Benchmarking sparse system identification with low-dimensional chaos
Sparse system identification is the data-driven process of obtaining parsimonious differential equations that describe the evolution of a dynamical system, balancing model complexity and accuracy. There has been rapid innovation in system identification across scientific domains, but there remains a gap in the literature for large-scale methodological comparisons that are evaluated on a variety of dynamical systems. In this work, we systematically benchmark sparse regression variants by utilizing the dysts standardized database of chaotic systems. In particular, we demonstrate how this open-source tool can be used to quantitatively compare different methods of system identification. To illustrate how this benchmark can be utilized, we perform a large comparison of four algorithms for solving the sparse identification of nonlinear dynamics (SINDy) optimization problem, finding strong performance of the original algorithm and a recent mixed-integer discrete algorithm. In all cases, we used ensembling to improve the noise robustness of SINDy and provide statistical comparisons. In addition, we show very compelling evidence that the weak SINDy formulation provides significant improvements over the traditional method, even on clean data. Lastly, we investigate how Pareto-optimal models generated from SINDy algorithms depend on the properties of the equations, finding that the performance shows no significant dependence on a set of dynamical properties that quantify the amount of chaos, scale separation, degree of nonlinearity, and the syntactic complexity.
Code (0)
등록된 구현이 없습니다.
Tasks
BenchmarkingSimilar Papers 제목 키워드 기반
Coded Hankel Polynomial Chaos: Spectral Identification of Dominant Polynomial-Chaos Modes
Identification of dominant polynomial-chaos modes is usually formulated as a sparse-regression problem on a sampled multivariate polynomial dictionary. We develop coded Hankel polynomial chaos (CH-PC), a complementary sp…
ChaosNetBench: Benchmarking Spatio-Temporal Graph Neural Networks on Chaotic Lattice Dynamics
Spatio-temporal graph neural networks (STGNNs) are widely used for short-term forecasting in dynamic physical systems such as traffic and weather. However, the prevailing evaluation practice uses real world benchmark dat…
Sparse Polynomial Chaos expansions using Variational Relevance Vector Machines
The challenges for non-intrusive methods for Polynomial Chaos modeling lie in the computational efficiency and accuracy under a limited number of model simulations. These challenges can be addressed by enforcing sparsity…
Compressive SensingComputational EfficiencyVariational InferenceGenMod: A generative modeling approach for spectral representation of PDEs with random inputs
We propose a method for quantifying uncertainty in high-dimensional PDE systems with random parameters, where the number of solution evaluations is small. Parametric PDE solutions are often approximated using a spectral …
compressed sensingUniform-in-time Propagation-of-Chaos for Stein Variational Gradient Descent
We study uniform-in-time propagation-of-chaos for continuous-time Stein Variational Gradient Descent (SVGD). Classical finite-time propagation-of-chaos estimates for mean-field systems typically deteriorate rapidly with …