Physics-integrated Neural Differentiable (PiNDiff) Model for Isothermal Chemical Vapor Infiltration Process

Composites are a class of materials actively considered for various applications in today’s aerospace, automotive, and civil industries owing to their high strength and lightweight. The performance, quality, and repeatability of the composite materials are greatly influenced by the manufacturing process. The mechanical properties of the composites depend on various variables and parameters of the manufacturing process, which are challenging, if not impossible, to determine and optimize experimentally. Traditional first-principle modeling approaches are not accessible due to the complex physics involved. Moreover, the functional form of the consultative relations used in the numerical model needs to be approximated with the help of experimental studies, thereby limiting its applicability. On the other hand, purely data-based DNN models, although showing great promise, heavily rely on “big data” and often suffer from the generalizability issue in out-of-training regimes, impeding their effective applications in modeling complex composite manufacturing processes. A hybrid model that combines incomplete physics knowledge with available measurement data within a differentiable programming framework opens new avenues to tackle the challenges. In this work, a physics-integrated neural differentiable (PiNDiff) model is developed, where the partially known physics is integrated into the recurrent network architecture to enable effective learning and generalization. The merit and potential of the proposed method have been demonstrated in modeling the densification behavior of composite during the isothermal chemical vapor infiltration (ICVI) process. The ICVI process, one of the chemical vapor infiltration (CVI) processes, is widely used to manufacture carbon-carbon (C/C) and C/SiC composites. Modeling the ICVI process using the traditional first-principle approach will be a near-to-impossible task owing to the number of species produced due to pyrolysis and the complex reaction occurring in the ICVI process. The proposed PiNDiff model handles these complexities using a homogenization approach and learns the unknown physics brought out by the homogenization assumption. The PiNDiff model learns unknown physics from limited, indirect data and, meanwhile, can be used to infer unobserved variables and parameters. The demonstrated PiNDiff strategy may provide a general strategy to model phenomena where physics is only partially known and sparse, indirect data are available.