Henrik Holst

Björn Engquist, Henrik Holst, Olof Runborg

Multiscale problems are computationally costly to solve by direct simulation because the smallest scales must be represented over a domain determined by the largest scales of the problem. We have developed and analyzed new numerical methods for multiscale wave propagation following the framework of the heterogeneous multiscale method. The numerical methods couple simulations on macro- and microscales for problems with rapidly fluctuating material coefficients. The computational complexity of the new method is significantly lower than that of traditional techniques. We focus on HMM approximation applied to long time integration of one-dimensional wave propagation problems in both periodic and non-periodic medium and show that the dispersive effect that appear after long time is fully captured.

Jack Harmer, Linus Gisslén, Jorge del Val et al.

In this work we describe a novel deep reinforcement learning architecture that allows multiple actions to be selected at every time-step in an efficient manner. Multi-action policies allow complex behaviours to be learnt that would otherwise be hard to achieve when using single action selection techniques. We use both imitation learning and temporal difference (TD) reinforcement learning (RL) to provide a 4x improvement in training time and 2.5x improvement in performance over single action selection TD RL. We demonstrate the capabilities of this network using a complex in-house 3D game. Mimicking the behavior of the expert teacher significantly improves world state exploration and allows the agents vision system to be trained more rapidly than TD RL alone. This initial training technique kick-starts TD learning and the agent quickly learns to surpass the capabilities of the expert.

Bjorn Engquist, Henrik Holst, Olof Runborg

Multi-scale wave propagation problems are computationally costly to solve by traditional techniques because the smallest scales must be represented over a domain determined by the largest scales of the problem. We have developed and analyzed new numerical methods for multi-scale wave propagation in the framework of heterogeneous multi-scale method. The numerical methods couples simulations on macro- and micro-scales for problems with rapidly oscillating coefficients. We show that the complexity of the new method is significantly lower than that of traditional techniques with a computational cost that is essentially independent of the micro-scale. A convergence proof is given and numerical results are presented for periodic problems in one, two and three dimensions. The method is also successfully applied to non-periodic problems and for long time integration where dispersive effects occur.