Speeding up Computational Morphogenesis with Online Neural Synthetic Gradients
This speeds up computational morphogenesis for engineering applications, but it is incremental as it builds on existing optimization methods with neural enhancements.
The paper tackles the slow optimization of PDE-constrained problems with high-resolution solutions by proposing an online neural synthetic gradients framework, achieving up to 7.5x speedup on a large-scale 3D design problem with 1.4 million variables while maintaining solution quality.
A wide range of modern science and engineering applications are formulated as optimization problems with a system of partial differential equations (PDEs) as constraints. These PDE-constrained optimization problems are typically solved in a standard discretize-then-optimize approach. In many industry applications that require high-resolution solutions, the discretized constraints can easily have millions or even billions of variables, making it very slow for the standard iterative optimizer to solve the exact gradients. In this work, we propose a general framework to speed up PDE-constrained optimization using online neural synthetic gradients (ONSG) with a novel two-scale optimization scheme. We successfully apply our ONSG framework to computational morphogenesis, a representative and challenging class of PDE-constrained optimization problems. Extensive experiments have demonstrated that our method can significantly speed up computational morphogenesis (also known as topology optimization), and meanwhile maintain the quality of final solution compared to the standard optimizer. On a large-scale 3D optimal design problem with around 1,400,000 design variables, our method achieves up to 7.5x speedup while producing optimized designs with comparable objectives.