Meta-modeling on detailed geography for accurate prediction of invasive alien species dispersal

Using remote sensing data within an optimal spatiotemporal model for invasive plant management: the case of Ailanthus altissima in the Alta Murgia National Park

We tackle the problem of coupling a spatiotemporal model for simulating the spread and control of an invasive alien species with data coming from image processing and expert knowledge. In this study, we implement a spatially explicit optimal control model based on a reaction-diffusion equation which includes an Holling II type functional response term for modeling the density control rate. The model takes into account the budget constraint related to the control program and searches for the optimal effort allocation for the minimization of the invasive alien species density. Remote sensing and expert knowledge have been assimilated in the model to estimate the initial species distribution and its habitat suitability, empirically extracted by a land cover map of the study area. The approach has been applied to the plant species Ailanthus altissima (Mill.) Swingle within the Alta Murgia National Park. This area is one of the Natura 2000 sites under the study of the ongoing National Biodiversity Future Center (NBFC) funded by the Italian National Recovery and Resilience Plan (NRRP), and pilot site of the finished H2020 project ECOPOTENTIAL, which aimed at the integration of modeling tools and Earth Observations for a sustainable management of protected areas. Both the initial density map and the land cover map have been generated by using very high resolution satellite images and validated by means of ground truth data provided by the EU Life Alta Murgia Project (LIFE12 BIO/IT/000213), a project aimed at the eradication of A. altissima in the Alta Murgia National Park.

Comparison of the performance and reliability between improved sampling strategies for polynomial chaos expansion

As uncertainty and sensitivity analysis of complex models grows ever more important, the difficulty of their timely realizations highlights a need for more efficient numerical operations. Non-intrusive Polynomial Chaos methods are highly efficient and accurate methods of mapping input-output relationships to investigate complex models. There is substantial potential to increase the efficacy of the method regarding the selected sampling scheme. We examine state-of-the-art sampling schemes categorized in space-filling-optimal designs such as Latin Hypercube sampling and L1-optimal sampling and compare their empirical performance against standard random sampling. The analysis was performed in the context of L1 minimization using the least-angle regression algorithm to fit the GPCE regression models. Due to the random nature of the sampling schemes, we compared different sampling approaches using statistical stability measures and evaluated the success rates to construct a surrogate model with relative errors of <0.1%, <1%, and <10%, respectively. The sampling schemes are thoroughly investigated by evaluating the y of surrogate models constructed for various distinct test cases, which represent different problem classes covering low, medium and high dimensional problems. Finally, the sampling schemes are tested on an application example to estimate the sensitivity of the self-impedance of a probe that is used to measure the impedance of biological tissues at different frequencies. We observed strong differences in the convergence properties of the methods between the analyzed test functions.

Application of Generalized Polynomial Chaos for Quantification of Uncertainties of Time Averages and Their Sensitivities in Chaotic Systems

In this paper, we consider the effect of stochastic uncertainties on non-linear systems with chaotic behavior. More specifically, we quantify the effect of parametric uncertainties to time-averaged quantities and their sensitivities. Sampling methods for Uncertainty Quantification (UQ), such as the Monte–Carlo (MC), are very costly, while traditional methods for sensitivity analysis, such as the adjoint, fail in chaotic systems. In this work, we employ the non-intrusive generalized Polynomial Chaos (gPC) for UQ, coupled with the Multiple-Shooting Shadowing (MSS) algorithm for sensitivity analysis of chaotic systems. It is shown that the gPC, coupled with MSS, is an appropriate method for conducting UQ in chaotic systems and produces results that match well with those from MC and Finite-Differences (FD).

Geometric Numerical Integration in Ecological Modelling

A major neglected weakness of many ecological models is the numerical method used to solve the governing systems of differential equations. Indeed, the discrete dynamics described by numerical integrators can provide spurious solution of the corresponding continuous model. The approach represented by the geometric numerical integration, by preserving qualitative properties of the solution, leads to improved numerical behaviour expecially in the long-time integration. Positivity of the phase space, Poisson structure of the flows, conservation of invariants that characterize the continuous ecological models are some of the qualitative characteristics well reproduced by geometric numerical integrators. In this paper we review the benefits induced by the use of geometric numerical integrators for some ecological differential models.