Data-Driven Governing Equations for Agricultural Biomass-Coal Co-Pyrolysis: SINDy Kinetics, Flory-Huggins Synergy, and High-Performance Char

Agricultural biomass co-pyrolysis with coal offers a near-term strategy for biomass valorisation and fossil carbon displacement, yet the mechanistic basis for the consistently observed equimolar blend optimum has remained unexplained. This study applies five interconnected mathematical layers — sparse governing equation discovery (SINDy), symbolic regression, transfer entropy analysis, persistent homology, and variational energy landscape formulation — to the co-pyrolysis of three South Asian agricultural residues (rice husk, areca husk, sugarcane husk) with Ramgarh coal at blend fractions of 25, 50, and 75 wt% across heating rates of 10-40 K/min. SINDy recovers a three-term governing differential law without any pre-assumed kinetic model, validated by three independent robustness tests. Symbolic regression identifies a Flory–Huggins configurational entropy origin for co-pyrolysis synergy, outperforming classical additive and Langmuir benchmarks. Persistent homology detects three distinct topological reaction phases and a statistically confirmed synergy loop at the equimolar blend. A variational energy landscape, proven stable by Lyapunov analysis, unifies all prior findings and links the 28.8% barrier reduction to a ~508-fold rate enhancement at 500 K via Transition State Theory. The 50 wt% biomass blend (B50) delivers super-additive BET surface areas, CO₂ uptake, and Pb²⁺ removal across all three biomass systems, with all chars exceeding EPA TCLP safety margins. A minimal 7-measurement protocol recovers full system governing laws, representing a 14-fold compression over standard characterisation effort.