Academic and Institutional Leadership
Prof. Dr. Rui A. Pita Perdigão is the Founding Chair of the Interuniversity College for the Physics of Complex Coevolutionary Systems and Fluid Dynamical Systems, the broader academic structure evolving from his original interuniversity chair as it expanded across the Atlantic. He is also the Founding Chair of the Meteoceanics Institute for Complex System Science and of the associated Doctoral School, with presences across Europe and North America, including through the North Atlantic Climate Centre.
More recently, he has also founded the Interuniversity Institute for Intelligence, Complexity and Security, academic spinoff with extended offerings in Quantum Information and Security, Quantum Aerospace Intelligence and Quantum Technologies in the Earth and Space Sciences, leveraging his research, development and innovation in the quantum, aerospace and intelligence industries.
Moreover, Prof. Rui Perdigão has also served multiple editorial board terms in international journals including as Editor at Earth System Dynamics (European Geosciences Union), Section Editor-in-Chief at Climate, Associate Editor for Interdisciplinary Physics at Frontiers in Physics, along with other editorial board memberships at e.g. Geosciences, Prevention and Treatment of Natural Disasters, Research in Ecology.
Prof. Perdigão has further been serving in scientific councils, evaluation and advisory panels from multiple international research and funding institutions. His broad track record spans across European Commission agencies such as REA (European Research Executive Agency), EISMEA (European Innovation Council and SMEs Executive Agency), CINEA (European Climate, Infrastructure and Environment Executive Agency), and also at regional and national agencies in Europe and North America.
University Teaching
For several years, Prof. Rui Perdigão has been designing, coordinating and delivering various university courses along with international courses, seminars and workshops. Some of his most relevant courses are linked to his inter university initiative and listed at the Meteoceanics Doctoral School here.
Moreover, he has been collaborating with the Doctoral Program on Climate Change and Sustainable Development Policies, an interdisciplinary doctorate promoted primarily by the University of Lisbon and the New University of Lisbon.
There, he has introduced, been coordinating and delivering some of his interdisciplinary courses, including on Complex System Dynamics and on Interdisciplinary Data Analytics and Model Design, which he tailored to a broad audience beyond the natural and exact science frontiers, being deployed not only to engineering and natural science students but also to those coming from social sciences, economics and management.
With the launch of the Interuniversity Institute for Intelligence, Complexity and Security, these academic offerings are now mainly delivered across the participating institutions and tailored to their respective priorities, ranging from classic academic to technical, executive and operational, promoting synergies among academia, industry and society.
Moreover, he is involved in doctoral thesis supervision, coordinating doctoral research in interdisciplinary problems spanning climate system dynamics, socio-environmental complexity, multi-hazards and quantum technological enablement for these problems.
Scientific Alliances
Prof. Rui Perdigão chairs the international alliance for Quantum Information Technologies in the Earth Sciences (QITES) and also the NORA Research Alliance (the latter with co-coordinator Dr. Julia Hall).
Moreover, he has been conducting research, development and innovation in the aerospace industry especially for the development of new aerospace sensors, information retrieval methods and model designs to further elicit multiscale Earth system dynamic processes and interactions from space, along with early warning signs of emerging hazards. Since the inception of his own organizations, his prior industry workplaces became valued customers.
Across the Earth System sciences, Rui Perdigão has taken part in various initiatives. In earlier years, he contributed as postdoctoral researcher to the development of satellite application facilities for Earth monitoring in the scope of Global Monitoring for the Environment and Security (GMES), precursor of the Copernicus program from the European Union. In the most recent years, he has been leading the development of the System-of-Systems for Multihazard Risk Intelligence Networks as WP2 leader for C2IMPRESS, Horizon Europe project funded by the European Union.
In between, among other activities he was also at the core team of the “Flood Change” consortium, headquartered at TU Wien, Vienna, Austria, and funded by the European Research Council. There, he has contributed as Earth System Dynamics representative, responsible for the development of mathematical physics methods for deciphering coevolutionary hydro-climate dynamics and river flood changes in the light of complex Earth System interactions. The collaborative effort resulted in the development of decision support products and in high-impact team publications, including in Science and in Nature.
Between 2019 and 2022 Rui Perdigão has revisited Lisbon, where he has been scientific council member of the Centre for Ecology, Evolution and Environmental Changes (CE3C) from the University of Lisbon, as research group leader for Climate Change Impacts, Adaptation and Modelling.
At the same time, he has also nurtured collaborations on Physics of Information with the Instituto de Telecomunicações at Instituto Superior Técnico from the University of Lisbon, and was co-founding signatory of the Portuguese Quantum Institute at its original incorporation.
In these areas, he has been developing theoretical studies on the physical nature of information, the informational nature of physics, along with conceiving quantum information systems for addressing complex mathematical challenges beyond the realms of traditional quantum theory. At a methodological level, he develops novel techniques for data exploration and model design of complex systems, and at a practical level he investigates new techniques for quantum technological sensing of environmental phenomena.
Scientific Background and Flow
Rui Perdigão holds a Doctorate in Physics with the highest honours. He has since then conducted independent and collaborative research on mathematical physics, predictability and uncertainty dynamics, from conceptual and methodological research to applications to information physics and fluid dynamical problems in natural sciences and engineering. He has also conducted R&D for large-scale international consortia, including the EU/ESA Copernicus Programme and the North Atlantic Alliance.
At a fundamental level, the research conducted by Rui Perdigão focuses on theoretical and methodological developments towards a novel theoretical physics paradigm bringing fundamental physical understanding to nonlinear dynamics and information theory. One of the core efforts in this regard has been the establishment of a nonlinear synergistic dynamic theory of complex coevolutionary systems, unveiling fundamental physical principles and canonic forms bringing complexity to its simplest yet fully generative form.
Prof Perdigão’s theoretical advances have been further implemented in generalised fluid dynamical systems and complex coevolutionary systems to address fundamental physics problems ranging across scales from quantum gravitation to coevolutionary earth system dynamics and thermodynamic cosmology. His research monographs, textbooks and courses share the most recent progress in these efforts and provide a unified framework bridging across the quantum-classical divide, with more to come.
With fluid dynamical system applications in mind relevant e.g. to the emergence of extreme events in climate dynamics, Rui Perdigão has developed a mathematical physics theory linking interaction information signatures in multiscale geophysical fluid dynamics with underlying mechanisms grounded on nonlinear scale interactions and synergistic emergence in wave mechanics and fluid flow.
In doing so, Rui Perdigão’s advances have brought out novel atmospheric insights on triadic wave resonance among planetary, synoptic and mesoscale waves 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.
Rui Perdigão has also introduced a non-ergodic coevolutionary theory of information physics, generalising information theory to the realm of far-from-equilibrium statistical mechanics, where there is event codependence and the traditional information theoretical measures do not hold. His novel measures unveil and quantify elusive sources of synergistic and coevolutionary predictability beyond post-critical spatiotemporal memory loss, long after nonlinear multi-information fades away. The collapse of dynamic regimes and nonlinear memory in far-from-equilibrium non-ergodic dynamics is thus no longer an obstacle for system understanding and prediction.
The theoretical advances from Rui Perdigão are now shedding light onto fundamental problems ranging across scales from evolutionary open quantum systems to coevolutionary earth system dynamics and thermodynamic cosmology, peering into the fundamental Physics of Evolutionary Complexity, and also shedding new light into Synergistic Dynamic Causation and Prediction in Coevolutionary Spacetimes.
Recent Mathematical Advances
On the mathematical side per se, the main recent branches of work encompass operator/functional analysis and nonlinear spectral dynamics, generalized nonassociative algebra and (n)-ary structures, discrete differential geometry and numerical PDEs, and non-Gaussian statistical and information-theoretic methods.
The Perdigão (2023) contribution on the polyadic inner product is the cleanest point at which the earlier higher-order information theoretic works acquire also an algebraic-geometric construction. It defines an n-ary inner product as a higher-order operation with more than two operands and introduces an associated n-angle. The illustrative ternary case is deliberately distinguished from expressions assembled as sequences of binary products: the numerator contains a genuine ternary operation, while lower-order unary and binary terms enter separately. The paper explicitly connects this construction to redundancy and synergy. A polyadic inner product is presented as a one-off higher-order operation capable of detecting structure that would otherwise require a sequence of binary comparisons; the n-angle is used to relate full n-way dependence to lower-order contributions.
Another paper, Martins-Ferreira & Perdigão (2023), begins a distinct but related algebraic line: a generalized construction for algebraic number systems. It relaxes structural assumptions in the classical Cayley-Dickson process and explores more general spaces than vector spaces. The Martins-Ferreira & Perdigão (2024) Mathematics paper “Towards a Generalized Cayley-Dickson Construction through Involutive Dimagmas” gives the construction a fuller formalization through magmas, dimagmas, involution, and a four-component tensor action. The decisive mathematical move is to treat the two basic operations as independent binary laws rather than assume the full package of associativity, commutativity, distributivity, and scalar linearity customary in familiar algebras. A dimagma, in this setting, is an elementary carrier set equipped with two binary operations. Involution and the generalized product then permit the construction to reproduce or extend familiar number systems while no longer being confined to the usual vector-space setting or to dimensions generated only by repeated doubling.
The 2025 paper “A minimal energy dimagma structure for complex plane discretization”, also with colleague Prof. Nelson Martins-Ferreira, is a natural continuation of the 2023-2024 algebraic construction. It explicitly states that it continues the dimagma investigation and seeks finite index-based algebraic configurations whose binary operations approximate the ordinary addition and multiplication of their complex realizations while minimizing an associated energy functional. The resulting object is intended as a discrete encoding of the complex plane whose quality is judged by the mismatch between operations performed in index space and operations performed after realization in the complex plane. This paper adds a variational and computational dimension to the algebraic strand. The central question is no longer only which generalized algebraic systems can be defined, but which discrete representations are optimal under an energy criterion. It therefore links nonassociative algebra, discretization, finite encoding, and optimization. Its own motivating discussion explicitly returns to triadic wave resonance as an example of why algebra on a discrete index space can provide an efficient representation of interactions in a continuous object space. That remark creates a conceptual loop back to the 2015 triadic wave-resonance paper (Pires & Perdigão 2015) at Nonlinear Processes in Geophysics.
While the 2023-2025 mathematical publications have a strong focus on algebra and geometry, the original non-Gaussian information-theoretic line coming from the earlier career remains active. A sabbatical from colleague Prof. Noriaki Ohara hosted by Prof. Rui Perdigão brought in additional collaborative contributions where Prof. Perdigão’s nonlinear methods found interesting new applications to Prof. Ohara’s domains. The 2024 Cryosphere paper on snow distributions quantifies departure from Gaussianity by sample negentropy, interpreted as Kullback-Leibler divergence from a Gaussian reference with matched low-order structure. In 2026, the Journal of Hydrology paper on estimating snow-water equivalent (SWE) from snow-cover fraction develops this line into a multivariate non-Gaussian predictive framework.
On the operator-theoretic functional-analytical side, a key recent work is Perdigão (2026), the Mathematics article “Resolvent-Generated Generalized Spectral Operators for Nonlinear Dynamical Systems via Koopman Semigroups”. Its starting point is a structural difficulty familiar throughout nonlinear dynamics, in that the Koopman operator associated with a nonlinear flow is linear on observables, but on natural function spaces it may be non-normal, possess continuous spectrum, and fail to admit a complete eigenfunction basis. The conventional harmonic picture inherited from normal spectral theory can therefore be inadequate, hence the paper responds by centering the resolvent of the generator of a Koopman C0-semigroup. Rather than requiring a complete eigenbasis, it develops generalized spectral operators through resolvent boundary behavior and weak integral representations. In bounded spectral windows, polynomial resolvent-growth conditions are used to obtain measure-valued representations; the normal-operator case is recovered as a limiting classical situation. Pseudospectral behavior and transient amplification enter naturally because non-normal operators can exhibit large resolvent norms even away from their spectrum. Genealogically, this work can be read as a high-level abstraction of questions that were present in the early predictability research. The 2010 thesis treated non-normality, propagators, and transient perturbation growth in the context of forecast-error dynamics. The 2026 work relocates the problem to the observable-space evolution of nonlinear flows and replaces local error-propagation formulas by a general resolvent-based spectral language. The common theme is the inadequacy of eigenvalues alone for describing transient or continuous-spectrum nonlinear behavior.
Most of Prof. Rui Perdigão’s advances in Nonlinear Dynamics, Analytics and Deep Tech have remained proprietary at the institutions he leads, securing a leading edge in providing decision support to institutions dealing with critical security challenges protecting the society and the environment. Even so, a subset of his work is available through his journal publications, academic courses and research monographs. These provide an overview of his most recent and ongoing original fundamental advances in mathematical physics, information physics and coevolutionary complexity, along with innovative methodological and technological developments, ranging from deep learning and artificial intelligence to quantum technologies, for empowering data analytics, modelling and decisions support to tackle critical challenges faced by our society and the environment.
