MoPINNEnKF / iPINNER: Iterative Physics-Informed Neural Network with Ensemble Kalman Filter

iPINNER (a.k.a. MoPINNEnKF) embeds a physics-informed neural network inside an ensemble Kalman filter, alternating between PINN-based forward solves and EnKF-based Bayesian updates. The iterative loop yields calibrated uncertainty estimates and robust parameter recovery for noisy, partially-observed PDE systems where pure PINN training is ill-conditioned.

Recommended citation: Lu, B., Mou, C., & Lin, G. (2025). "iPINNER: An iterative physics-informed neural network with ensemble Kalman filter." Journal of Computational Physics, 114592.
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