Piecewise DMD for Reconstructing and Forecasting Chemotaxis-Driven Soil Carbon Spot Patterns
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Spatially explicit models of soil organic carbon (SOC) coupled with microbial dynamics can generate self-organized patterns driven by chemotaxis and transient amplification. We investigate reaction-diffusion-chemotaxis formulations in which, above a critical chemotactic sensitivity, a spatially uniform state destabilizes and the dynamics consistently develop spot-like structures [1]. Moreover, we consider parameter regimes where patterning may arise outside classical Turing-unstable conditions through reactivity-induced transient growth [2]. A data-driven description of these spatiotemporal dynamics is presented using piecewise Dynamic Mode Decomposition (pDMD). The aim is to accurately reconstructs the evolution of spot patterns and forecast their dynamics over moderate time horizons. The piecewise approach captures regime changes and nonlinear transients more effectively than global linear decompositions [3], yielding reliable reconstructions and improved short-to-mid-term prediction. These results support pDMD as a practical tool for analyzing and forecasting spatiotemporal data in soil microbial ecology, with potential implications for environmental monitoring and sustainable agriculture. REFERENCES [1] A. Monti, F. Diele, D. Lacitignola, C. Marangi, Patterns in soil organic carbon dynamics: Integrating microbial activity, chemotaxis and data-driven approaches, Mathematics and Computers in Simulation, vol. 234, pp. 86–101, 2025 [2] F. Diele, A. L. Krause, D. Lacitignola, C. Marangi, A. Monti, E. Villar-Sepùlveda, Transient Instability and Patterns of Reactivity in Diffusive-Chemotaxis Soil Carbon Dynamics, Bulletin of Mathematical Biology, vol. 87, art. 162, 2025. [3] A. Alla, A. Monti, I. Sgura, Piecewise DMD for oscillatory and Turing spatio-temporal dynamics, Computers & Mathematics with Applications, vol. 160, pp. 108–124, 2024.
