Machine Learning for Inverse Design

Abstract

"Inverse design" formulates the design process as an inverse problem; optimal values of a parameterized design space are sought so to best reproduce quantitative outcomes from the forwards dynamics of the design's intended environment. Arguably, two subtasks are necessary to iteratively solve such a design problem; the generation and evaluation of designs. This thesis work documents two experiments leveraging machine learning (ML) to facilitate each subtask. Included first is a review of relevant physics and machine learning theory. Then, analysis on the theoretical foundations of ensemble methods realizes a novel equation describing the effect of Bagging and Random Forests on the expected mean squared error of a base model.

Complex models of design evaluation may capture environmental dynamics beyond those that are useful for a design optimization. These constitute unnecessary time and computational costs. The first experiment attempts to avoid these by replacing EGSnrc, a Monte Carlo simulation of coupled electron-photon transport, with an efficient ML "surrogate model". To investigate the benefits of surrogate models, a simulated annealing design optimization is twice conducted to reproduce an arbitrary target design, once using EGSnrc and once using a random forest regressor as a surrogate model. It is found that using the surrogate model produced approximately an 100x speed-up, and converged upon an effective design in fewer iterations. In conclusion, using a surrogate model is faster and (in this case) also more effective per-iteration.

The second experiment of this thesis work leveraged machine learning for design generation. As a proof-of-concept design objective, the work seeks to efficiently sample 2D Ising spin model configurations from an optimized design space with a uniform distribution of internal energies. Randomly sampling configurations yields a narrow Gaussian distribution of internal energies. Convolutional neural networks (CNN) trained with NeuroEvolution, a mutation-only genetic algorithm, were used to statistically shape the design space. Networks contribute to sampling by processing random inputs, their outputs are then regularized into acceptable configurations. Samples produced with CNNs had more uniform distribution of internal energies, and ranged across the entire space of possible values. In combination with conventional sampling methods, these CNNs can facilitate the sampling of configurations with uniformly distributed internal energies.