Researchers have developed a hybrid modeling framework that combines pre-trained numerics-informed neural networks (NINNs) with classical full order models (FOMs) using the overlapping Schwarz alternating method. This approach was tested on a two-dimensional advection-diffusion equation in an advection-dominated regime. The study demonstrated that a monolithic NINN can be accurately trained without domain decomposition, unlike traditional physics-informed neural networks (PINNs). The hybrid framework couples a pre-trained NINN with a neighboring FOM, keeping the NINN weights fixed during the Schwarz iteration, and achieves comparable accuracy to full FOM-FOM Schwarz solutions through both top-down and bottom-up training strategies. AI
IMPACT This research could lead to more efficient and accurate simulations by combining the strengths of neural networks and traditional numerical methods.
RANK_REASON Academic paper detailing a new computational method. [lever_c_demoted from research: ic=1 ai=1.0]
- full order models
- NINNs
- numerics-informed neural networks
- physics-informed neural network
- Schwarz alternating method
- two-dimensional advection-diffusion equation
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