14 lines
1.3 KiB
Markdown
14 lines
1.3 KiB
Markdown
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Outlook
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=======================
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TODO
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hybrid methods!
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We demonstrate that neural networks can be successfully trained if they can interact with the respective PDE solver during training. To achieve this, we leverage differentiable simulations [1, 68]. Differentiable simulations allow a trained model to autonomously explore and experience the physical environment and receive directed feedback regarding its interactions throughout the solver iterations. Hence, our work fits into the broader context of machine learning as differentiable programming, and we specifically target recurrent interactions of highly non-linear PDEs with deep neural networks.
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This combination bears particular promise: it improves generalizing capabilities of the trained models by letting the PDE-solver handle large-scale changes to the data distribution such that the learned model can focus on localized structures not captured by the discretization. While physical models generalize very well, learned models often specialize in data distributions seen at training time. However, we will show that, by combining PDE-based solvers with a learned model, we can arrive at hybrid methods that yield improved accuracy while handling solution manifolds with significant amounts of varying physical behavior.
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