Time-critical and confidence-based abstraction dropping methods

One paradigm of Monte Carlo Tree Search (MCTS) improvements is to build and use state and/or action abstractions during the tree search. Non-exact abstractions, however, introduce an approximation error making convergence to the optimal action in the abstract space impossible. Hence, as proposed as a component of Elastic Monte Carlo Tree Search by Xu et al., abstraction algorithms should eventually drop the abstraction. In this paper, we propose two novel abstraction dropping schemes, namely OGA-IAAD and OGA-CAD which can yield clear performance improvements whilst being safe in the sense that the dropping never causes any notable performance degradations contrary to Xu's dropping method. OGA-IAAD is designed for time critical settings while OGA-CAD is designed to improve the MCTS performance with the same number of iterations.

Generalization capabilities of MeshGraphNets to unseen geometries for fluid dynamics

This works investigates the generalization capabilities of MeshGraphNets (MGN) [Pfaff et al. Learning Mesh-Based Simulation with Graph Networks. ICML 2021] to unseen geometries for fluid dynamics, e.g. predicting the flow around a new obstacle that was not part of the training data. For this purpose, we create a new benchmark dataset for data-driven computational fluid dynamics (CFD) which extends DeepMind's flow around a cylinder dataset by including different shapes and multiple objects. We then use this new dataset to extend the generalization experiments conducted by DeepMind on MGNs by testing how well an MGN can generalize to different shapes. In our numerical tests, we show that MGNs can sometimes generalize well to various shapes by training on a dataset of one obstacle shape and testing on a dataset of another obstacle shape.