A physics-informed multi-fidelity approach for the estimation of differential equations parameters in low-data or large-noise regimes
In this article, the authors introduce a multi-fidelity approach to estimate an unknown parameter based on Physics-Informed Neural Networks (PINNs). The authors developed two different multi-fidelity approaches: MPINN-v1 and MPINN-v2. The first one is based on a parameter-independent low-fidelity solution which acts only as the parameter's initial guess, to estimate the solution of the PDE. The second approach is based on a parameter-dependent low-fidelity solution with a training procedure designed to minimize simultaneously the distance between the solution of PDE and the data, the distance between the solution of PDE and the low-fidelity approximation for the same parameter value, and the residual of the equation. Numerical tests were performed for an advection-diffusion-reaction equation, and the Bueno-Orovio ionic nonlinear model describing the ionic dynamics of cardiac cells, focusing on the case of few noisy measurements. Finally, they conclude that the multi-fidelity approach is promising for solving realistic optimization problems involving noisy measurements and complex multiscale and multiphysics phenomena.
scientific article; zbMATH DE number 7473888
scientific article