Scientific Talks

Talk Title:    From individual models to PDEs: spatial dynamics and interactions in forests (1h00)

Abstract:  Understanding the dynamics of forest plants requires taking into account both local demographic processes and spatial interactions simultaneously. In this talk, I will present a stochastic, individual-based model in which each plant follows its own matrix population model and disperses spatially. This framework allows us to explicitly represent intraspecific and interspecific interactions between several tree species coexisting within the same forest ecosystem.

I will then show that, under an appropriate scale limit, the model formally converges to a deterministic system of partial differential equations describing the spatio-temporal evolution of species densities. I will analyse the qualitative behaviour of this system, highlighting the role of dispersal and interspecific interactions in persistence, coexistence and invasion dynamics.

Finally, I will present the use of physics-informed neural networks (PINNs) to efficiently simulate this PDE system, providing a scalable numerical approach for the study of complex, spatially explicit forest dynamics.

Joint work with K. Burdeos (Caraga State University and the University of Picardie).

By:    Youcef Mammeri; Université Jean Monnet, St. Etienne, France

Talk Title:    Cancelled (because of speaker's health condition)

By:    Bouasy Doungsavanh; National University of Laos, Vientiane, Lao PDR; CIMA, Universidade de Évora, Évora, Portugal

Talk Title:    Travelling waves in a saturating diffusion–linear dispersion equation (1h00)

Abstract:  We consider a scalar hyperbolic conservation law perturbed by a generalised Rosenau-type diffusion  and linear dispersion,

\begin{equation*}

u_t + f(u)_x = \epsilon\Big(\dfrac{u_x}{\big(1+u_x^2\big)^\alpha}\Big)_x + \delta u_{xxx}

\end{equation*}

where $\alpha \geq 0$, and $\epsilon, \delta$ are positive parameters. 

To understand the singular limit as the diffusion strength $\varepsilon$ and dispersion strength $\delta$ vanish, we analyze travelling wave solutions, which provide crucial insights into the convergence to the physical entropy solution. We classify travelling wave  profiles across three distinct regimes of the saturation parameter $\alpha$ that is $\alpha < 1/2$, $\alpha = 1/2$, and $\alpha > 1/2$. Combining phase-plane analysis with numerical simulations, we determine the minimal diffusion threshold $\varepsilon_{\min}(\alpha, \delta)$ required to maintain wave monotonicity. Finally, based on the results of the travelling waves, we formulate conjectures about the convergence of the regularised solutions to the entropy weak solution of the hyperbolic conservation law as $\varepsilon$ and $\delta$ tend to zero.

By:    Gnord Maypaokha; National University of Laos, Vientiane, Lao PDR; CIMA, Universidade de Évora, Évora, Portugal

Talk Title:    A Comparative Study of Regularization Techniques in Machine Learning for Community-Based Health Screening Tools (1h00)

Abstract:  TBA

By:    Pornsarp Pornsawad; Silpakorn University, Nakhon Pathom, Thailand