arXiv subjects

Fabio Pereira dos Santos

Publications and source records attributed to Fabio Pereira dos Santos.

7 recordsLinked to original sources

arXiv2026

Adaptive Quantum Physics-Informed Neural Networks for Differential Equations with Applications to Fluid Dynamics

Physics-informed neural networks (PINNs) have emerged as a versatile approach for solving nonlinear partial differential equations (PDEs), yet achieving high accuracy efficiently using these techniques remains challenging for high-dimensional or multiscale systems. Here, we present a hybrid quantum-classical framework that enhances Quantum PINNs (QPINNs) through adaptive collocation point sampling and loss-aware attention mechanisms. By dynamically prioritizing points in regions with large PDE residuals or steep solution gradients, our method mitigates the spectral bias inherent in conventional PINNs. Current Quantum Physics-Informed Neural Networks are commonly assumed to be limited by the expressive power of quantum circuits. In our work, we observed that, across diverse differential equations, optimization - not only expressivity - can be an important bottleneck. Furthermore, a trainable loss-weighting scheme balances contributions from physics residuals, boundary conditions, and data fidelity during training. Integrating these strategies with quantum computing techniques (including variational quantum circuits and quantum gradient estimation) can yield at least a 60% improvement in solution accuracy under specific regimes for benchmark fluid flows and reaction-diffusion systems. Finally, we argue that merely increasing model expressivity is insufficient for resolving complex PDEs via QPINNs, as they remain constrained by the structural optimization limitations of classical PINNs. This framework provides a scalable pathway for quantum-enhanced scientific machine learning, bridging physics-based modeling with emerging quantum computational capabilities.

cs.LG↗

arXiv2026

Shearlet Neural Operators for Anisotropic-Shock-Dominated and Multi-scale parametric partial differential equations

Neural operators have emerged as powerful data-driven surrogates for learning solution operators of parametric partial differential equations (PDEs). However, widely used Fourier Neural Operators (FNOs) rely on global Fourier representations, which can be inefficient for resolving anisotropic structures, sharp gradients, and spatially localized discontinuities that arise in shock-dominated and multiscale regimes. To address these limitations, we introduce the Shearlet Neural Operator (SNO), a neural operator architecture that replaces the Fourier transform with a shearlet-based representation. Shearlets offer directional, multiscale, and spatially localized atoms with near-optimal sparse approximation of anisotropic features, providing an inductive bias aligned with PDE solutions containing edges, fronts, and shocks. SNO learns in the shearlet domain and reconstructs predictions via the inverse transform, retaining efficient spectral computation while improving locality and directional selectivity. Across seven benchmark PDE families, including strongly anisotropic advection, anisotropic diffusion, and nonlinear conservation laws with straight, curved, interacting, spiral, and polygonal shock structures, SNO consistently improves predictive accuracy and feature fidelity over FNO baselines, with the largest gains observed in anisotropic and discontinuity-dominated settings.

cs.LG↗

arXiv2025

Statistical machine learning tools for probabilistic closures of turbulence models

Turbulent flow remains a challenging subject, despite extensive efforts to find analytical descriptions. Modeling small scales of motion is crucial for saving time and resources in numerical simulations, particularly in industrial applications. Here we attempt to model small scales of motion by creating closures for a Shell model of turbulence, more specifically for Sabra. Shell models are infinite dimensional dynamical systems that retain most key properties of Navier-Stokes equation, such as energy cascade and intermittency, while being computationally treatable. To account for Sabra's intermittent fluctuations we employ a set of scaling relations that recover a hidden symmetry and leaves us with universal statistics across the inertial range. On data from these rescaled variables we then adapt and apply two machine learning tools, a variational auto-encoder and sparse identification of non-linear dynamics. We estimate the data's densities and dynamics in order to then generate new instances of data. Given a mid-inertial range cutoff scale, we evolve reduced models in time, resolving only scales of motion larger than the cutoff scale, closing the reduced model with data generated by the machine learning tools. We compare statistics of our reduced models against a Sabra's fully resolved simulation to evaluate each closure's performances. Our results show improvement regarding previous work, and all our closures are probabilistic and cutoff-independent.

physics.flu-dyn↗

arXiv2024

Predictive Model and Optimization of Micromixers Geometry using Gaussian Process with Uncertainty Quantification and Genetic Algorithm

Microfluidic devices are gaining attention for their small size and ability to handle tiny fluid volumes. Mixing fluids efficiently at this scale, known as micromixing, is crucial. This article builds upon previous research by introducing a novel optimization approach in microfluidics, combining Computational Fluid Dynamics (CFD) with Machine Learning (ML) techniques. The research focuses on improving global optimization while reducing computational expenses. It draws inspiration from a Y-type micromixer, initially featuring cylindrical grooves on the main channel's surface and internal obstructions. Simulations, conducted using OpenFOAM software, evaluate the impact of circular obstructions on mixing percentage and pressure drop, considering variations in obstruction diameter and offset. A Gaussian Process (GP) was utilized to model the data, providing model uncertainty. Thus, this study optimizes geometries by using genetic algorithm (GA) and least-square optimization based on the reduced order model provided by GP. Results align with previous research, showing that medium-sized obstructions (137 mm diameter, 10 mm offset) near the channel wall are optimal. This approach not only provides efficient microfluidic optimization with uncertainty quantification but also highlights the effectiveness of combining CFD and ML techniques in achieving desired outcomes.

physics.flu-dyn↗

arXiv2022

Computational Fluid Dynamics and Machine Learning as tools for Optimization of Micromixers geometry

This work explores a new approach for optimization in the field of microfluidics, using the combination of CFD (Computational Fluid Dynamics), and Machine Learning techniques. The objective of this combination is to enable global optimization with lower computational cost. The initial geometry is inspired in a Y-type micromixer with cylindrical grooves on the surface of the main channel and obstructions inside it. Simulations for circular obstructions were carried out using the OpenFOAM software to observe the influences of obstacles. The effects of obstruction diameter (OD), and offset (OF) in the range of [20,140] mm and [10,160] mm, respectively, on percentage of mixing ($φ$), pressure drop ($ΔP$) and energy cost ($ΔP/φ$) were investigated. Numerical experiments were analyzed using machine learning. Firstly, a neural network was used to train the dataset composed by the inputs OD and OF and outputs $φ$ and $ΔP$. The objective functions (ObF) chosen to numerically optimize the performance of micromixers with grooves and obstructions were $φ$, $ΔP$, $ΔP/φ$. The genetic algorithm obtained the geometry that offers the maximum value of $φ$ and the minimum value of $ΔP_s$. The results show that $φ$ increases monotonically with increasing OD at all values of OF. The inverse is observed with increasing offset. Furthermore, the results reveal that $ΔP$ e $ΔP/φ$ also increase with OD. On the other hand, the pressure drop and the cost of mixing energy present a maximum close to the lowest values of OF. Finally, the optimal value obtained for the diameter was OD=131 mm and for the offset OF=10 mm, which corresponds to obstruction of medium size close to the channel wall.

physics.flu-dyn↗

arXiv2020

A generalized spray-flamelet formulation by means of a monotonic variable

The external structure of the spray-flamelet can be described using the Schvab-Zel'dovich-Liñan formulation. The gaseous mixture-fraction variable as function of the physical space, Z(x_i), typically employed for the description of gaseous diffusion flames leads to non-monotonicity behaviour for spray flames due to the extra fuel supplied by vaporisation of droplets distributed into the flow. As a result, the overall properties of spray flames depend not only on Z and the scalar dissipation rate, but also on the spray source term, S_v. We propose a new general coordinate variable which takes into account the spatial information about the entire mixture fraction due to the gaseous phase and droplet vaporisation. This coordinate variable, Z_C(x_i) is based on the cumulative value of the gaseous mixture fraction Z(x_i), and is shown to be monotonic. For pure gaseous flow, the new cumulative function, Z_C, yields the well-established flamelet structure in Z-space. In the present manuscript, the spray-flamelet structure and the new equations for temperature and mass fractions in terms of Z_C are derived and then applied to the canonical counterflow configuration with potential flow. Numerical results are obtained for ethanol and methanol sprays, and the effect of Lewis and Stokes numbers on the spray-flamelet structure are analyzed. The proposed formulation agrees well when mapping the structure back to physical space thereby confirming our integration methodology.

physics.flu-dyn↗

arXiv2016

Scalar dark matter in an extra dimension inspired model

In this work we consider a singlet scalar propagating in a flat large extra dimension. The first Kaluza-Klein mode associated to this singlet scalar will be a viable dark matter candidate. The tower of new particles enriches the calculation of the relic density due effect of coannihilation. For large mass splitting, the model converges to the predictions of the singlet dark matter model. For nearly degenerate mass spectrum, coannihilations increase the cross sections used for direct and indirect dark matter searches. We investigate the impact of the Kaluza-Klein tower associated to singlet scalar for indirect and direct detection of dark matter.

hep-ph↗