Tenfem
What is Tenfem?
Tenfem is a Tensorflow + FEM (the Finite Element Method) which according to Wikipedia is the "The mostly widely used method for solving problems in engineering" [citation needed] . While there already exist excellent open and closed source FEM solving software, this library is introduced to allow a more transparent integration of this software as used by engineers with more machine learning techniques through the TensorFlow ecosystem.
This project is still in its early stages, and it primarily viewed as a research tool. We do not intend to achieve the full power of modern FEM solving software, but we do plan to make it much more straight-forward to mix machine learning components with components coming from a FEM solver, enabling greater collaboration between classical engineering approaches motivated by fundamental physical principles, and the flexible, data-driven methods that have fuelled modern machine learning.
PDEs as mechanistically inspired convolutions
| GP Source | Transport Vector Field | GP Solution |
|---|---|---|
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In the when the partial differential equations (PDEs) take the form of linear elliptic operators we can convolve an input Gaussian process, for example a source field of pollutants, with a mechanistically inspired PDE which describes how these pollutants are spread and transported, to create an output GP which can encode these prior knowledge, without losing the appealing flexibility of the GP framework!