Accelerating GMRES with Deep Learning in Real-Time

Authors: Kevin Luna (University of Arizona) and Johannes Blaschke (Lawrence Berkeley National Laboratory)

Abstract: Deep learning methods show great promise, however, applications where simulation data is expensive to obtain do not lend themselves easily to applications of deep learning without incurring a high cost to produce data. Real-time online learning is a novel strategy to minimize this cost: a model "learns as we go", only requesting additional (expensive) data if it encounters a situation where it needs additional training. We demonstrate the feasibility of this approach by accelerating a partial differential equation solver as it runs by training a convolution neural network in real-time to propose initial solutions which are optimized to accelerate the solver. To overcome typical challenges associated with online training of neural networks we introduce a methodology to selectively construct the training set as more data becomes available. We present results on physically motivated test problems that demonstrate the acceleration achieved using this real-time deep learning methodology.

Best Poster Finalist (BP): yes

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