Identifying parameter couplings and uncertainties of mixed-noise stochastic systems via full-covariance Gaussian mixture network

Parameter identification of stochastic dynamical systems driven by mixed noises is challenging due to intractable likelihood functions. We propose PENN-GMD, a parameter estimation neural network that maps partially observed trajectories to a Gaussian mixture distribution (GMD) over the system parameters. Unlike conventional uncertainty estimates, the GMD employs full covariance matrices to explicitly reveal parameter couplings and multi-modal likelihood structures. The network is trained by minimizing the negative log-likelihood via a surjective parameterization that hard-encodes all GMD constraints, thereby approximating the true likelihood. We validate the method on five numerical examples with increasing complexity, including systems driven by fractional Gaussian and Lévy noises, oscillators with colored noise, coupled neurons under different observability, and an aeroelastic airfoil with unidentifiable stochastic disturbances. Results demonstrate that PENN-GMD accurately recovers likelihood distributions, captures parameter couplings, and naturally diagnoses non-identifiability through variance broadening or mode splitting. These capabilities establish PENN-GMD as a practical tool for uncertainty-aware parameter identification in complex stochastic systems where conventional likelihood-based methods are infeasible.

Physics-Informed Neural Learning for State Reconstruction and Parameter Identification in Coupled Greenhouse Climate Dynamics

Physics-informed neural networks (PINNs) have recently emerged as a promising framework for integrating data-driven learning with physical knowledge. In this work, we propose a coupled PINN approach for the joint reconstruction of indoor temperature and humidity dynamics in greenhouse environments, together with simultaneous identification of key model parameters. The method incorporates a reduced-order physically motivated model into the learning process, enabling consistent estimation under sparse and noisy observations. The artificial intelligence contribution lies in the development of a coupled physics-informed neural learning framework that integrates governing dynamical constraints into neural network training, while the engineering application focuses on greenhouse climate state reconstruction and parameter identification. The proposed framework is evaluated on a controlled synthetic benchmark that mimics diurnal forcing conditions. Compared with a purely data-driven neural network baseline, the coupled PINN achieves improved reconstruction accuracy, reducing temperature and humidity errors while maintaining high coefficients of determination. The improvement is particularly pronounced in the humidity channel, where latent moisture dynamics are more difficult to infer from limited measurements. In addition to accurate state reconstruction, the method successfully recovers the dominant physical parameters governing the system dynamics, demonstrating its ability to learn interpretable representations beyond data interpolation. These results highlight the potential of physics-informed learning for greenhouse climate modeling and, more broadly, for data-scarce environmental systems.