Globally optimized dynamic mode decomposition: A first study in particulate systems modelling - Abhishek Gupta; Barada Kanta Mishra (Theoretical and Applied Mechanics Letters)
This paper introduces dynamic mode decomposition (DMD) as a novel approach to model the breakage kinetics of particulate systems. DMD provides a data-driven framework to identify a best-fit linear dynamics model from a sequence of system measurement snapshots, bypassing the nontrivial task of determining appropriate mathematical forms for the breakage kernel functions. A key innovation of our method is the instilling of physics-informed constraints into the DMD eigenmodes and eigenvalues, ensuring they adhere to the physical structure of particle breakage processes even under sparse measurement data. The integration of eigen-constraints is computationally aided by a zeroth-order global optimizer for solving the nonlinear, nonconvex optimization problem that elicits system dynamics from data. Our method is evaluated against the state-of-the-art optimized DMD algorithm using both generated data and real-world data of a batch grinding mill, showcasing over an order of magnitude lower prediction errors in data reconstruction and forecasting.