CTSR: Cartesian tensor-based sparse regression for data-driven discovery of high-dimensional invariant governing equations
This addresses a bottleneck in data-driven modeling for complex physical systems where existing methods are limited to low-dimensional scenarios or lack invariance properties.
The paper tackles the problem of automatically discovering high-dimensional governing equations from data while ensuring rotation and reflection invariance, proposing a Cartesian tensor-based sparse regression method that achieves superior accuracy and efficiency compared to conventional techniques in 2D and 3D test cases.
Accurate and concise governing equations are crucial for understanding system dynamics. Recently, data-driven methods such as sparse regression have been employed to automatically uncover governing equations from data, representing a significant shift from traditional first-principles modeling. However, most existing methods focus on scalar equations, limiting their applicability to simple, low-dimensional scenarios, and failing to ensure rotation and reflection invariance without incurring significant computational cost or requiring additional prior knowledge. This paper proposes a Cartesian tensor-based sparse regression (CTSR) technique to accurately and efficiently uncover complex, high-dimensional governing equations while ensuring invariance. Evaluations on two two-dimensional (2D) and two three-dimensional (3D) test cases demonstrate that the proposed method achieves superior accuracy and efficiency compared to the conventional technique.