Tensor-train method finds patterns in high-dimensional dynamics fast
Tensor-Train Weak SINDy: Identifying High-Dimensional Nonlinear Dynamics
Machine LearningComputational Engineering, Finance, and Science
Summary
Finding rules that explain complex systems becomes very hard when many factors interact at once. The authors combine two existing approaches and use a special data structure called tensor-train to handle many variables efficiently. Their method can pick out important patterns from huge sets of possible functions without slowing down too much. This helps avoid the problem where computations become unmanageable as the number of variables grows.
What this means in practice
- •For control system engineers: Identify governing equations of complex systems with many interacting parts using less computation and memory.
- •For machine learning engineers: Efficiently find sparse models from high-dimensional time-series data with improved scalability.
Authors
Will Houser, Vanja Dukic, David M. Bortz
Abstract
In recent years, weak-form methods have made significant advances in data-driven discovery of dynamical systems. However, in high-dimensional settings, current techniques can prove expensive in both computation and memory. In this work, we introduce TT-WSINDy, which combines techniques of the Multidimensional Approximation of Nonlinear Dynamics (MANDy) and Weak Sparse Identification of Nonlinear Dynamics (WSINDy) methods, implementing requisite computations in the tensor-train (TT) format. We demonstrate that this method is able to search an exponentially-growing space of candidate functions -- performing weak-form transformation, regression, and sparsification -- without suffering from the curse of dimensionality.