This session welcomes frontier research on foundational mathematical constructs underlying system dynamic complexity and intelligence, with emphasis on rigorous, unifying formalisms that advance theoretical understanding across nonlinear, multiscale dynamics, including far-from-equilibrium behavior, 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 problems.

Of interest is also how foundational mathematical structures inform and constrain formal paradigms in machine learning, explainable AI, physically informed and unified systems intelligence, enabling advances in interpretability, generalization, and robustness.

Contributions are also encouraged where novel mathematical insights yield further understanding of scaling, regime behavior, extremes, and interacting hazards across the Earth system.

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

• A - Atmospheric Sciences
• H - Hydrology
• IN - Informatics
• NH - Natural Hazards