I will talk about using neural networks to solve constrained optimization problems with functionals and constraints depending on solutions of physical problems. These solutions can be complex and nonsmooth (e.g., simulation of lighting and contact), which make conventional approaches computationally very expensive and numerically challenging. I will describe a specific example of such problem, related to optimization of tactile and visual properties of surfaces, for which replacing actual simulation with neural network-based surrogates allowed us to solve a nearly intractable problem, with modest computational expense. Many textured surfaces combine visual and tactile aspects, each serving important purposes; a texture alters the object's appearance or tactile feeling as well as serving for visual or tactile identification. The tactile feel and visual appearance of objects are often linked, but they may interact in unpredictable ways. Advances in high-resolution 3D printing enable highly flexible control of geometry to permit manipulation of both visual appearance and tactile properties. We describe an optimization method to independently control the tactile properties and visual appearance of a texture. Our optimization makes it possible to create textured surfaces with a desired tactile feeling while preserving its visual appearance at a relatively low computational cost. This is joint work with Chelsea Tymms.
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