A stochastic optimal control framework for quantifying and
reducing uncertainties in deep learning
Project description:
We propose to develop a stochastic optimal control framework for
quantifying and reducing uncertainties in deep learning by exploiting
the connection between probabilistic network architectures and optimal
control of stochastic dynamical systems. Despite neural networks
achieving impressive results in many machine learning tasks, current
network models often produce unrealistic decisions due to the
computational intractability of existing uncertainty quantification
(UQ) methods in measuring uncertainties of very deep networks. As UQ is
increasingly important to the safe use of deep learning in decision
making for scientific applications, the computing capability developed
in this effort will significantly advance the reliability of
machine-learning assisted scientific predictions for DOE applications.
Funding
period: 2019 -- 2021
Accelerating Reinforcement Learning with
a Directional-Gaussian-Smoothing Evolution Strategy
Other Support: ORNL AI Initiative (https://www.ornl.gov/ai-initiative).
A Scalable Evolution Strategy for High-Dimensional Blackbox Optimization
We developed an Evolution Strategy with Directional Gaussian Smoothing (DGS-ES) which exploits nonlocal searching to maximize/minimize high-dimensional non-convex blackbox functions. The main contributions of this effort include (i) development of the a new DGS-gradient operator and its Gauss-Hermite estimator, which introduces, for the first time, an accurate nonlocal searching technique into the family of Evolution Strategy (ES). (ii) Theoretical analysis verifies that the scalability of the DGS-ES method, i.e., the number of iterations needed for convergence, is independent of the dimension for convex functions. (iii) Demonstration of the DGS-ES method on both high-dimensional non-convex benchmark optimization problems, as well as a real-world material design problem for rocket shell manufacture. (iv) Massive parallelization: the DGS-ES method is suited to be scaled up to a large number of parallel workers. All the function evaluations within each iteration can be simulated totally in parallel, and each worker only needs to return a scalar to the master, such that the communication cost among workers is minimal.Publication: Jiaxin Zhang, Hoang Tran, Dan Lu, and Guannan Zhang, A Scalable Evolution Strategy with Directional Gaussian Smoothing for Blackbox Optimization, (https://arxiv.org/abs/2002.03001).
Other Support: ORNL AI Initiative (https://www.ornl.gov/ai-initiative).
Learning nonlinear level sets for dimensionality reduction in function approximation
We developed a Nonlinear Level-set Learning (NLL) method for dimensionality reduction in high-dimensional function approximation with small data. This work is motivated by a variety of design tasks in real-world engineering applications, where practitioners would replace their computationally intensive physical models (e.g., high-resolution fluid simulators) with fast-to-evaluate predictive machine learning models, so as to accelerate the engineering design processes. There are two major challenges in constructing such predictive models: (a) high-dimensional inputs (e.g., many independent design parameters) and (b) small training data, generated by running extremely time-consuming simulations. Thus, reducing the input dimension is critical to alleviate the over-fitting issue caused by data insufficiency. Existing methods, including sliced inverse regression and active subspace approaches, reduce the input dimension by learning a linear coordinate transformation; our main contribution is to extend the transformation approach to a nonlinear regime. Specifically, we exploit reversible networks (RevNets) to learn nonlinear level sets of a high-dimensional function and parameterize its level sets in low-dimensional spaces. A new loss function was designed to utilize samples of the target functions’ gradient to encourage the transformed function to be sensitive to only a few transformed coordinates.
Publication: Guannan Zhang, Jiaxin Zhang and Jacob Hinkle, Learning nonlinear level sets for dimensionality reduction in function approximation, Advances in Neural Information Processing Systems (NeurIPS), 32, pp. 13199-13208, 2019.
Other Support: ORNL AI Initiative (https://www.ornl.gov/ai-initiative).
Scalable Machine-Learning-based Optimal Design for Additively Manufactured Materials
We developed a scalable deep-learning-based optimal design method that exploits SUMMIT to significantly accelerate composite material design process with up to 85% cost reduction. The new method addresses three grand challenges in optimal design: (i) high-dimensional design space, (ii) computationally expensive multi-physics models, (iii) non-parallelizable optimization algorithms. Those challenges are addressed based on our observation that an optimizer only walks along a 1-D search path to find the optimum, regardless of the dimension of the design space. Thus, our goal is to construct a low-dimensional ML-model that can cover the 1-D search path. To this end, we developed a sequence of local deep neural networks (DNNs), each of which only covers a segment of the search path. To further reduce the dimensionality, we designed a new sampling strategy that can concentrate the training samples along the gradient descent direction. Our algorithm was implemented on SUMMIT, where hundreds of CPUs are used to produce training data, and hundreds of GPUs are used to train DNN models.Presentation: Sirui Bi, Jiaxin Zhang, and Guannan Zhang, Scalable Machine-Learning-based Optimal Design for Additively Manufactured Materials, ORNL AI Expo, 2019.
Other Support: ORNL AI Initiative (https://www.ornl.gov/ai-initiative).