Inductive biases play a critical role in enabling Graph Networks (GN) to learn particle and
mesh-based physics simulations. In this paper, we propose two generalizable inductive
biases that minimize rollout error and energy accumulation. GNs conditioned on the input
states and relying on the Mean Squared Error (MSE) loss function implicitly assume
Gaussian-distributed output errors. Consequently, GNs may either assign probability
densities to infeasible regions in the state space of the deterministic physics problem or fail …

Inductive biases play a critical role in enabling Graph Networks (GN) to learn particle and
mesh-based physics simulations. In this paper, we propose two generalizable inductive
biases that minimize rollout error and energy accumulation. Conditioned on the input states,
GNs currently assume Gaussian distributed targets. As a consequence, GNs either assign
probability densities to infeasible regions in the state space of the physics problem or fails to
assign densities to feasible regions. Instead, we replace the existing assumption with a …