This session welcomes frontier research on foundational mathematical constructs underlying geophysically consistent system dynamic intelligence, with emphasis on rigorous, unifying formalisms that advance fundamental theoretical understanding across complex multiscale dynamics, including far-from-equilibrium behaviour, non-ergodicity, criticality, and emergence.

Mathematical contributions may encompass foundational paradigms (categorical, topological, algebraic), analytical frameworks (functional, geometric, stochastic), generalized operators (fractional, nonlocal, integro-differential, information theoretical), and unveil principled perspectives, theoretical advances and systems intelligence to shed light onto complex geophysical and multi-hazard problems.

Of interest is also how foundational mathematical structures inform and constrain modern paradigms in machine learning, explainable AI, physically informed and unified systems intelligence, enabling advances in interpretability, generalization, and robustness. Contributions are also encouraged where deep mathematical insight yields new understanding of scaling, regime behavior, extremes, and interacting hazards across the Earth system.

Collaborative dialogue is fostered among foundational mathematics, geophysical sciences and information technologies, co-evolving to shape new mathematical physics pathways in complexity science and systems intelligence.

Just as mathematical and systems intelligence advances can empower breakthroughs in the geophysical sciences, geophysical problems can inspire the development of new mathematical and systems intelligence methods and techniques that then vastly transcend the disciplinary scope that gave rise to it. Our session is therefore aimed not only at how mathematics can be developed and used to advance the geosciences, but also how new mathematics can fundamentally emerge from the challenges facing our planet.