Numerics-Informed Neural Networks (NINNs)

The overall goal is to develop numerics-informed neural networks (NINNs) and DeepOnets for chemical reactions and for PDEs with spatial derivatives improve the computational efficiency of the chemical kinetics models for chemical weapon agents and simulants. Based on the first NINN developed by the Karniadakis’s group in 2018, which blends the multi-step time-stepping with deep neural networks, to distill the mechanisms that govern the evolution of a given data-set, we will reformulate the multi-step formulation to include high-order stiffly stable schemes using high-order backwards difference formulas (BDFs) to improve accuracy and stability. Our unique DeepOnet for operator regression maps continuous functions as inputs to continuous functions as output. It was demonstrated that DeepOnet can learn to predict the non-equilibrium chemistry at a speed more than 50,000 times than a CFD solver! The major innovation we propose is the development of physics-informed DeepOnet (PI-DeepOnet) that will use the chemical reaction equations only during training to learn the operator (system of ODEs) and will make accurate and robust predictions at a fraction of second given new reaction rates and new initial conditions.  The effectiveness of proposed approaches will be tested for several benchmark problems in chemical reactions and incompressible turbulent flows.