arXiv subjects

Roberto M. Velho

Publications and source records attributed to Roberto M. Velho.

7 recordsLinked to original sources

arXiv2026

AGENTS4GEOS: agentic platform for open-source multi-physics simulation

Multi-physics simulations are essential for understanding and monitoring intricate subsurface processes such as CO2 storage. Their computational demands call for surrogate models and, for unstructured meshes, Graph Neural Networks (GNNs) are natural candidates. The main bottleneck in developing them is generating and managing the large, physically consistent simulation datasets required for training. To address this challenge, we present Agents4GEOS, an AI-agent framework built on the Model Context Protocol (MCP) that provides 52 domain-aware tools for natural-language-driven workflows with GEOS, an open-source multi-physics simulator. The agent facilitates input-file creation, mesh inspection, fluid-property computation, and result post-processing. Through human-curated skills and fresh-context subagents coordinated by an orchestrator, the system executes complex workflows, evaluates simulation outputs, diagnoses issues, and suggests improvements, grounding every quantity in actual computation. By automating routine tasks, Agents4GEOS allows domain experts to focus on the most challenging aspects of their work.

physics.geo-ph↗

arXiv2026

Towards Fast GNN Surrogates for CO2 Migration in Complex Geological Formations

This chapter discusses how a data-driven machine learning approach can reproduce key aspects of the physical behavior of multiphase flows in complex geological formations. We propose an end-to-end graph neural surrogate tailored to CO$_2$ plume migration forecasting in geological storage. The method is evaluated on the SPE11A benchmark, a well-known industry test case designed to assess CO$_2$ storage scenarios and characterized by sharp gas-water interfaces, strong advective transport, and rapid convective mixing with fingering development. The benchmark is reformulated as a graph in which nodes represent computational cells and edges encode transmissibility-based interactions enriched with geometric attributes. Directional transport arising from grid geometry, permeability contrasts, and geological heterogeneity is captured through an anisotropic message-passing mechanism, where interaction weights are computed via geometry-conditioned edge embeddings, biasing message aggregation toward physically relevant transport directions. Temporal evolution is modeled in latent space using an autoregressive residual formulation trained with multi-step supervision. The proposed model produces competitive forecasts of gas saturation and liquid-phase density, which are key indicators for CO$_2$ storage monitoring, with cumulative errors that remain moderate over extended forecasting horizons.

cs.LG↗

arXiv2020

Estimating, Monitoring, and Forecasting the Covid-19 Epidemics: A Spatio-Temporal Approach Applied to NYC Data

We propose an SEIR-type meta-population model to simulate and monitor the Covid-19 epidemic evolution. The basic model consists of seven compartments, namely susceptible (S), exposed (E), three infective classes, recovered (R), and deceased (D). We define these compartments for n age and gender groups in m different spatial locations. So, the resulting model has, for each age group, gender, and place, all epidemiological classes. The mixing between them is accomplished by means of time-dependent infection rate matrices. The model is calibrated with the curve of daily new infections in New York City and its boroughs, including census data, and the proportions of infections, hospitalizations, and deaths for each age range. We end up with a model that matches the reported curves and predicts accurately infection information for different places and age classes.

q-bio.PE↗

arXiv2017

An Adjoint-based Numerical Method for a class of nonlinear Fokker-Planck Equations

Here, we introduce a numerical approach for a class of Fokker-Planck (FP) equations. These equations are the adjoint of the linearization of Hamilton-Jacobi (HJ) equations. Using this structure, we show how to transfer the properties of schemes for HJ equations to the FP equations. Hence, we get numerical schemes with desirable features such as positivity and mass-preservation. We illustrate this approach in examples that include mean-field games and a crowd motion model.

math.AP↗

arXiv2016

On the Hughes Model and Numerical Aspects

We study a crowd model proposed by R. Hughes and we describe a numerical approach to solve it. The Hughes model comprises a Fokker-Planck equation coupled with an eikonal equation with Dirichlet or Neumann data. First, we establish a priori estimates for the solutions. Second, we study radial solutions and identify a shock formation mechanism. Third, we illustrate the existence of congestion, the breakdown of the model, and the trend to the equilibrium. Finally, we propose a new numerical method and consider two numerical examples.

math.AP↗

arXiv2014

Dual two-state mean-field games

In this paper, we consider two-state mean-field games and its dual formulation. We then discuss numerical methods for these problems. Finally, we present various numerical experiments, exhibiting different behaviours, including shock formation, lack of invertibility, and monotonicity loss.

math.AP↗

arXiv2014

Socio-economic applications of finite state mean field games

In this paper we present different applications of finite state mean field games to socio-economic sciences. Examples include paradigm shifts in the scientific community or the consumer choice behaviour in the free market. The corresponding finite state mean field game models are hyperbolic systems of partial differential equations, for which we present and validate different numerical methods. We illustrate the behaviour of solutions with various numerical experiments, which show interesting phenomena like shock formation. Hence we conclude with an investigation of the shock structure in the case of two-state problems.

math.AP↗