  Recent advances show that neural networks embedded with physics-informed
priors significantly outperform vanilla neural networks in learning and
predicting the long term dynamics of complex physical systems from noisy data.
Despite this success, there has only been a limited study on how to optimally
combine physics priors to improve predictive performance. To tackle this
problem we unpack and generalize recent innovations into individual inductive
bias segments. As such, we are able to systematically investigate all possible
combinations of inductive biases of which existing methods are a natural
subset. Using this framework we introduce Variational Integrator Graph Networks
- a novel method that unifies the strengths of existing approaches by combining
an energy constraint, high-order symplectic variational integrators, and graph
neural networks. We demonstrate, across an extensive ablation, that the
proposed unifying framework outperforms existing methods, for data-efficient
learning and in predictive accuracy, across both single and many-body problems
studied in recent literature. We empirically show that the improvements arise
because high order variational integrators combined with a potential energy
constraint induce coupled learning of generalized position and momentum updates
which can be formalized via the Partitioned Runge-Kutta method.
