Deep Learning for Bayesian Optimization of Scientific Problems with High-Dimensional Structure
This work addresses the need for scalable optimization methods in physics and chemistry, offering incremental improvements by adapting existing neural network techniques to Bayesian optimization.
The authors tackled the challenge of applying Bayesian optimization to high-dimensional, structured scientific problems by using Bayesian neural networks as surrogate models, demonstrating improved sampling efficiency and computational cost compared to Gaussian processes on tasks like photonic crystal and molecule optimization.
Bayesian optimization (BO) is a popular paradigm for global optimization of expensive black-box functions, but there are many domains where the function is not completely a black-box. The data may have some known structure (e.g. symmetries) and/or the data generation process may be a composite process that yields useful intermediate or auxiliary information in addition to the value of the optimization objective. However, surrogate models traditionally employed in BO, such as Gaussian Processes (GPs), scale poorly with dataset size and do not easily accommodate known structure. Instead, we use Bayesian neural networks, a class of scalable and flexible surrogate models with inductive biases, to extend BO to complex, structured problems with high dimensionality. We demonstrate BO on a number of realistic problems in physics and chemistry, including topology optimization of photonic crystal materials using convolutional neural networks, and chemical property optimization of molecules using graph neural networks. On these complex tasks, we show that neural networks often outperform GPs as surrogate models for BO in terms of both sampling efficiency and computational cost.