Timezone: »

Learning nonlinear level sets for dimensionality reduction in function approximation
Guannan Zhang · Jiaxin Zhang · Jacob Hinkle

Thu Dec 12 05:00 PM -- 07:00 PM (PST) @ East Exhibition Hall B + C #14

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. The NLL approach is demonstrated by applying it to three 2D functions and two 20D functions for showing the improved approximation accuracy with the use of nonlinear transformation, as well as to an 8D composite material design problem for optimizing the buckling-resistance performance of composite shells of rocket inter-stages.

Author Information

Guannan Zhang (Oak Ridge National Laboratory)
Jiaxin Zhang (Oak Ridge National Laboratory)

I am now a Research Staff in Machine Learning and Data Analytics Group, Computer Science and Mathematics Division at Oak Ridge National Laboratory (ORNL). My current research interest is on Artificial Intelligence for Science and Engineering (AISE). My broad interests revolve around robust machine learning, uncertainty quantification, inverse problems, and numerical optimization.

Jacob Hinkle (Oak Ridge National Lab)

More from the Same Authors