Bayesian differential programming for robust systems identification under uncertainty
This provides a robust workflow for data-driven model discovery under uncertainty, which is incremental as it builds on existing differentiable programming and Bayesian methods for systems identification.
The paper tackles the problem of identifying nonlinear dynamical systems from noisy, sparse, and irregular observations by developing a Bayesian framework that uses differentiable programming and Hamiltonian Monte Carlo to infer posterior distributions over model parameters with quantified uncertainty, resulting in interpretable and parsimonious models as demonstrated in numerical studies on systems like nonlinear oscillators and chaotic dynamics.
This paper presents a machine learning framework for Bayesian systems identification from noisy, sparse and irregular observations of nonlinear dynamical systems. The proposed method takes advantage of recent developments in differentiable programming to propagate gradient information through ordinary differential equation solvers and perform Bayesian inference with respect to unknown model parameters using Hamiltonian Monte Carlo. This allows us to efficiently infer posterior distributions over plausible models with quantified uncertainty, while the use of sparsity-promoting priors enables the discovery of interpretable and parsimonious representations for the underlying latent dynamics. A series of numerical studies is presented to demonstrate the effectiveness of the proposed methods including nonlinear oscillators, predator-prey systems, chaotic dynamics and systems biology. Taken all together, our findings put forth a novel, flexible and robust workflow for data-driven model discovery under uncertainty.