The Physics in Nonlinear Science

Statement from the Course Coordinator:

My academic and research activities are pursued in a fundamental Physics perspective, with core principles in mind. In this sense, Nonlinear Science focuses not only on the mathematical characterisation but also on the fundamental physical understanding of complexity in its essence, grounded on first principles and aiming at universality. This contrasts with the traditional statistical and kinematic geometric approaches that describe system states and evolution without any underlying physics.

In my work, Dynamical Systems such as the Climate System are formulated in a physically consistent manner, constrained by conservation, dynamic and thermodynamic principles shaping the coevolution laws among physical processes. These ensure sustainable rates of process mixing, bounded by maximum entropy production rates associated with process-triggering gradients and free energy depletion, along with reactive or connective limits in the energy flow paths regulating how processes interact. Moreover, they ensure physically sustainable energy bounds in the dynamics, as no system can produce more work than the energy that it possesses or imports.

These principles are then reflected in the dynamic model design and information-theoretical data analytics and characterisation of the system dynamics, which are then endowed with thermodynamically consistent information metrics. In this sense, entropy is not taken in the statistical sense as an uncertainty measure, but in the physical sense as an intrinsic physical property of a coevolutionary dynamical system. With or without information uncertainties, a dissipative system is producing entropy, and that is seen in the statistics and in the kinematic geometry captured by data records. Overall, my take on information theory and machine learning is not an abstract blind statistic construct, but rather in a fundamental physical sense, peering into the dynamic mechanisms behind the statistical and geometric features detected in the records.

An example of that is my work peering into the physical mechanisms behind information-theoretical measures of synergy and redundancy, endowing interaction information signatures in geophysical fluid dynamics with underlying mechanisms grounded on nonlinear scale interactions in wave mechanics and fluid flow. Novel atmospheric insights on triadic wave resonance among planetary, synoptic and mesoscale waves are brought out in fundamental fluid dynamic terms, explaining observed information-theoretical and nonlinear signatures of emergence, and shedding further light on elusive emergent behaviours in multiscale atmospheric flow e.g. behind far from equilibrium transient dynamics behind “extreme” meteorological phenomena.

Other atmospheric science applications of my approaches include the disentanglement of physically consistent nonlinear spatiotemporal atmospheric controls on precipitation, the long-term dynamic prescription of its evolving distributions from first principles and the dynamic understanding of underlying cooperative interactions among fundamental processes in atmospheric dynamics as represented by synergistic interactions among non-redundant dynamic sources regulating thermodynamic mixing and dynamic circulation in the upper-level troposphere. In this sense, more than a model user, I am fundamentally a model builder.

Hydro-meteorologic and hydro-climatic applications of my work include the dynamic prediction (theoretical and operational) of flood occurrences, multiscale flood regimes, transitions and sustained changes under far-from-equilibrium landscape-climate dynamics in the coevolutionary earth system.

My publications, some of which are listed here, are examples of a constructive interaction between advanced methodological developments in Nonlinear Science with profound physical insights and relevant applications to further the fundamental dynamic understanding and predictability of Atmospheric and Earth System problems.