  In the past years, the application of neural networks as an alternative to
classical numerical methods to solve Partial Differential Equations has emerged
as a potential paradigm shift in this century-old mathematical field. However,
in terms of practical applicability, computational cost remains a substantial
bottleneck. Classical approaches try to mitigate this challenge by limiting the
spatial resolution on which the PDEs are defined. For neural PDE solvers, we
can do better: Here, we investigate the potential of state-of-the-art
quantization methods on reducing computational costs. We show that quantizing
the network weights and activations can successfully lower the computational
cost of inference while maintaining performance. Our results on four standard
PDE datasets and three network architectures show that quantization-aware
training works across settings and three orders of FLOPs magnitudes. Finally,
we empirically demonstrate that Pareto-optimality of computational cost vs
performance is almost always achieved only by incorporating quantization.
