Dr Amonya studies infrastructure and public investment as complex adaptive systems. His central concern is what happens when the conventional assumptions of equilibrium, separability and predictable cause and effect are relaxed. Infrastructure then ceases to be simply a collection of physical assets or projects to be optimised. It becomes part of a dynamic human system in which the state, market and society continuously act upon one another, generating feedback, adaptation, novelty and occasionally instability.
His research therefore seeks a stronger mathematical foundation for infrastructure and policy. He draws from dynamical systems, information theory, network theory, statistical mechanics and the calculus of variations to examine questions normally treated through engineering judgement, economics or institutional narrative alone. Public investment can be read on a Hamiltonian frame. PPP can be examined as a Lagrangian problem concerned with possible trajectories through institutional and economic space. Lyapunov stability provides a language for asking whether disturbances dissipate or accumulate. Shannon entropy and information gradients provide ways of thinking about how rapidly changing information strains the norms, trust and institutional structures through which societies coordinate themselves.
This mathematics is not introduced as decoration. Its purpose is to expose assumptions that conventional appraisal frequently leaves hidden. Cost-benefit analysis remains useful, but it represents only one reduction of a much larger system. The deeper problem is how societies navigate strongly non-linear and non-ergodic environments in which the intervention itself changes subsequent possibilities. This has led his work from optimisation towards navigation, from projects towards fields and networks, and from infrastructure as an object towards infrastructure as an operator on society.
A recurring object in this research is the city. Cities concentrate physical networks, institutions, people, capital, information and political power. Sustainability, resilience, congestion, accessibility and growth are consequently treated not merely as policy heuristics but as properties emerging from an evolving topology. His work asks how these properties might be mathematised without stripping away the human relationships that produce them.
The empirical terrain ranges from Britain to Africa, with particular attention to infrastructure finance, transport networks, cities and institutional development. Climate change, digitalisation and the emergence of AI are treated as major excitations of an already complex system, rather than as external subjects to be appended to conventional infrastructure analysis. Across this work runs one question: how can public institutions sense, learn and steer when the world they are attempting to govern is itself changing?