Deep Learning Topological Invariants of Band Insulators

In this work we design and train deep neural networks to predict topological invariants for one-dimensional four-band insulators in AIII class whose topological invariant is the winding number, and two-dimensional two-band insulators in A class whose topological invariant is the Chern number. Given Hamiltonians in the momentum space as the input, neural networks can predict topological invariants for both classes with accuracy close to or higher than 90%, even for Hamiltonians whose invariants are beyond the training data set. Despite the complexity of the neural network, we find that the output of certain intermediate hidden layers resembles either the winding angle for models in AIII class or the solid angle (Berry curvature) for models in A class, indicating that neural networks essentially capture the mathematical formula of topological invariants. Our work demonstrates the ability of neural networks to predict topological invariants for complicated models with local Hamiltonians as the only input, and offers an example that even a deep neural network is understandable.Comment: 8 pages, 5 figure

Multi-Modal Medical Imaging Analysis with Modern Neural Networks

Medical imaging is an important non-invasive tool for diagnostic and treatment purposes in medical practice. However, interpreting medical images is a time consuming and challenging task. Computer-aided diagnosis (CAD) tools have been used in clinical practice to assist medical practitioners in medical imaging analysis since the 1990s. Most of the current generation of CADs are built on conventional computer vision techniques, such as manually defined feature descriptors. Deep convolutional neural networks (CNNs) provide robust end-to-end methods that can automatically learn feature representations. CNNs are a promising building block of next-generation CADs. However, applying CNNs to medical imaging analysis tasks is challenging. This dissertation addresses three major issues that obstruct utilizing modern deep neural networks on medical image analysis tasks---lack of domain knowledge in architecture design, lack of labeled data in model training, and lack of uncertainty estimation in deep neural networks. We evaluated the proposed methods on six large, clinically-relevant datasets. The result shows that the proposed methods can significantly improve the deep neural network performance on medical imaging analysis tasks