arXiv subjects

Ulisses Braga-Neto

Publications and source records attributed to Ulisses Braga-Neto.

At least 19 recordsLinked to original sources

arXiv2026

High-Redshift Type Ia Supernovae Exhibit Enhanced Calcium Abundances

Type Ia supernovae (SNe Ia) are major contributors to cosmic chemical enrichment, and their elemental abundances provide a probe of progenitor properties and explosion physics across cosmic time. We employ an artificial intelligence-assisted inversion technique to analyze spectra of high-redshift SNe Ia from the Supernova Legacy Survey and of gravitationally lensed SNe Ia observed by the James Webb Space Telescope, extending the sample to redshift 2.05. We find a positive correlation between SN Ia calcium abundance and redshift. The redshift-dependent variation in calcium abundance exceeds that predicted by SN Ia nucleosynthesis simulations with varying progenitor metallicities, suggesting that high-redshift SNe Ia may undergo different explosion mechanisms from nearby SNe Ia.

astro-ph.HE↗

arXiv2026

An Agentic AI Scientific Community for Automated Neural Operator Discovery

We present an agentic approach to autonomous neural operator discovery based on an AI scientific community, which consists of a swarm of virtual laboratories that interact under a citation-based economy of influence. Highly-cited labs found new labs that follow their research direction and replace non-performing labs. Each virtual lab contains three agents: an LLM planner that proposes an architecture, a numerical worker that trains and measures it, and an LLM reviewer that participates in cross-lab peer review. All labs share a common vocabulary consisting of DeepONet (branch-trunk), Fourier, Transformer (attention), wavelet, and residual convolutional neural operator building blocks. We evaluate the neural operator AI scientific community on five problems, namely piecewise regression, the linear advection and Burgers 1D PDEs, and the Navier-Stokes and Darcy flow 2D PDEs, while repeating the simulation three times for each problem. The results show that the neural operator AI scientific community is capable of discovering high-accuracy, low-parameter-count neural operator architectures. All 9,623 LLM calls are logged and audited, which reveals that the virtual lab LLM planners choose to hybridize in 99.8% of their logged decisions, consistently returning multi-family hybrids. Moreover, we conducted an ablation study by replacing the LLM agents in each lab by rule-based alternatives, which caused the scientific community to collapse to non-hybridized single-family stacks in several cases, showing that LLM agency is needed to preserve diversity. The results suggest a no-free-lunch theorem for neural operators: there is no universal winner. The code, configurations, and the complete LLM transcripts are released at https://github.com/luislootx/AI-SC.

cs.LG↗

arXiv2026

The AI Scientific Community: Agentic Virtual Lab Swarms

In this short note we propose using agentic swarms of virtual labs as a model of an AI Science Community. In this paradigm, each particle in the swarm represents a complete virtual laboratory instance, enabling collective scientific exploration that mirrors real-world research communities. The framework leverages the inherent properties of swarm intelligence - decentralized coordination, balanced exploration-exploitation trade-offs, and emergent collective behavior - to simulate the behavior of a scientific community and potentially accelerate scientific discovery. We discuss architectural considerations, inter-laboratory communication and influence mechanisms including citation-analogous voting systems, fitness function design for quantifying scientific success, anticipated emergent behaviors, mechanisms for preventing lab dominance and preserving diversity, and computational efficiency strategies to enable large swarms exhibiting complex emergent behavior analogous to real-world scientific communities. A working instance of the AI Science Community is currently under development.

cs.AI↗

arXiv2026

BumpNet: A Sparse MLP Framework for Learning PDE Solutions

We introduce BumpNet, a sparse multilayer perceptron (MLP) framework for PDE numerical solution and operator learning. BumpNet is based on basis function expansion, which makes them superficially similar to radial-basis function (RBF) networks. However, the basis functions in BumpNet are constructed from ordinary sigmoid activation functions in a sparse multi-layer framework. This makes BumpNet a MLP, not a RBF neural network, enabling the efficient use of modern training techniques optimized for MLPs. All parameters of the basis functions, including shape, location, and amplitude, are fully trainable. Model parsimony is encouraged through a basis function pruning scheme. BumpNet is a general meshless framework that can be combined with existing neural architectures for learning PDE solutions: here, we propose Bump-PINNs (BumpNet with physics-informed neural networks) for solving general PDEs; Bump-EDNN (BumpNet with evolutionary deep neural networks) to solve time-evolution PDEs; and Bump-DeepONet (BumpNet with deep operator networks) for PDE operator learning. We prove that BumpNets and Bump-DeepONets are universal approximators of continuous functions and continuous operators, respectively. Bump-PINNs are trained using the same collocation-based approach used by PINNs; Bump-EDNN uses a BumpNet only in the spatial domain and uses EDNNs to advance the solution in time; while Bump-DeepONets employ a BumpNet regression network as the trunk network of a DeepONet. Extensive numerical experiments demonstrate the efficiency and accuracy of BumpNets.

cs.LG↗

arXiv2026

Free-RBF-KAN: Kolmogorov-Arnold Networks with Adaptive Radial Basis Functions for Efficient Function Learning

Kolmogorov-Arnold Networks (KANs) offer a promising framework for approximating complex nonlinear functions, yet the original B-spline formulation suffers from significant computational overhead due to De Boor algorithm. While recent RBF-based variants improve efficiency, they often sacrifice the approximation accuracy inherent in the original spline-based design. To bridge this gap, we propose Free-RBF-KAN, an architecture that integrates adaptive learning grids and trainable smoothness parameters to enable expressive, high-resolution function approximation. Our method utilizes learnable RBF shapes that dynamically align with activation patterns, and we provide the first formal universal approximation proof for the RBF-KAN family. Empirical evaluations across multiscale regression, physics-informed PDEs, and operator learning demonstrate that Free-RBF-KAN can achieve accuracy comparable to its B-spline counterparts while delivering significantly faster training and inference. These results establish Free-RBF-KAN as an efficient and adaptive alternative for high-dimensional structured modeling tasks.

cs.LG↗

arXiv2026

Convolution Operator Network for Forward and Inverse Problems (FI-Conv): Application to Plasma Turbulence Simulations

We propose the Convolutional Operator Network for Forward and Inverse Problems (FI-Conv), a framework capable of predicting system evolution and estimating parameters in complex spatio-temporal dynamics, such as turbulence. FI-Conv is built on a U-Net architecture, in which most convolutional layers are replaced by ConvNeXt V2 blocks. This design preserves U-Net performance on inputs with high-frequency variations while maintaining low computational complexity. FI-Conv uses an initial state, PDE parameters, and evolution time as input to predict the system future state. As a representative example of a system exhibiting complex dynamics, we evaluate the performance of FI-Conv on the task of predicting turbulent plasma fields governed by the Hasegawa-Wakatani (HW) equations. The HW system models two-dimensional electrostatic drift-wave turbulence and exhibits strongly nonlinear behavior, making accurate approximation and long-term prediction particularly challenging. Using an autoregressive forecasting procedure, FI-Conv achieves accurate forward prediction of the plasma state evolution over short times (t ~ 3) and captures the statistic properties of derived physical quantities of interest over longer times (t ~ 100). Moreover, we develop a gradient-descent-based inverse estimation method that accurately infers PDE parameters from plasma state evolution data, without modifying the trained model weights. Collectively, our results demonstrate that FI-Conv can be an effective alternative to existing physics-informed machine learning methods for systems with complex spatio-temporal dynamics.

cs.LG↗

arXiv2026

In-Context Multi-Operator Learning with DeepOSets

An important application of neural networks to scientific computing has been the learning of non-linear operators. In this framework, a neural network is trained to fit a non-linear map between two infinite dimensional spaces, for example, the solution operator of ordinary and partial differential equations. Recently, inspired by the discovery of in-context learning for large language models, an even more ambitious paradigm has been explored, called multi-operator learning. In this approach, a neural network is trained to learn many different operators at the same time. In order to evaluate one of the learned operators, the network is passed example inputs and outputs to disambiguate the desired operator. In this work, we provide a precise mathematical formulation of the multi-operator learning problem. In addition, we modify a simple efficient architecture, called DeepOSets, for multi-operator learning and prove its universality for multi-operator learning. Finally, we provide a comprehensive set of experiments that demonstrate the ability of DeepOSets to learn multiple operators corresponding to different initial-value and boundary-value differential equations and use in-context examples to predict accurately the solutions corresponding to queries and differential equations not seen during training. The main advantage of DeepOSets is its architectural simplicity, which allows the derivation of theoretical guarantees and training times that are in the order of minutes, in contrast to similar transformer-based alternatives that are empirically justified and require hours of training.

cs.LG↗

arXiv2025

DeepOSets: Non-Autoregressive In-Context Learning with Permutation-Invariance Inductive Bias

In-context learning (ICL) is the remarkable ability displayed by some machine learning models to learn from examples provided in a user prompt without any model parameter updates. ICL was first observed in the domain of large language models, and it has been widely assumed that it is a product of the attention mechanism in autoregressive transformers. In this paper, using stylized regression learning tasks, we demonstrate that ICL can emerge in a non-autoregressive neural architecture with a hard-coded permutation-invariance inductive bias. This novel architecture, called DeepOSets, combines the set learning properties of the DeepSets architecture with the operator learning capabilities of Deep Operator Networks (DeepONets). We provide a representation theorem for permutation-invariant regression learning operators and prove that DeepOSets are universal approximators of this class of operators. We performed comprehensive numerical experiments to evaluate the capabilities of DeepOSets in learning linear, polynomial, and shallow neural network regression, under varying noise levels, dimensionalities, and sample sizes. In the high-dimensional regime, accuracy was enhanced by replacing the DeepSets layer with a Set Transformer. Our results show that DeepOSets deliver accurate and fast results with an order of magnitude fewer parameters than a comparable transformer-based alternative.

cs.LG↗

arXiv2025

SEDONA-GesaRaT: an AI-Accelerated Radiative Transfer Program for 3-D Supernova Simulations

We present SEDONA-GesaRaT, a rapid code for supernova radiative transfer simulation developed based on the Monte-Carlo radiative transfer code SEDONA. We use a set of atomic physics neural networks (APNN), an artificial intelligence (AI) solver for the non-local thermodynamic equilibrium (NLTE) atomic physics level population calculation, which is trained and validated on 119 1-D type Ia supernova (SN Ia) radiative transfer simulation results showing great computation speed and accuracy. SEDONA-GesaRaT has been applied to the 3-D SN Ia explosion model N100 to perform a 3-D NLTE radiative transfer calculation. The spatially resolved linear polarization data cubes of the N100 model are successfully retrieved with a high signal-to-noise ratio using the integral-based technique (IBT). The overall computation cost of a 3-D NLTE spectropolarimetry simulation using SEDONA-GesaRaT is only $\sim$3000 core-hours, while the previous codes could only finish 1-D NLTE simulation, or 3-D local thermodynamic equilibrium (LTE) simulation, with similar computation resources. The excellent computing efficiency allows SEDONA-GesaRaT for future large-scale simulations that systematically study the internal structures of supernovae.

astro-ph.HE↗

arXiv2024

Generalized Resubstitution for Regression Error Estimation

We propose generalized resubstitution error estimators for regression, a broad family of estimators, each corresponding to a choice of empirical probability measures and loss function. The usual sum of squares criterion is a special case corresponding to the standard empirical probability measure and the quadratic loss. Other choices of empirical probability measure lead to more general estimators with superior bias and variance properties. We prove that these error estimators are consistent under broad assumptions. In addition, procedures for choosing the empirical measure based on the method of moments and maximum pseudo-likelihood are proposed and investigated. Detailed experimental results using polynomial regression demonstrate empirically the superior finite-sample bias and variance properties of the proposed estimators. The R code for the experiments is provided.

cs.LG↗

arXiv2024

Physics-Informed Neural Networks for Multi-Phase Flow in Porous Media Considering Dual Shocks and Interphase Solubility

Physics-Informed Neural Networks (PINNs) integrate physical principles into machine learning, finding wide applications in various science and engineering fields. However, solving nonlinear hyperbolic partial differential equations (PDEs) with PINNs presents challenges due to inherent discontinuities in the solutions. This is particularly true for the Buckley-Leverett (B-L) equation, a key model for multi-phase fluid flow in porous media. In this paper, we demonstrate that PINNs, in conjunction with Welge's Construction, can achieve superior precision in handling the B-L equations in different scenarios including one shock and one rarefaction wave, two shocks connected by a rarefaction wave traveling in the same direction, and two shocks connected by a rarefaction wave traveling in opposite directions. Our approach accounts for variations in fluid mobility, fluid solubility, and gravity effects, with applications in modeling 1D water flooding, polymer flooding, gravitational flow, and CO$_2$ injection into saline aquifers. Additionally, we applied PINNs to inverse problems to estimate multiple PDE parameters from observed data, demonstrating robustness under conditions of slight scarcity and up to 5% impurity of labeled data, as well as shortages in collocation data.

physics.flu-dyn↗

arXiv2024

Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanism

Physics-Informed Neural Networks (PINNs) have emerged recently as a promising application of deep neural networks to the numerical solution of nonlinear partial differential equations (PDEs). However, it has been recognized that adaptive procedures are needed to force the neural network to fit accurately the stubborn spots in the solution of "stiff" PDEs. In this paper, we propose a fundamentally new way to train PINNs adaptively, where the adaptation weights are fully trainable and applied to each training point individually, so the neural network learns autonomously which regions of the solution are difficult and is forced to focus on them. The self-adaptation weights specify a soft multiplicative soft attention mask, which is reminiscent of similar mechanisms used in computer vision. The basic idea behind these SA-PINNs is to make the weights increase as the corresponding losses increase, which is accomplished by training the network to simultaneously minimize the losses and maximize the weights. In addition, we show how to build a continuous map of self-adaptive weights using Gaussian Process regression, which allows the use of stochastic gradient descent in problems where conventional gradient descent is not enough to produce accurate solutions. Finally, we derive the Neural Tangent Kernel matrix for SA-PINNs and use it to obtain a heuristic understanding of the effect of the self-adaptive weights on the dynamics of training in the limiting case of infinitely-wide PINNs, which suggests that SA-PINNs work by producing a smooth equalization of the eigenvalues of the NTK matrix corresponding to the different loss terms. In numerical experiments with several linear and nonlinear benchmark problems, the SA-PINN outperformed other state-of-the-art PINN algorithm in L2 error, while using a smaller number of training epochs.

cs.LG↗

arXiv2024

Stability in Training PINNs for Stiff PDEs: Why Initial Conditions Matter

Training physics-informed neural networks (PINNs) on stiff, time-dependent PDEs remains a fundamental challenge due to optimization instabilities and gradient pathologies. Through a series of rigorous ablation studies and Neural Tangent Kernel (NTK) analysis, we identify that the exact enforcement of initial conditions (ICs) is a decisive factor in stabilizing the training landscape. We present the first systematic ablation of two core strategies: hard initial-condition constrained transformation and self-adaptive loss weighting. Our findings demonstrate that embedding ICs directly into the network architecture provides an implicit time-marching effect, effectively reducing spectral bias and enabling the solution of highly stiff benchmarks, including sharp transitions and high-frequency coupled systems, primarily under periodic boundary conditions, with a Dirichlet extension reported as an additional robustness check. This work provides a scalable framework for developing reliable and physically-consistent neural solvers for complex mechanical systems.

math.NA↗

arXiv2024

Label Propagation Training Schemes for Physics-Informed Neural Networks and Gaussian Processes

This paper proposes a semi-supervised methodology for training physics-informed machine learning methods. This includes self-training of physics-informed neural networks and physics-informed Gaussian processes in isolation, and the integration of the two via co-training. We demonstrate via extensive numerical experiments how these methods can ameliorate the issue of propagating information forward in time, which is a common failure mode of physics-informed machine learning.

cs.LG↗

arXiv2023

Auto-PINN: Understanding and Optimizing Physics-Informed Neural Architecture

Physics-informed neural networks (PINNs) are revolutionizing science and engineering practice by bringing together the power of deep learning to bear on scientific computation. In forward modeling problems, PINNs are meshless partial differential equation (PDE) solvers that can handle irregular, high-dimensional physical domains. Naturally, the neural architecture hyperparameters have a large impact on the efficiency and accuracy of the PINN solver. However, this remains an open and challenging problem because of the large search space and the difficulty of identifying a proper search objective for PDEs. Here, we propose Auto-PINN, the first systematic, automated hyperparameter optimization approach for PINNs, which employs Neural Architecture Search (NAS) techniques to PINN design. Auto-PINN avoids manually or exhaustively searching the hyperparameter space associated with PINNs. A comprehensive set of pre-experiments using standard PDE benchmarks allows us to probe the structure-performance relationship in PINNs. We find that the different hyperparameters can be decoupled, and that the training loss function of PINNs is a good search objective. Comparison experiments with baseline methods demonstrate that Auto-PINN produces neural architectures with superior stability and accuracy over alternative baselines.

cs.LG↗

arXiv2023

Characteristics-Informed Neural Networks for Forward and Inverse Hyperbolic Problems

We propose characteristics-informed neural networks (CINN), a simple and efficient machine learning approach for solving forward and inverse problems involving hyperbolic PDEs. Like physics-informed neural networks (PINN), CINN is a meshless machine learning solver with universal approximation capabilities. Unlike PINN, which enforces a PDE softly via a multi-part loss function, CINN encodes the characteristics of the PDE in a general-purpose deep neural network by adding a characteristic layer. This neural network is trained with the usual MSE data-fitting regression loss and does not require residual losses on collocation points. This leads to faster training and can avoid well-known pathologies of gradient descent optimization of multi-part PINN loss functions. This paper focuses on linear transport phenomena, in which case it is shown that, if the characteristic ODEs can be solved exactly, then the output of a CINN is an exact solution of the PDE, even at initialization, preventing the occurrence of non-physical solutions. In addition, a CINN can also be trained with soft penalty constraints that enforce, for example, periodic or Neumman boundary conditions, without losing the property that the output satisfies the PDE automatically. We also propose an architecture that extends the CINN approach to linear hyperbolic systems of PDEs. All CINN architectures proposed here can be trained end-to-end from sample data using standard deep learning software. Experiments with the simple advection equation, a stiff periodic advection equation, and an acoustics problem where data from one field is used to predict the other, unseen field, indicate that CINN is able to improve on the accuracy of the baseline PINN, in some cases by a considerable margin, while also being significantly faster to train and avoiding non-physical solutions. An extension to nonlinear PDEs is also briefly discussed.

cs.LG↗

arXiv2022

Plastic Contaminant Detection in Aerial Imagery of Cotton Fields with Deep Learning

Plastic shopping bags that get carried away from the side of roads and tangled on cotton plants can end up at cotton gins if not removed before the harvest. Such bags may not only cause problem in the ginning process but might also get embodied in cotton fibers reducing its quality and marketable value. Therefore, it is required to detect, locate, and remove the bags before cotton is harvested. Manually detecting and locating these bags in cotton fields is labor intensive, time-consuming and a costly process. To solve these challenges, we present application of four variants of YOLOv5 (YOLOv5s, YOLOv5m, YOLOv5l and YOLOv5x) for detecting plastic shopping bags using Unmanned Aircraft Systems (UAS)-acquired RGB (Red, Green, and Blue) images. We also show fixed effect model tests of color of plastic bags as well as YOLOv5-variant on average precision (AP), mean average precision (mAP@50) and accuracy. In addition, we also demonstrate the effect of height of plastic bags on the detection accuracy. It was found that color of bags had significant effect (p < 0.001) on accuracy across all the four variants while it did not show any significant effect on the AP with YOLOv5m (p = 0.10) and YOLOv5x (p = 0.35) at 95% confidence level. Similarly, YOLOv5-variant did not show any significant effect on the AP (p = 0.11) and accuracy (p = 0.73) of white bags, but it had significant effects on the AP (p = 0.03) and accuracy (p = 0.02) of brown bags including on the mAP@50 (p = 0.01) and inference speed (p < 0.0001). Additionally, height of plastic bags had significant effect (p < 0.0001) on overall detection accuracy. The findings reported in this paper can be useful in speeding up removal of plastic bags from cotton fields before harvest and thereby reducing the amount of contaminants that end up at cotton gins.

cs.CV↗

arXiv2022

Using Physics Informed Neural Networks for Supernova Radiative Transfer Simulation

We use physics informed neural networks (PINNs) to solve the radiative transfer equation and calculate a synthetic spectrum for a Type Ia supernova (SN~Ia) SN 2011fe. The calculation is based on local thermodynamic equilibrium (LTE) and 9 elements are included. Physical processes included are approximate radiative equilibrium, bound-bound transitions, and the Doppler effect. A PINN based gamma-ray scattering approximation is used for radioactive decay energy deposition. The PINN synthetic spectrum is compared to an observed spectrum, a synthetic spectrum calculated by the Monte-Carlo radiative transfer program TARDIS, and the formal solution of the radiative transfer equation. We discuss the challenges and potential of this deep-learning based radiative transfer equation solver. In fact, PINNs offer the prospect of simultaneous solution of the atmosphere problem for both radiation field and thermal state throughout spacetime. We have made modest steps to realizing that prospect with our calculations which required many approximations in order to be feasible at this point in the development of PINN atmosphere solutions.

astro-ph.HE↗