  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.
