Deep learning achieves tremendous success in image and speech recognition and machine translation. However, deep learning is not trustworthy. 1. How to improve the robustness of deep neural networks? Deep neural networks are well known to be vulnerable to adversarial attacks. For instance, malicious attacks can fool the Tesla self-driving system by making a tiny change on the scene acquired by the intelligence system. 2. How to compress high-capacity deep neural networks efficiently without loss of accuracy? It is notorious that the computational cost of inference by deep neural networks is one of the major bottlenecks for applying them to mobile devices. 3. How to protect the private information that is used to train a deep neural network? Deep learning-based artificial intelligence systems may leak the private training data. Fredrikson et al. recently showed that a simple model-inversion attack can recover the portraits of the victims whose face images are used to train the face recognition system. In this talk, I will present some recent work on developing PDE-principled robust neural architecture and optimization algorithms for robust, accurate, private, and efficient deep learning. I will also present some potential applications of the data-driven approach for bio-molecule simulation and computer-aided drug design.

Accelerating stochastic gradient-based optimization and sampling algorithms are of crucial importance for modern machine learning, in particular, deep learning. Developing mathematically principled architectures for deep neural nets (DNNs) is another important direction to advance deep learning. In this talk, I will present some recent progress in leveraging Nesterov Accelerated Gradient (NAG) with scheduled restarting to accelerate SGD and to improve training DNNs. Moreover, I will talk about some recent results on PDE based techniques for accelerating stochastic gradient descent and Langevin dynamics. Finally, I will discuss a momentum-based formulation for DNN design.