Mechanical Substrates for Analog Computing via Inverse-Designed Topological Optimization

The increasing demand for real-time, low-power data processing has renewed interest in analog computing paradigms that operate directly in the physical domain. In this work, we explore the use of mechanical substrates as computational units, designed through inverse topology optimization. By defining input gates as force applications and output gates as displacement measurements, computational tasks are encoded into the elastic response of the material. Our framework couples a numerical model with an optimization scheme, enabling the discovery of geometries that perform target operations. We illustrate the versatility of this approach through study cases including classification, function approximation, and matrix-vector multiplication, demonstrating how stress propagation and tailored structural topologies can perform such tasks without digitization. These results highlight the potential of mechanical metamaterials as physical computing substrates, paving the way for ultralow-power and embedded analog processors.