The decoder extracts dynamics information from the nodes of the final graph with
. Learning
should result in
being the velocity to the next time step as relevant dynamics information reflects, so that
is semantically meaningful for the update procedure.
The dynamics of the Material-Flow scene can be learned by the Machine Learning model, because the average MSE between the estimated trajectory and the test data trajectory
is small with
. It can be seen that especially the dynamics of the test data sets with a stopper angle α between 40° and 50° can be predicted very well. For stopper angles
that deviate further from the mean value of the stopper angles of all training data sets
, the simulated trajectories of the learned simulator become less accurate. This is especially true for test data sets with small stopper angle
, since the unit loads collide more frequently in these data sets and are thus more difficult to simulate. The evaluation of the computation time for simulating a trajectory shows that the learned simulator with an average computation time of
simulates significantly faster than the physics-based simulator with
.