Uncovering solutions from data corrupted by systematic errors: A physics-constrained convolutional neural network approach
This addresses the challenge of removing systematic errors from data in physics and engineering, offering a tool for improving model and measurement accuracy, though it appears incremental as it builds on existing physics-informed neural network approaches.
The paper tackles the problem of uncovering spatiotemporal solutions from data corrupted by systematic errors by proposing a physics-constrained convolutional neural network (PC-CNN) that combines governing equations and data, showing robustness in handling large multimodal errors and producing physical solutions for phenomena like linear convection and Burgers equation.
Information on natural phenomena and engineering systems is typically contained in data. Data can be corrupted by systematic errors in models and experiments. In this paper, we propose a tool to uncover the spatiotemporal solution of the underlying physical system by removing the systematic errors from data. The tool is the physics-constrained convolutional neural network (PC-CNN), which combines information from both the systems governing equations and data. We focus on fundamental phenomena that are modelled by partial differential equations, such as linear convection, Burgers equation, and two-dimensional turbulence. First, we formulate the problem, describe the physics-constrained convolutional neural network, and parameterise the systematic error. Second, we uncover the solutions from data corrupted by large multimodal systematic errors. Third, we perform a parametric study for different systematic errors. We show that the method is robust. Fourth, we analyse the physical properties of the uncovered solutions. We show that the solutions inferred from the PC-CNN are physical, in contrast to the data corrupted by systematic errors that does not fulfil the governing equations. This work opens opportunities for removing epistemic errors from models, and systematic errors from measurements.