Constraint-based graph network simulator
This work addresses the need for more flexible and accurate neural-network-based simulators in physics and engineering, offering incremental improvements by integrating traditional simulation techniques into machine learning.
The paper tackles the problem of physical simulation by introducing a constraint-based learned simulation framework that uses a graph neural network as a constraint function and solves an optimization problem for predictions, achieving comparable or better accuracy than top learned simulators on challenging physical domains.
In the area of physical simulations, nearly all neural-network-based methods directly predict future states from the input states. However, many traditional simulation engines instead model the constraints of the system and select the state which satisfies them. Here we present a framework for constraint-based learned simulation, where a scalar constraint function is implemented as a graph neural network, and future predictions are computed by solving the optimization problem defined by the learned constraint. Our model achieves comparable or better accuracy to top learned simulators on a variety of challenging physical domains, and offers several unique advantages. We can improve the simulation accuracy on a larger system by applying more solver iterations at test time. We also can incorporate novel hand-designed constraints at test time and simulate new dynamics which were not present in the training data. Our constraint-based framework shows how key techniques from traditional simulation and numerical methods can be leveraged as inductive biases in machine learning simulators.