Macroskopische Modellierung

Makroskopische Modellierung und Prognose der Verteilung von aquatischen Wirbellosen basierend auf mathematischen Netzwerken.

Projektleiter: Prof. Dr. Stefan Ruzika

Doktorandin: Henriette Heer

Macroscopic modeling and forecasting of aquatic invertebrates distribution based on
mathematical networks

This subproject aims at a rigorous mathematical modelling and analysis of population dynamics for ecological scenarios. The scientific relevance of this subproject consists of addressing three major open research questions: in tight cooperation with subproject 1, the first goal is to develop and understand novel macroscopic dynamic mathematical models suitable for modelling the dispersal of species. For a detailed description of the model features, we refer to the description of subproject 1.The second goal of this subproject is dedicated to the research question of finding “models for models”: since the model developed in cooperation with subproject 1 is detailed and computationally expensive, the idea of building a lean and quickly-to-solve surrogate model will be explored. Certainly, the latter model is limited in its explanatory power but the advantages are obvious especially for the case of using it in extensive Monte-Carlo simulations. Using the surrogate model in guiding an inverse simulation will be tested and evaluated. The third goal of this subproject addresses mathematical and numerical questions mainly relating to uncertainty quantifications and inverse simulation. Uncertainty quantification is a technique for assessing risk (e.g. environmental stochasticity, structural and model uncertainties, data errors), which is inevitably present in any mathematical model. Knowing about uncertainties and risk is essential for judging the predictive power of a model. Inverse simulation addresses the question of how to choose or adapt parameters (e.g. land use or management options) such that a system reaches a pre-defined state. Inverse simulation is the key to step from predictive modelling to goal-directed resource management. Both, techniques for analysing risk and for inverse simulation, have so far been rarely developed for and applied to ecological modelling.

Research questions:

  • Modeling Paradigm: Are there general techniques to extract surrogate models of a given cellular automata based model (in the context of distribution modeling of aquatic invertebrates)?
  • Exactness: To which extent do uncertainty and sensitivity increase when developing a surrogate model?
  • Speed-up: What is the gain in computation time and memory of the surrogate model compared to the original model?
  • Trade-off and robustness: How can the trade-off between exactness and speed-up be evaluated and how robust is this trade-off information?