arXiv subjects

Téo Granger

Publications and source records attributed to Téo Granger.

3 recordsLinked to original sources

arXiv2026

Linear and Nonlinear Latent-Space Reduced-Order Models for the Rayleigh--Taylor Instability

We use a large database of direct numerical simulations to investigate the transition of the Rayleigh--Taylor instability to turbulence and its evolution toward a late-time self-similar regime. In addition to tracking the growth of the mixing layer through the mean heavy-fluid concentration profile, we analyze one-dimensional profiles of turbulent kinetic energy and dissipation, two key quantities in classical turbulent-mixing models. We consider two reduced-order modeling strategies that differ in where nonlinearity is introduced: either in the construction of the latent space or in the description of its temporal evolution. The first method uses a linear encoder--decoder obtained using Proper Orthogonal Decomposition (POD), with nonlinear reduced dynamics learned by a physics-informed neural network (PINN). The second uses a nonlinear encoder--decoder learned by an autoencoder, while constraining the latent dynamics to remain linear and satisfy physical constraints. Both approaches achieve satisfactory performance in reconstructing, interpolating, and extrapolating the dynamics of the Rayleigh--Taylor instability.

physics.flu-dyn↗

arXiv2026

Learning Turbulence Closures with Physics-Informed Neural Networks for the Rayleigh-Taylor Transition to Turbulence

Reynolds-averaged Navier-Stokes (RANS) turbulence models are known to perform poorly in predicting the dynamics of Rayleigh-Taylor mixing when turbulence is not fully developed, particularly during the transition from an initially perturbed interface. In this work, we investigate the use of data-driven strategies to enhance a simple $k$-$\varepsilon$-$b$ model for this transitional regime. The turbulence model is first embedded within a surrogate physics-informed neural network (PINN), enabling the calibration of coefficients that account for parametric errors and the identification of corrective terms representing structural errors associated with missing physical processes. The learned corrections are then re-expressed onto the model state variables and relevant flow indicators, leading to explicit analytical modifications of the closure. The resulting fully interpretable corrected model is assessed against an extensive database of direct numerical simulations (DNS) of Rayleigh-Taylor flows. This framework enables improved predictions of the mixing-layer growth during the transition to turbulence.

physics.flu-dyn↗

arXiv2025

From random walks to epidemic spreading: Compartment model with mortality for vector transmitted diseases

We propose a compartmental model for vector-transmitted diseases, such as Malaria and Dengue, spreading over complex networks. Individuals are represented by independent random walkers and vectors by infected nodes. Both walkers and nodes can be susceptible (S) or infected (I). Infected walkers may die (entering the dead compartment D), while infected nodes remain alive. Susceptible walkers can be infected by visiting infected nodes, and susceptible nodes by visits from infected walkers. We derive explicit expressions for the basic reproduction numbers $R_0$ (without mortality) and $R_M$ (with mortality), proving that $R_M < R_0$. When $R_M , R_0 > 1$, the healthy state is unstable, and for zero mortality, an endemic equilibrium emerges. We also study the effects of confinement measures. Simulations align well with mean-field predictions on strongly connected graphs but deviate for weakly connected networks. Our model has various interdisciplinary applications which include the modeling of chemical reaction kinetics, contaminant spread, and wildfire propagation.

q-bio.PE↗