Physics and equality constrained artificial neural networks: Application to forward and inverse problems with multi-fidelity data fusion
نویسندگان
چکیده
Physics-informed neural networks (PINNs) have been proposed to learn the solution of partial differential equations (PDE). In PINNs, residual form PDE interest and its boundary conditions are lumped into a composite objective function as soft penalties. Here, we show that this specific way formulating is source severe limitations in PINN approach when applied different kinds PDEs. To address these limitations, propose versatile framework based on constrained optimization problem formulation, where use augmented Lagrangian method (ALM) constrain with any high-fidelity data may be available. Our adept at forward inverse problems multi-fidelity fusion. We demonstrate efficacy versatility our physics- equality-constrained deep-learning by applying it several involving multi-dimensional achieves orders magnitude improvements accuracy levels comparison state-of-the-art physics-informed networks.
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ژورنال
عنوان ژورنال: Journal of Computational Physics
سال: 2022
ISSN: ['1090-2716', '0021-9991']
DOI: https://doi.org/10.1016/j.jcp.2022.111301