arXiv subjects

Maxime Theillard

Publications and source records attributed to Maxime Theillard.

9 recordsLinked to original sources

arXiv2025

Characteristic Bending in Incompressible Flows

We present the Characteristic Bending (CB) method, a general framework for advecting quantities under incompressible velocity fields. The method builds on standard semi-Lagrangian advection by interpreting the backward-in-time characteristic reconstruction as the construction of a reference map, a diffeomorphism between the current and initial geometries of the advected space. From this viewpoint, the CB method applies a volume-preserving projection to the map, systematically removing spurious compressible errors arising from time integration, interpolation, or from velocity fields that are only approximately divergence-free. This projection bends the characteristics toward the divergence-free space, preserving mass and geometric features of the advected fields, even in the presence of significant error. We demonstrate the method in both two and three dimensions using benchmark problems and for multiphase flows governed by the incompressible Navier-Stokes equations. The results show that the CB method serves as a drop-in replacement for traditional semi-Lagrangian schemes and as an augmentation of reference map formulations, offering improved robustness and accuracy in incompressible flow simulations.

physics.flu-dyn↗

arXiv2025

Surfer 2: The Next Generation of Cross-Platform Computer Use Agents

Building agents that generalize across web, desktop, and mobile environments remains an open challenge, as prior systems rely on environment-specific interfaces that limit cross-platform deployment. We introduce Surfer 2, a unified architecture operating purely from visual observations that achieves state-of-the-art performance across all three environments. Surfer 2 integrates hierarchical context management, decoupled planning and execution, and self-verification with adaptive recovery, enabling reliable operation over long task horizons. Our system achieves 97.1% accuracy on WebVoyager, 69.6% on WebArena, 60.1% on OSWorld, and 87.1% on AndroidWorld, outperforming all prior systems without task-specific fine-tuning. With multiple attempts, Surfer 2 exceeds human performance on all benchmarks. These results demonstrate that systematic orchestration amplifies foundation model capabilities and enables general-purpose computer control through visual interaction alone, while calling for a next-generation vision language model to achieve Pareto-optimal cost-efficiency.

cs.AI↗

arXiv2025

Sharp Collocated Projection Method for Immiscible Two-Phase Flows

We present a sharp collocated projection method for solving the immiscible, two-phase Navier-Stokes equations in two- and three-dimensions. Our method is built using non-graded adaptive quadtree and octree grids, where all of the fluid variables are defined on the nodes, and we leverage this framework to design novel spatial and temporal discretizations for the two-phase problem. The benefits of the nodal collocation framework are best exemplified through our novel discretizations, which employ a hybrid finite difference-finite volume methodology to treat the boundary and interfacial jump conditions in an entirely sharp manner. We demonstrate the capabilities of our novel approach using a variety of canonical two- and three-dimensional examples and outline how our framework can be extended to address more complicated physics. The overall algorithm achieves high accuracy with simplified data structures, making this solver ideal for scientific and engineering applications.

math.NA↗

arXiv2025

Surfer-H Meets Holo1: Cost-Efficient Web Agent Powered by Open Weights

We present Surfer-H, a cost-efficient web agent that integrates Vision-Language Models (VLM) to perform user-defined tasks on the web. We pair it with Holo1, a new open-weight collection of VLMs specialized in web navigation and information extraction. Holo1 was trained on carefully curated data sources, including open-access web content, synthetic examples, and self-produced agentic data. Holo1 tops generalist User Interface (UI) benchmarks as well as our new web UI localization benchmark, WebClick. When powered by Holo1, Surfer-H achieves a 92.2% state-of-the-art performance on WebVoyager, striking a Pareto-optimal balance between accuracy and cost-efficiency. To accelerate research advancement in agentic systems, we are open-sourcing both our WebClick evaluation dataset and the Holo1 model weights.

cs.AI↗

arXiv2024

Least SQuares Discretizations (LSQD): a robust and versatile meshless paradigm for solving elliptic PDEs

Searching for numerical methods that combine facility and efficiency, while remaining accurate and versatile, is critical. Often, irregular geometries challenge traditional methods that rely on structured or body-fitted meshes. Meshless methods mitigate these issues but oftentimes require the weak formulation which involves defining quadrature rules over potentially intricate geometries. To overcome these challenges, we propose the Least Squares Discretization (LSQD) method. This novel approach simplifies the application of meshless methods by eliminating the need for a weak formulation and necessitates minimal numerical analysis. It offers significant advantages in terms of ease of implementation and adaptability to complex geometries. In this paper, we demonstrate the efficacy of the LSQD method in solving elliptic partial differential equations for a variety of boundary conditions, geometries, and data layouts. We monitor h-P convergence across these parameters and construct an a posteriori built-in error estimator to establish our method as a robust and accessible numerical alternative.

math.NA↗

arXiv2023

Stable nodal projection method on octree grids

We propose a novel collocated projection method for solving the incompressible Navier-Stokes equations with arbitrary boundaries. Our approach employs non-graded octree grids, where all variables are stored at the nodes. To discretize the viscosity and projection steps, we utilize supra-convergent finite difference approximations with sharp boundary treatments. We demonstrate the stability of our projection on uniform grids, identify a sufficient stability condition on adaptive grids, and validate these findings numerically. We further demonstrate the accuracy and capabilities of our solver with several canonical two- and three-dimensional simulations of incompressible fluid flows. Overall, our method is second-order accurate, allows for dynamic grid adaptivity with arbitrary geometries, and reduces the overhead in code development through data collocation.

math.NA↗

arXiv2021

Projection Method for the Fluctuating Hydrodynamics Equations

Computational fluctuating hydrodynamics aims at understanding the impact of thermal fluctuations on fluid motions at small scales through numerical exploration. These fluctuations are modeled as stochastic flux terms and incorporated into the classical Navier-Stokes equations, which need to be solved numerically. In this paper, we present a novel projection-based method for solving the incompressible fluctuating hydrodynamics (FHD) equations. By analyzing the equilibrium structure factor spectrum of the velocity field for the linearized FHD equations, we investigate how the inherent splitting errors affect the numerical solution of the stochastic partial differential equations in the presence of non-periodic boundary conditions, and how iterative corrections can reduce these errors. Our computational examples demonstrate both the capability of our approach to reproduce correctly stochastic properties of fluids at small scales as well as its potential use in the simulations of multi-physics problems.

physics.flu-dyn↗

arXiv2020

Retention of rising droplets in density stratification

In this study, we present results from experiments on the retention of single oil droplets rising through a two-layer density stratification. These experiments confirm the significant slowdown observed in past literature of settling and rising particles and droplets in stratification, and are the first experiments to study single liquid droplets as opposed to solid particles. By tracking the motion of the droplets as they rise through a stratified fluid, we identify two timescales which quantitatively describe this slowdown: an entrainment timescale, and a retention timescale. The entrainment timescale is a measure of the time that a droplet spends below its upper-layer terminal velocity and relates to the length of time over which the droplet's rise is affected by entrained dense fluid. The retention time is a measure of the time that the droplet is delayed from reaching an upper threshold far from the density transition. Both timescales are found to depend on the Froude and Reynolds numbers of the system, Fr $=U_u/(Nd)$ and Re $=ρ_u U_u d/ν$. We find that both timescales are only significantly large for Fr $\lesssim1$, indicating that trapping dynamics in a relatively sharp stratification arise from a balance between drop inertia and buoyancy. Finally, we present a theoretical formulation for the drag enhancement $Γ$, the ratio between the maximum stratification force and the corresponding drag force on the droplet, based on a simple force balance at the point of the velocity minimum. Using our experimental data, we find that our formulation compares well with recent theoretical and computational work by Zhang et al. [J. Fluid Mech. 875, 622-656 (2019)] on the drag enhancement on a solid sphere settling in a stratified fluid, and provides the first experimental data supporting their approach.

physics.flu-dyn↗

arXiv2016

Geometric control of active collective motion

Recent experimental studies have shown that confinement can profoundly affect self-organization in semi-dilute active suspensions, leading to striking features such as the formation of steady and spontaneous vortices in circular domains and the emergence of unidirectional pumping motions in periodic racetrack geometries. Motivated by these findings, we analyze the two-dimensional dynamics in confined suspensions of active self-propelled swimmers using a mean-field kinetic theory where conservation equations for the particle configurations are coupled to the forced Navier-Stokes equations for the self-generated fluid flow. In circular domains, a systematic exploration of the parameter space casts light on three distinct states: equilibrium with no flow, stable vortex, and chaotic motion, and the transitions between these are explained and predicted quantitatively using a linearized theory. In periodic racetracks, similar transitions from equilibrium to net pumping to traveling waves to chaos are observed in agreement with experimental observations and are also explained theoretically. Our results underscore the subtle effects of geometry on the morphology and dynamics of emerging patterns in active suspensions and pave the way for the control of active collective motion in microfluidic devices.

physics.flu-dyn↗