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In this\ntwo part treatise, we present our developments in the context of solving two\nmain classes of problems: data-driven solution and data-driven discovery of\npartial differential equations. Depending on the nature and arrangement of the\navailable data, we devise two distinct classes of algorithms, namely continuous\ntime and discrete time models. The resulting neural networks form a new class\nof data-efficient universal function approximators that naturally encode any\nunderlying physical laws as prior information. In this first part, we\ndemonstrate how these networks can be used to infer solutions to partial\ndifferential equations, and obtain physics-informed surrogate models that are\nfully differentiable with respect to all input coordinates and free parameters.","url_abs":"http://arxiv.org/abs/1711.10561v1","url_pdf":"http://arxiv.org/pdf/1711.10561v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 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