Computing in Miniature: Differentiable Representations for Simulating and Optimizing Small Physical Systems

Step into a magnificent miniature wonderland where small insects gracefully traverse pond surfaces, raindrops delicately splash onto vibrating foliage, and dragonflies glide through the air. In this talk, I will showcase my group's recent advances in creating sophisticated differentiable representations and computational tools, all designed to address the complexities of these captivating physical systems while overcoming the challenges posed by the curse of dimensionality. Our work is threefold: first, we introduce novel geometric representations and solvers to accurately simulate the complex processes of small-scale solids and fluids; second, we employ geometric design and optimization algorithms to push performance boundaries and synthesize designs inspired by nature's ingenuity; and lastly, we utilize machine-learning algorithms grounded in physical principles to unearth the mechanics that govern these intricate systems. Throughout the talk, I will demonstrate the wide-ranging applications of these computational tools across various disciplines.