Physics Informed Constrained Learning of Dynamics from Static Data
This work addresses a bottleneck in applying physics-informed models to systems where time-course data is scarce or unavailable, offering a novel method for domain-specific applications like metabolic flux analysis.
The paper tackles the problem of learning system dynamics from static or partially observed data, which is challenging for existing physics-informed neural networks (PINNs) that require fully observed time-course data. It introduces a new PINN paradigm called Constrained Learning and an optimization approach, MPOCtrL, which outperforms existing data-driven flux estimators on metabolic flux analysis tasks.
A physics-informed neural network (PINN) models the dynamics of a system by integrating the governing physical laws into the architecture of a neural network. By enforcing physical laws as constraints, PINN overcomes challenges with data scarsity and potentially high dimensionality. Existing PINN frameworks rely on fully observed time-course data, the acquisition of which could be prohibitive for many systems. In this study, we developed a new PINN learning paradigm, namely Constrained Learning, that enables the approximation of first-order derivatives or motions using non-time course or partially observed data. Computational principles and a general mathematical formulation of Constrained Learning were developed. We further introduced MPOCtrL (Message Passing Optimization-based Constrained Learning) an optimization approach tailored for the Constrained Learning framework that strives to balance the fitting of physical models and observed data. Its code is available at github link: https://github.com/ptdang1001/MPOCtrL Experiments on synthetic and real-world data demonstrated that MPOCtrL can effectively detect the nonlinear dependency between observed data and the underlying physical properties of the system. In particular, on the task of metabolic flux analysis, MPOCtrL outperforms all existing data-driven flux estimators.