About
I heard interesting research IsoGCN, which is designed for solving physics problem to take isometric transformation invariant and equivariant features into account with a computationally efficient manner. (https://arxiv.org/abs/2005.06316). This research is used in a product which is developed by ROCOS(https://www.ricos.co.jp/).
I briefly summarized their experimental result.
Learning Differential Operator
We would all be grateful if physical simulations could be solved quickly. But many simulations take considerable time to compute, necessary to apply operators to fields over and over again to evolve over time. Therefore, in the experiments in this paper, they take an approach of estimating the time evolution from the initial state by learning this operator. The specific calculation part looks complicated, so we will leave it for later, but the important thing is how much data this operator can learn and how accurately it can estimate the field.
Experiments and Feature of IsoGCN
- It can scale up to 1 M vertices
- They compare FEA with IsoGCN using nonlinear HEAT equation dataset
- The shape which is used in experiments are generated in ABC (3DCAD) dataset. They randomly generated initial condition with shapes
- 439 FEA results for training, 143 for validation, and 140 for testing.
- IsoGCN is 3-5 times faster than the FEA with same level of accuracy
- It does not consume memory usage so much comparing with the other NN based approach
