publications

2026

1. Hybrid DeepONet Surrogates for Multiphase Flow in Porous Media

   Ezequiel S. Santos, Gabriel F. Barros, Amanda C.N. Oliveira, and 6 more authors

   Journal of Computational Physics, 2026

   Abs DOI

   The solution of partial differential equations (PDEs) plays a central role in numerous applications in science and engineering, particularly those involving multiphase flow in porous media. Complex, nonlinear systems govern these problems and are notoriously computationally intensive, especially in real-world applications and reservoirs. Recent advances in deep learning have spurred the development of data-driven surrogate models that approximate PDE solutions with reduced computational cost. Among these, Neural Operators such as Fourier Neural Operator (FNO) and Deep Operator Networks (DeepONet) have shown strong potential for learning parameter-to-solution mappings, enabling the generalization across families of PDEs. However, both methods face challenges when applied independently to complex porous media flows, including high memory requirements and difficulty handling the time dimension. To address these limitations, this work introduces hybrid neural operator surrogates based on DeepONet models that integrate Fourier Neural Operators, Multi-Layer Perceptrons (MLPs), and Kolmogorov-Arnold Networks (KANs) within their branch and trunk networks. The proposed framework decouples spatial and temporal learning tasks by splitting these structures into the branch and trunk networks, respectively. We evaluate these hybrid models on multiphase flow in porous media problems ranging in complexity from the steady 2D Darcy flow to the 2D and 3D problems belonging to the 10th Comparative Solution Project from the Society of Petroleum Engineers. Results demonstrate that hybrid schemes achieve accurate surrogate modeling with significantly fewer parameters while maintaining strong predictive performance on large-scale reservoir simulations.

2025

1. AEDA: an adversarial architecture for deep surrogates applied to uncertainty quantification in seismic imaging

   Rodolfo S. M. Freitas, Carlos H. S. Barbosa, Charlan D. S. Alves, and 4 more authors

   Computational Geosciences, Dec 2025

   DOI

2024

1. A PINN-based level-set formulation for reconstruction of bubble dynamics

   Rômulo M. Silva, Malú Grave, and Alvaro L. G. A. Coutinho

   Archive of Applied Mechanics, May 2024

   DOI
2. Uncertainty Quantification for CO\textsubscript2 Sequestration Using Neural Operators

   Rodolfo S. M. Freitas, Fernando A. Rochinha, Alvaro L. G. A. Coutinho, and 3 more authors

   In XLV Ibero-Latin American Congress on Computational Methods in Engineering (CILAMCE), May 2024

2021

1. Capturing Provenance to Improve the Model Training of \uppercasePINNs: first hand-on experiences with Grid5000

   R M Silva, D Pina, L Kunstmann, and 4 more authors

   In Iberian Latin-American Congress on Computational Methods in Engineering, May 2021
2. \uppercasePINNs for Parametric Incompressible Newtonian Flows

   R M Silva and A L G A Coutinho

   In Iberian Latin-American Congress on Computational Methods in Engineering, May 2021

2020

1. Physics-Informed Neural Networks for the Factored Eikonal Equation

   R M Silva and A L G A Coutinho

   In Iberian Latin-American Congress on Computational Methods in Engineering, May 2020
2. A workflow for seismic imaging with quantified uncertainty

   Carlos H. S. Barbosa, Liliane N. O. Kunstmann, Rômulo M. Silva, and 6 more authors

   May 2020
3. EdgeCFD: a parallel residual-based variational multiscale code for multiphysics

   Adriano M. A. Cortes, Erb F. Lins, Gabriel M. Guerra, and 5 more authors

   International Journal of Computational Fluid Dynamics, May 2020

   DOI

2019

1. 

   A Scientific Workflow for Reverse Time Migration under Uncertainty

   Henrique S Carlos, Barbosa, Bruno S Silva, and 9 more authors

   May 2019

   DOI

2018

1. Communication-Free Parallel Mesh Multiplication for Large Scale Simulations

   R M Silva, B S J Lima, J J Camata, and 2 more authors

   Lecture Notes in Computer Science, May 2018
2. Finite Element Mesh Multiplication with Boundary Smoothing

   R M Silva, R N Elias, and A L G A Coutinho

   In II Brazilian Conference of Computational Fluid Dynamics (CBCFD), May 2018

   Abs

   A procedure to recover the geometry boundary of refined finite element meshes is presented. Initially, the coarse mesh is submitted to an uniform refinement by splitting the elements, but maintaining the coarse boundary. Then, the boundary nodes of the refined mesh are filtered. To avoid search overheads, the boundary nodes and the STL vertexes are subdivided into sub-regions called BINs, and the search for closest nodes is performed only to the nodes in the same sub-region. The capability of the proposed procedure is illustrated on an example.

2017

1. Structural Reliability Analysis of Composite Material Pipes under Hydrostatic Pressure

   R M Silva and M A A Cavalcante

   In Iberian Latin-American Congress on Computational Methods in Engineering, May 2017

   DOI

2016

1. Comparative Study between Homogeneous and Composite Material Pipes under Hydrostatic Pressure

   R M Silva and M A A Cavalcante

   In Iberian Latin-American Congress on Computational Methods in Engineering, May 2016

2015

1. Critical Pressure Analysis of Composite Material Pipes Reinforced by Long Fibers

   R M Silva and M A A Cavalcante

   In Iberian Latin-American Congress on Computational Methods in Engineering, May 2015