Benoît Delahaye

We propose a simulation-based technique for the parameterization and the stability analysis of parametric Ordinary Differential Equations. This technique is an adaptation of Statistical Model Checking, often used to verify the validity of biological models, to the setting of Ordinary Differential Equations systems. The aim of our technique is to estimate the probability of satisfying a given property under the variability of the parameter or initial condition of the ODE, with any metrics of choice. To do so, we discretize the values space and use statistical model checking to evaluate each individual value w.r.t. provided data. Contrary to other existing methods, we provide statistical guarantees regarding our results that take into account the unavoidable approximation errors introduced through the numerical integration of the ODE system performed while simulating. In order to show the potential of our technique, we present its application to two case studies taken from the literature, one relative to the growth of a jellyfish population, and the other concerning a well-known oscillator model.

Data science is a powerful field for gaining insights, comparing, and predicting behaviors from datasets. However, the diversity of methods and hypotheses needed to abstract a dataset exhibits a lack of genericity. Moreover, the shape of a dataset, which structures its contained information and uncertainties, is rarely considered. Inspired by state-of-the-art manifold learning and hull estimations algorithms, we propose a novel framework, the datascape, that leverages topology and graph theory to abstract heterogeneous datasets. Built upon the combination of a nearest neighbor graph, a set of convex hulls, and a metric distance that respects the shape of the data, the datascape allows exploration of the dataset’s underlying space. We show that the datascape can uncover underlying functions from simulated datasets, build predictive algorithms with performance close to state-of-the-art algorithms, and reveal insightful geodesic paths between points. It demonstrates versatility through ecological, medical, and simulated data use cases.

While Ocean modeling has made significant advances over the last decade, its complex biological component is still oversimplified. In particular, modeling organisms in the ocean system must integrate parameters to fit both physiological and ecological behaviors that are together very difficult to determine. Such difficulty occurs for modeling Pelagia noctiluca. This jellyfish has a high abundance in the Mediterranean Sea and could contribute to several biogeochemical processes. However, gelatinous zooplanktons remain poorly represented in biogeochemical models because uncertainties about their ecophysiology limit our understanding of their potential role and impact. To overcome this issue, we propose, for the first time, the use of the Statistical Model Checking Engine (SMCE), a probability-based computational framework that considers a set of parameters as a whole. Contrary to standard parameter inference techniques, SMCE identifies sets of parameters that fit both laboratory-culturing observations and in situ patterns while considering uncertainties. Doing so, we estimated the best parameter sets of the ecophysiological model that represents the jellyfish growth and degrowth in laboratory conditions as well as its size. Behind this application, SMCE remains a computational framework that supports the projection of a model with uncertainties in broader contexts such as biogeochemical processes to drive future studies.

For decades, microbiologists have considered uncertainties as an undesired side effect of experimental protocols. As a consequence, standard microbial system modeling strives to hide uncertainties for the sake of deterministic understanding.