250 citations · 1.1k across the 130 of their papers we have counts for
16 papers · 1 filter
Physics-informed token transformer methodology for nonlinear balance laws. I. Schwarzschild--Burgers fluid flows
Philippe G. LeFloch, Shuyang Xiang
We introduce a Physics-Informed Token Transformer (PITT) methodology for nonlinear hyperbolic balance laws in one space dimension, using piecewise steady-state profiles for the rep…
A class of kernel-based scalable algorithms for data science
Philippe G. LeFloch, Jean-Marc Mercier, Shohruh Miryusupov
We present several generative and predictive algorithms based on the RKHS (reproducing kernel Hilbert spaces) methodology, which, most importantly, are scale up efficiently with la…
Extrapolation and generative algorithms for three applications in finance
Philippe G. LeFloch, Jean-Marc Mercier, Shohruh Miryusupov
For three applications of central interest in finance, we demonstrate the relevance of numerical algorithms based on reproducing kernel Hilbert space (RKHS) techniques. Three use c…
Reproducing kernel methods for machine learning, PDEs, and statistics
Philippe G. LeFloch, Jean-Marc Mercier, Shohruh Miryusupov
This monograph develops a unified, application-driven framework for kernel methods grounded in reproducing kernel Hilbert spaces (RKHS) and optimal transport (OT). Part I lays the…
A class of mesh-free algorithms for some problems arising in finance and machine learning
Philippe G. LeFloch, Jean-Marc Mercier
We introduce a numerical methodology, referred to as the transport-based mesh-free method, which allows us to deal with continuous, discrete, or statistical models in the same unif…
A well-balanced positivity preserving cell-vertex finite volume method satisfying the discrete maximum-minimum principle for coupled models of surface water flow and scalar transport
Hasan Karjoun, Abdelaziz Beljadid, Philippe G. LeFloch
We develop a new finite volume method using unstructured mesh-vertex grids for coupled systems modeling shallow water flows and solute transport over complex bottom topography. Nov…