Chemistry

Programming language

Transformation (genetics)

Coordinate system

Artificial intelligence

Representation (politics)

Biochemistry

Autoencoder

Physics

Nonlinear system

Dynamical systems theory

Biology

Politics

Gene

Political science

Quantum mechanics

Computer science

Botany

Algorithm

Interpretability

Theoretical computer science

Identification (biology)

occam

Artificial neural network

Proceedings of the National Academy of Sciences

The discovery of governing equations from scientific data has the potential to transform data-rich fields that lack well-characterized quantitative descriptions. Advances in sparse regression are currently enabling the tractable identification of both the structure and parameters of a nonlinear dynamical system from data. The resulting models have the fewest terms necessary to describe the dynamics, balancing model complexity with descriptive ability, and thus promoting interpretability and generalizability. This provides an algorithmic approach to Occam’s razor for model discovery. However, this approach fundamentally relies on an effective coordinate system in which the dynamics have a simple representation. In this work, we design a custom deep autoencoder network to discover a coordinate transformation into a reduced space where the dynamics may be sparsely represented. Thus, we simultaneously learn the governing equations and the associated coordinate system. We demonstrate this approach on several example high-dimensional systems with low-dimensional behavior. The resulting modeling framework combines the strengths of deep neural networks for flexible representation and sparse identification of nonlinear dynamics (SINDy) for parsimonious models. This method places the discovery of coordinates and models on an equal footing.

Data-driven discovery of coordinates and governing equations