DETONATE: Nonlinear Dynamic Evolution Modeling of Time-dependent 3-dimensional Point Cloud Profiles

Abstract

Modeling the evolution of a 3D profile over time as a function of heterogeneous input data and the previous time steps’ 3D shape is a challenging, yet fundamental problem in many applications. We introduce a novel methodology for the nonlinear modeling of dynamically evolving 3D shape profiles. Our model integrates heterogeneous, multimodal inputs that may affect the evolvement of the 3D shape profiles. We leverage the forward and backward temporal dynamics to preserve the underlying temporal physical structures. Our approach is based on the Koopman operator theory for high-dimensional nonlinear dynamical systems. We leverage the theoretical Koopman framework to develop a deep learning-based framework for nonlinear, dynamic 3D modeling with consistent temporal dynamics. We evaluate our method on multiple high-dimensional and short-term dependent problems, and it achieves accurate estimates, while also being robust to noise.

Keywords:

• Nonlinear dynamic evolution modeling
• 3D profiles
• Koopman operator theory
• heterogenous data fusion
• unstructured 3D data

Acknowledgments

We would like to express our gratitude to the three anonymous referees whose insightful comments and suggestions have significantly enhanced the quality of our manuscript.

Funding

We acknowledge the generous support provided by the National Science Foundation (NSF) under Award Number 2019378.

Additional information

Notes on contributors

Michael Biehler

Michael Biehler received his BS and MS degrees in industrial engineering with a major in production engineering from the Karlsruhe Institute of Technology (KIT) in 2017 and 2020, respectively. He is currently pursuing a PhD degree with the H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology. His research rests at the interface between 3D machine learning and cyber-physical security, where he aims to develop methods for monitoring, prognostics, and control.

Daniel Lin

Daniel Lin is a junior at Walton High School in Marietta, GA. He is interested in applying machine learning to a wide range of applications such as advanced manufacturing and biology and plans to pursue a career in science or engineering in the future.

Jianjun Shi

Dr. Jianjun Shi received the BS and MS degrees in automation from the Beijing Institute of Technology in 1984 and 1987, respectively, and the PhD degree in mechanical engineering from the University of Michigan in 1992. Currently, he is the Carolyn J. Stewart Chair and a Professor at the H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology. His research interests include the fusion of advanced statistical and domain knowledge to develop methodologies for modeling, monitoring, diagnosis, and control of complex manufacturing systems. He is a fellow of four professional societies, including ASME, IISE, INFORMS, and SME, an Elected Member of the International Statistics Institute (ISI), a Life Member of ASA, an Academician of the International Academy for Quality (IAQ), and a member of the National Academy of Engineers (NAE).