A Hybrid QLM–Chebyshev Spectral and PINN Framework for Nonlinear CO2 Sequestration Dynamics

Carbon dioxide (CO2) sequestration plays a central role in mitigating climate change, yet its underlying dynamics are governed by strongly nonlinear interactions between injection, storage capacity, mineralization, pressure buildup, leakage risk, and thermal effects. In this work, we propose a novel six-dimensional nonlinear dynamical system describing the temporal evolution of stored CO2, dissolved CO2, mineralized carbon, pressure-induced activation, leakage potential, and temperature variation within a sequestration reservoir. We first establish the mathematical well posedness of the proposed model by proving the positivity and boundedness of solutions, ensuring that all state variables remain physically meaningful for nonnegative initial conditions. A rigorous qualitative analysis is provided, leading to the construction of a positively invariant absorbing region. To compute accurate long-term solutions, a high-order numerical framework based on a quasilinearization method (QLM) combined with a shifted Chebyshev spectral collocation technique and a domain decomposition strategy is developed. This approach transforms the nonlinear system into a sequence of linear subproblems that are solved efficiently on consecutive subintervals, preserving spectral accuracy over extended time horizons. Convergence and error properties of the Chebyshev approximation are discussed in the L2 norm, and residual error functions are employed to assess solution accuracy in the absence of closed-form solutions. In addition, the physics-informed neural network (PINN) framework is employed as an independent, mesh-free validation tool rather than as a primary solver, enabling cross-verification of the spectral solutions. The PINN enforces the governing equations through automatic differentiation and provides a data-free learning framework for validating the spectral solutions. Numerical experiments demonstrate excellent agreement between the QLM–Chebyshev and PINN solutions, confirming the robustness, accuracy, and long-term stability of the proposed hybrid computational framework. The presented methodology offers a powerful and flexible tool for the analysis and simulation of complex CO2 sequestration dynamics and can be extended to other nonlinear environmental and energy-related systems.