Manifold learning using geometrical and topological descriptors for know-how based optimization.
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Those last years have seen a growing maturity in optimization tools, particularly topological optimization [1]. The development of 3D printing, allowing to, more or less, create an object of any shape, has given still reinforced interest in advanced optimization tools. Nevertheless, those methods ignore all the accumulated knowledge of industrial manufacturers. Moreover, they face substantial limitations to include all the various constraints that govern the realization of industrial products. Industrial know-how is often difficult to be synthesized in a set of rules or steps as it remains in the intuition and expertise of engineers, designers. Assuming that the existing designs live in a manifold we propose a synergistic use of existing Machine Learning tools to infer a reduced manifold from the existing limited set of designs. Our first attempt in this direction has allowed us to begin to understand what type of information and tools may allow us to interpolate properly within the existing design. Those tools combine reduced modelling and manifold learning approaches (like Locally Linear Embedding) geometrical characterization (Level set , Topological Data Characterization and optimal transport . The basic concepts will be illustrated with 2D examples mimicking bumpers. Once extracted from the data base a manifold of bumpers it is possible to interpolate and to optimize along the variety of “validated design’, that is, to create know-how optimization tools.
