arXiv subjects

Alvaro L. G. A. Coutinho

Publications and source records attributed to Alvaro L. G. A. Coutinho.

At least 19 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

Advances in Scientific Machine Learning for Coupled Fluid Flow and Transport

This chapter reviews recent advances in Scientific Machine Learning (SciML) for modeling coupled fluid flow and transport phenomena governed by the incompressible Navier-Stokes and scalar transport equations. Such systems, found in applications like turbidity currents and thermal convection, feature strong nonlinear coupling and multiscale behavior that make high-fidelity simulations computationally expensive. To address this, the chapter surveys state-of-the-art SciML methods for building efficient surrogate models, including linear reduced-order techniques based on Singular Value Decomposition (such as Dynamic Mode Decomposition) and nonlinear neural network approaches like Physics-Informed Neural Networks (PINNs) and $β$-Variational Autoencoders ($β$-VAEs). It first covers the authors' work combining these models with High Performance Computing strategies, including Adaptive Mesh Refinement/Coarsening (AMR/C) and scientific floating-point data compression. It then presents two new contributions: surrogate modeling of turbidity currents via PINNs, and the extraction of disentangled nonlinear modes from thermal flows using $β$-VAEs. Governing equations and representative benchmarks, including lock-exchange flows and Rayleigh-Bénard convection, illustrate these methodologies. The chapter is intentionally long, covering both the mathematical and physical foundations of coupled fluid flow and the computational aspects of state-of-the-art modeling. Overall, it demonstrates how SciML enables fast, accurate approximations of complex coupled systems within the specific data regimes and modeling assumptions considered, while substantially reducing computational cost relative to full-order simulations. Broader capabilities such as real-time prediction and uncertainty quantification remain active research directions whose feasibility depends strongly on the problem at hand.

cs.LG↗

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↗

arXiv2026

Chemotaxis-inspired PDE models of airborne infectious disease transmission: epidemiologically-motivated mathematical and numerical analyses

Partial differential equation (PDE) models for infectious diseases, while less common than their ordinary differential equation (ODE) counterparts, have found successful applications for many years. Such models are typically of reaction-diffusion type, and model spatial propagation as a diffusive process. However, given the complex nature of human mobility, such models are limited in their ability to describe airborne infectious diseases in human populations. Recent work has advocated for the inclusion of an additional chemotaxis-type term as an alternative; spatial propagation of infection fronts is assumed additionally to flow from low-to-high concentrations of susceptible populations. The present work extends the study of such models by providing an epidemiologically interpretable analysis, directly connecting model behavior to information readily available to policymakers. In particular, we derive a spatially-aware basic reproduction number, which accounts for spatial heterogeneity in population density. Furthermore, we discuss several important aspects concerning the numerical solution of the model, including the introduction of a stabilization scheme. Finally, we perform a series of simulation studies in the Italian region of Lombardy (severely affected by the COVID-19 outbreak in 2020) and in the US state of Georgia, in which we demonstrate the model's potential to better capture important spatiotemporal dynamics observed in real-world data compared to pure reaction-diffusion models.

q-bio.PE↗

arXiv2025

A multiresolution weather dataset for the Southwestern South Atlantic (2017-2018)

The Southwestern South Atlantic (SWSA) is a key region for climate research and renewable energy assessment, yet high-resolution meteorological data are scarce. We present a multiresolution dataset spanning February 2017--November 2018, combining Weather Research and Forecasting (WRF) simulations with Sentinel-1A/B Synthetic Aperture Radar (SAR) wind fields processed using the CMOD5 model. WRF outputs were generated every 30 minutes for three nested domains (9 km, 3 km, 1 km) through 975 short-term simulations. SAR/CMOD5 wind fields are provided at 500 m and 1 km resolution across 104 acquisition dates. Validation shows strong agreement: daily spatial averages of 10 m wind speed yield RMSE and MAE below 3 m/s on over 93% of acquisition days, while more than 91.5% of pixel-level residuals fall within $\pm$3 m/s. In situ measurements from the Itajaí buoy further confirmed the reliability of both sources. The dataset supports regional climate studies, wind energy resource assessment, and machine-learning applications in forecasting and downscaling, with usage examples included to aid practical adoption.

physics.ao-ph↗

arXiv2025

Hybrid DeepONet Surrogates for Multiphase Flow in Porous Media

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 $10$th 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.

cs.CE↗

arXiv2022

Enhancing Dynamic Mode Decomposition Workflow with In-Situ Visualization and Data Compression

Modern computational science and engineering applications are being improved by the advances in scientific machine learning. Data-driven methods such as Dynamic Mode Decomposition (DMD) can extract coherent structures from spatio-temporal data generated from dynamical systems and infer different scenarios for said systems. The spatio-temporal data comes as snapshots containing spatial information for each time instant. In modern engineering applications, the generation of high-dimensional snapshots can be time and/or resource-demanding. In the present study, we consider two strategies for enhancing DMD workflow in large numerical simulations: (i) snapshots compression to relieve disk pressure; (ii) the use of in situ visualization images to reconstruct the dynamics (or part of) in runtime. We evaluate our approaches with two 3D fluid dynamics simulations and consider DMD to reconstruct the solutions. Results reveal that snapshot compression considerably reduces the required disk space. We have observed that lossy compression reduces storage by almost $50\%$ with low relative errors in the signal reconstructions and other quantities of interest. We also extend our analysis to data generated on-the-fly, using in-situ visualization tools to generate image files of our state vectors during runtime. On large simulations, the generation of snapshots may be slow enough to use batch algorithms for inference. Streaming DMD takes advantage of the incremental SVD algorithm and updates the modes with the arrival of each new snapshot. We use streaming DMD to reconstruct the dynamics from in-situ generated images. We show that this process is efficient, and the reconstructed dynamics are accurate.

cs.GR↗

arXiv2022

Modeling nonlocal behavior in epidemics via a reaction-diffusion system incorporating population movement along a network

The outbreak of COVID-19, beginning in 2019 and continuing through the time of writing, has led to renewed interest in the mathematical modeling of infectious disease. Recent works have focused on partial differential equation (PDE) models, particularly reaction-diffusion models, able to describe the progression of an epidemic in both space and time. These studies have shown generally promising results in describing and predicting COVID-19 progression. However, people often travel long distances in short periods of time, leading to nonlocal transmission of the disease. Such contagion dynamics are not well-represented by diffusion alone. In contrast, ordinary differential equation (ODE) models may easily account for this behavior by considering disparate regions as nodes in a network, with the edges defining nonlocal transmission. In this work, we attempt to combine these modeling paradigms via the introduction of a network structure within a reaction-diffusion PDE system. This is achieved through the definition of a population-transfer operator, which couples disjoint and potentially distant geographic regions, facilitating nonlocal population movement between them. We provide analytical results demonstrating that this operator does not disrupt the physical consistency or mathematical well-posedness of the system, and verify these results through numerical experiments. We then use this technique to simulate the COVID-19 epidemic in the Brazilian region of Rio de Janeiro, showcasing its ability to capture important nonlocal behaviors, while maintaining the advantages of a reaction-diffusion model for describing local dynamics.

q-bio.PE↗

arXiv2022

Seismic Modeling and Migration with Random Boundaries on the NEC SX-Aurora TSUBASA

Seismic imaging is a computationally demanding and data-intensive activity in the oil and gas industry. Reverse Time Migration (RTM) used in seismic applications needs to store the forward-propagated wavefield (or source wavefield) on disk. Aiming to mitigate the storage demand, we develop an RTM that implements the source wavefield reconstruction by introducing a new wave equation to the problem. We adjust the initial and boundary conditions to take advantage of the properties of random boundary conditions (RBC). The RBC does not suppress unwanted waves coming from the artificial boundary enabling the full wavefield recovery. Besides, it explores low correlations with non-coherent signals due to the random velocities in the boundary. We also develop compiler-guided implementations on a vector processor for seismic modeling and RTM, essential for Least-square Migration, Full Waveform Inversion, and Uncertainty Quantification applications. We test the seismic modeling and RTM on the 2-D Marmousi benchmark and 3-D HPC4E Seismic Test Suite. The numerical experiments show that the RTM which implements the wavefield reconstruction presents the best results in terms of execution time and hard disk demand. Lastly, the vector processor implementation is the one that requires fewer code modifications compared to the optimized baseline versions of the seismic modeling and RTM and GPU implementations, particularly for large 3D grids.

physics.geo-ph↗

arXiv2022

Data-driven simulation of Fisher-Kolmogorov tumor growth models using Dynamic Mode Decomposition

The computer simulation of organ-scale biomechanistic models of cancer personalized via routinely collected clinical and imaging data enables to obtain patient-specific predictions of tumor growth and treatment response over the anatomy of the patient's affected organ. These patient-specific computational forecasts have been regarded as a promising approach to personalize the clinical management of cancer and derive optimal treatment plans for individual patients, which constitute timely and critical needs in clinical oncology. However, the computer simulation of the underlying spatiotemporal models can entail a prohibitive computational cost, which constitutes a barrier to the successful development of clinically-actionable computational technologies for personalized tumor forecasting. To address this issue, here we propose to utilize Dynamic-Mode Decomposition (DMD) to construct a low-dimensional representation of cancer models and accelerate their simulation. DMD is an unsupervised machine learning method based on the singular value decomposition that has proven useful in many applications as both a predictive and a diagnostic tool. We show that DMD may be applied to Fisher-Kolmogorov models, which constitute an established formulation to represent untreated solid tumor growth that can further accommodate other relevant cancer phenomena. Our results show that a DMD implementation of this model over a clinically-relevant parameter space can yield impressive predictions, with short to medium-term errors remaining under 1% and long-term errors remaining under 20%, despite very short training periods. We posit that this data-driven approach has the potential to greatly reduce the computational overhead of personalized simulations of cancer models, thereby facilitating tumor forecasting, parameter identification, uncertainty quantification, and treatment optimization.

physics.bio-ph↗

arXiv2022

Comparing the convected level-set and the Allen-Cahn phase-field methods in AMR/C simulations of two-phase flows

The modeling and simulation of two-phase flows is still an active research area, mainly when surface tension is present. One way to model the different phases is with interface capturing methods. Two well-established interface capturing approaches are the level-set and phase-field methods. The level-set method is known for its ability to compute the surface tension accurately, and phase-field models satisfy the second law of thermodynamics. This paper reviews and compares a level-set and a phase-field approach to simulate two-phase flows. We use a modified level-set method, called convected level-set. The difference to the standard level-set method is that the re-initialization step is embedded in the convection equation, avoiding a separate step during the calculation. We also apply a global mass conservation procedure to enforce the mass balance between phases. On the other hand, the phase-field approach uses a conservative Allen-Cahn equation with a Lagrange multiplier to conserve the mass. The methods are implemented in libMesh, a parallel adaptive finite element library, using the same finite element formulations, time-marching schemes, solvers, and mesh adaptivity strategies. We present numerical solutions for the two methods considering adaptive mesh refinement and coarsening (AMR/C). Results are analyzed and discussed.

physics.flu-dyn↗

arXiv2021

Coupled and Uncoupled Dynamic Mode Decomposition in Multi-Compartmental Systems with Applications to Epidemiological and Additive Manufacturing Problems

Dynamic Mode Decomposition (DMD) is an unsupervised machine learning method that has attracted considerable attention in recent years owing to its equation-free structure, ability to easily identify coherent spatio-temporal structures in data, and effectiveness in providing reasonably accurate predictions for certain problems. Despite these successes, the application of DMD to certain problems featuring highly nonlinear transient dynamics remains challenging. In such cases, DMD may not only fail to provide acceptable predictions but may indeed fail to recreate the data in which it was trained, restricting its application to diagnostic purposes. For many problems in the biological and physical sciences, the structure of the system obeys a compartmental framework, in which the transfer of mass within the system moves within states. In these cases, the behavior of the system may not be accurately recreated by applying DMD to a single quantity within the system, as proper knowledge of the system dynamics, even for a single compartment, requires that the behavior of other compartments is taken into account in the DMD process. In this work, we demonstrate, theoretically and numerically, that, when performing DMD on a fully coupled PDE system with compartmental structure, one may recover useful predictive behavior, even when DMD performs poorly when acting compartment-wise. We also establish that important physical quantities, as mass conservation, are maintained in the coupled-DMD extrapolation. The mathematical and numerical analysis suggests that DMD may be a powerful tool when applied to this common class of problems. In particular, we show interesting numerical applications to a continuous delayed-SIRD model for Covid-19, and to a problem from additive manufacturing considering a nonlinear temperature field and the resulting change of material phase from powder, liquid, and solid states.

cs.LG↗

arXiv2021

Dynamic Mode Decomposition in Adaptive Mesh Refinement and Coarsening Simulations

Dynamic Mode Decomposition (DMD) is a powerful data-driven method used to extract spatio-temporal coherent structures that dictate a given dynamical system. The method consists of stacking collected temporal snapshots into a matrix and mapping the nonlinear dynamics using a linear operator. The standard procedure considers that snapshots possess the same dimensionality for all the observable data. However, this often does not occur in numerical simulations with adaptive mesh refinement/coarsening schemes (AMR/C). This paper proposes a strategy to enable DMD to extract features from observations with different mesh topologies and dimensions, such as those found in AMR/C simulations. For this purpose, the adaptive snapshots are projected onto the same reference function space, enabling the use of snapshot-based methods such as DMD. The present strategy is applied to challenging AMR/C simulations: a continuous diffusion-reaction epidemiological model for COVID-19, a density-driven gravity current simulation, and a bubble rising problem. We also evaluate the DMD efficiency to reconstruct the dynamics and some relevant quantities of interest. In particular, for the SEIRD model and the bubble rising problem, we evaluate DMD's ability to extrapolate in time (short-time future estimates).

cs.LG↗

arXiv2021

Assessing the spatio-temporal spread of COVID-19 via compartmental models with diffusion in Italy, USA, and Brazil

The outbreak of COVID-19 in 2020 has led to a surge in interest in the mathematical modeling of infectious diseases. Such models are usually defined as compartmental models, in which the population under study is divided into compartments based on qualitative characteristics, with different assumptions about the nature and rate of transfer across compartments. Though most commonly formulated as ordinary differential equation (ODE) models, in which the compartments depend only on time, recent works have also focused on partial differential equation (PDE) models, incorporating the variation of an epidemic in space. Such research on PDE models within a Susceptible, Infected, Exposed, Recovered, and Deceased (SEIRD) framework has led to promising results in reproducing COVID-19 contagion dynamics. In this paper, we assess the robustness of this modeling framework by considering different geometries over more extended periods than in other similar studies. We first validate our code by reproducing previously shown results for Lombardy, Italy. We then focus on the U.S. state of Georgia and on the Brazilian state of Rio de Janeiro, one of the most impacted areas in the world. Our results show good agreement with real-world epidemiological data in both time and space for all regions across major areas and across three different continents, suggesting that the modeling approach is both valid and robust.

q-bio.PE↗

arXiv2020

Adaptive Mesh Refinement and Coarsening for Diffusion-Reaction Epidemiological Models

The outbreak of COVID-19 in 2020 has led to a surge in the interest in the mathematical modeling of infectious diseases. Disease transmission may be modeled as compartmental models, in which the population under study is divided into compartments and has assumptions about the nature and time rate of transfer from one compartment to another. Usually, they are composed of a system of ordinary differential equations (ODE's) in time. A class of such models considers the Susceptible, Exposed, Infected, Recovered, and Deceased populations, the SEIRD model. However, these models do not always account for the movement of individuals from one region to another. In this work, we extend the formulation of SEIRD compartmental models to diffusion-reaction systems of partial differential equations to capture the continuous spatio-temporal dynamics of COVID-19. Since the virus spread is not only through diffusion, we introduce a source term to the equation system, representing exposed people who return from travel. We also add the possibility of anisotropic non-homogeneous diffusion. We implement the whole model in \texttt{libMesh}, an open finite element library that provides a framework for multiphysics, considering adaptive mesh refinement and coarsening. Therefore, the model can represent several spatial scales, adapting the resolution to the disease dynamics. We verify our model with standard SEIRD models and show several examples highlighting the present model's new capabilities.

q-bio.PE↗

arXiv2020

Finite element solution of nonlocal Cahn-Hilliard equations with feedback control time step size adaptivity

In this study, we evaluate the performance of feedback control-based time step adaptivity schemes for the nonlocal Cahn-Hilliard equation derived from the Ohta-Kawasaki free energy functional. The temporal adaptivity scheme is recast under the linear feedback control theory equipped with an error estimation that extrapolates the solution obtained from an energy-stable, fully implicit time marching scheme. We test three time step controllers with different properties: a simple Integral controller, a complete Proportional-Integral-Derivative controller, and the PC11 predictive controller. We assess the performance of the adaptive schemes for the nonlocal Cahn-Hilliard equation in terms of the number of time steps required for the complete simulation and the computational effort measured by the required number of nonlinear and linear solver iterations. We also present numerical evidence of mass conservation and free energy decay for simulations with the three different time step controllers. The PC11 predictive controller is the best in all three-dimensional test cases.

cs.CE↗

arXiv2020

An encoder-decoder deep surrogate for reverse time migration in seismic imaging under uncertainty

Seismic imaging faces challenges due to the presence of several uncertainty sources. Uncertainties exist in data measurements, source positioning, and subsurface geophysical properties. Reverse time migration (RTM) is a high-resolution depth migration approach useful for extracting information such as reservoir localization and boundaries. RTM, however, is time-consuming and data-intensive as it requires computing twice the wave equation to generate and store an imaging condition. RTM, when embedded in an uncertainty quantification algorithm (like the Monte Carlo method), shows a many-fold increase in its computational complexity due to the high input-output dimensionality. In this work, we propose an encoder-decoder deep learning surrogate model for RTM under uncertainty. Inputs are an ensemble of velocity fields, expressing the uncertainty, and outputs the seismic images. We show by numerical experimentation that the surrogate model can reproduce the seismic images accurately, and, more importantly, the uncertainty propagation from the input velocity fields to the image ensemble.

physics.comp-ph↗

arXiv2020

A workflow for seismic imaging with quantified uncertainty

The interpretation of seismic images faces challenges due to the presence of several uncertainty sources. Uncertainties exist in data measurements, source positioning, and subsurface geophysical properties. Understanding uncertainties' role and how they influence the outcome is an essential part of the decision-making process in the oil and gas industry. Geophysical imaging is time-consuming. When we add uncertainty quantification, it becomes both time and data-intensive. In this work, we propose a workflow for seismic imaging with quantified uncertainty. We build the workflow upon Bayesian tomography, reverse time migration, and image interpretation based on statistical information. The workflow explores an efficient hybrid parallel computational strategy to decrease the reverse time migration execution time. High levels of data compression are applied to reduce data transfer among workflow activities and data storage. We capture and analyze provenance data at runtime to improve workflow execution, monitoring, and debugging with negligible overhead. Numerical experiments on the Marmousi2 Velocity Model Benchmark demonstrate the workflow capabilities. We observe excellent weak and strong scalability, and results suggest that the use of lossy data compression does not hamper the seismic imaging uncertainty quantification.

physics.geo-ph↗