arXiv subjects

Jose Luis Lima de Jesus Silva

Publications and source records attributed to Jose Luis Lima de Jesus Silva.

8 recordsLinked to original sources

arXiv2026

Computer-assisted global regularity across nonlinear families of three-dimensional periodic Navier-Stokes flows

Numerical simulations reveal how vortices stretch and transfer energy, but establishing smooth evolution requires bounds that remain valid beyond the simulated resolution. Here I develop a computer-assisted framework that establishes global regularity for continuous families of three-dimensional periodic Navier-Stokes flows. Its central construction combines finite reference trajectories with a common error bound that covers an interval of centre fields and infinitely many smooth perturbation modes. The method retains the complete nonlinear residual before spectral truncation and controls the evolution until viscous decay guarantees regularity for all subsequent times. Applications to cyclic-shear, Arnold-Beltrami-Childress and three-component Taylor-Green fields yield explicit perturbation radii and include initial conditions outside the direct Fourier-Wiener smallness criterion. A parameter-uniform extension covers a connected family of non-Beltrami Taylor-Green centres without repeating the proof for individual parameter values. An ensemble of 4,096 configurations, supplemented by 1,600 refinement trajectories and public turbulence data, connects the mathematical observables to spectral transfer and vortex geometry. Matched neural-operator experiments show that physics-informed training improves physical prediction, while also revealing that these gains do not necessarily improve the discovery of proof-limiting initial conditions. Together, these results provide a reusable method for establishing regularity across prescribed flow families and a quantitative setting for evaluating how learned predictions can assist rigorous computation.

physics.flu-dyn↗

arXiv2026

Response Renormalization for Critical Deep Equilibrium Models

Deep Equilibrium Models (DEQs) compute predictions from a hidden representation unchanged by the model update. Training through this equilibrium uses implicit differentiation and requires solving an adjoint system built from the residual Jacobian. If this Jacobian is nearly singular along loss-sensitive directions, small perturbations can be strongly amplified in the adjoint response, producing large, highly sensitive gradients that can make optimization unreliable. We introduce Response Renormalization, a backward-pass framework that lifts selected near-pole denominators while leaving unlifted response channels unchanged. Collective Mode Response Renormalization (CMR) applies this correction in a low-dimensional critical subspace, while Phi-adaptive CMR computes a bounded response mass from a positive susceptibility rule. We derive dense and matrix-free collective formulations, distinguish exact gradients of a modified frozen-anchor residual from backward-response surrogates, and extend the construction to Structured Implicit Layers and Vector Attractors (SILVA). Across 23 multiphysics families spanning partial differential equations, three-dimensional fields, operator maps, complex geometries, and particle systems, CMR and Phi-CMR yield test errors no more than five percent higher than those from models trained with exact implicit differentiation in more than 98% of static and 95% of transient family-seed comparisons. Solver-index experiments show convergence toward the static adjoint, while physical-time rollouts retain predictive fidelity under the evaluated conditions. These results demonstrate that selective response renormalization can control near-critical adjoint amplification without globally damping well-conditioned sensitivity. Therefore, the method can make parameter updates more reliable while preserving the useful gradient information needed for learning.

cs.LG↗

arXiv2026

SILVA Networks as Structured Implicit Layers and Vector Attractors via Dynamic Interaction Fields

Many learning problems require representations that reconcile direct input, nearby structure, and broader context. In implicit neural layers, these influences are usually absorbed into a single fixed-point update, making it hard to identify what enters from the stimulus, what propagates locally, what comes from global context, and what is produced by solver dynamics. Here we introduce SILVA Networks, Structured Implicit Layers and Vector Attractors via Dynamic Interaction Fields. SILVA separates stimulus, local interaction, global interaction, damping, and readout inside one fixed-point architecture. The same template is instantiated for images, molecules, citation networks, and long-range graph benchmarks through domain-specific definitions of nodes, neighborhoods, and global summaries. Experiments and ablations show task-dependent roles for these terms: local interactions are load-bearing in the graph tasks, MNIST gains little from recurrence at the tested capacity, and the clearest global benefit appears in a long-range node-classification benchmark. SILVA therefore provides an implicit representation whose internal interaction dynamics can be trained, ablated, visualized, and diagnosed.

cs.LG↗

arXiv2026

A Symbolic Neural CPU for Quantization-Simulated Writeback and Interpretable Program Execution

Neural networks can learn algorithmic input-output mappings, but trusting a learned executor requires more than a correct final answer because the state transitions that produce it are usually hidden. To make those transitions visible, we introduce a trace-supervised symbolic neural CPU, a factorized learned execution architecture that combines recurrent control, an explicit operation router over a fixed differentiable arithmetic-logic unit bank, destination-masked register writeback, complete trajectory supervision and matched fixed-point replay. The model exposes the selected operation, source and destination registers, register trajectory, memory signals and writeback semantics at every step. On the principal 16-wide benchmark, the non-quantized executor reproduces reference execution exactly, while the eight-bit quantization-simulated executor preserves the symbolic operation path through programs of 1,000 instructions. When the same execution is evaluated against a matched fixed-point replay, the residual numerical drift disappears, showing that it comes from a mismatch between continuous and low-precision reference semantics rather than from execution failure. We compare recurrent, Transformer, temporal-convolution, temporal graph-inspired and state-space controllers, and the ablations show that operation-gate supervision is necessary for an inspectable execution path. Hidden-opcode memory-pressure tasks expose the remaining limits in delayed state use and temporal binding. We also extend the interface with ValueMemory, hybrid adaptive leaky integrate-and-fire controllers, candidate-constrained symbolic control trained through behaviour cloning and actor-critic reinforcement learning, and an RV32I base-integer semantic bridge. Together, these results establish a trace-verifiable framework for interpretable, low-precision and controllable neural execution.

cs.AI↗

arXiv2026

Safety-Contract Graph Multi-Agent Reinforcement Learning for Autonomous Network Security Response

Autonomous network-security response systems promise to reduce Security Operations Centre (SOC) reaction latency, but reward-only multi-agent reinforcement learning (MARL) can improve security reward while remaining non-deployable. We present a safety-contract graph MARL framework and instantiate it as ACD$^3$-GAT (Adaptive Constrained Counterfactual Decisioning with a Graph Attention Network encoder), an architecture that separates simulator observations from reusable operational budgets, constrained optimization, graph state encoding, and counterfactual action screening. We evaluate the method in CAGE Challenge 4, where agents operate under budgets for Mean Time to Recover (MTTR), false-positive response, and firewall change-management disruption. Across the benchmark, every unconstrained method violates the SOC downtime budget in 100% of evaluated episodes, with mean downtime proxy costs of 311-430 against a budget of 50. This complements prior CAGE Challenge 4 findings by showing that reward-only learning lacks operational discipline. Constrained MAPPO-GAT (C-MAPPO-GAT) isolates Lagrangian operational-cost control and budget-aware screening, while ACD$^3$-GAT adds budget context, CVaR tail-risk estimation, opponent-belief state, and Graph Counterfactual Risk Propagation (G-CRP). The replicated comparison includes three 200-episode seeds for IPPO, MAPPO-GAT, C-MAPPO-GAT, and ACD$^3$-GAT. C-MAPPO-GAT reduces downtime violation from 100% to 0.3% and mean downtime cost from 355.4 to 15.5 relative to MAPPO-GAT. ACD$^3$-GAT reduces mean downtime cost to 48.2 with a 13.8% violation rate, placing it on the safety-contract frontier rather than at the most conservative compliance point. Topology-seed and coupled adaptive Red-process stress tests preserve this contrast and show lower worst adaptive degradation for safety-constrained policies than reward-only MAPPO-GAT.

cs.MA↗

arXiv2026

Weakly supervised multimodal segmentation of acoustic borehole images with depth-aware cross-attention

Acoustic borehole images provide high-resolution borehole-wall structure, but large-scale interpretation remains difficult because dense expert annotations are rarely available and subsurface information is intrinsically multimodal. The challenge is developing weakly supervised methods combining two-dimensional image texture with depth-aligned one-dimensional well-logs. Here, we introduce a weakly supervised multimodal segmentation framework that refines threshold-guided pseudo-labels through learned models. This preserves the annotation-free character of classical thresholding and clustering workflows while extending them with denoising, confidence-aware pseudo-supervision, and physically structured fusion. We establish that threshold-guided learned refinement provides the most robust improvement over raw thresholding, denoised thresholding, and latent clustering baselines. Multimodal performance depends strongly on fusion strategy: direct concatenation provides limited gains, whereas depth-aware cross-attention, gated fusion, and confidence-aware modulation substantially improve agreement with the weak supervisory reference. The strongest model, confidence-gated depth-aware cross-attention (CG-DCA), consistently outperforms threshold-based, image-only, and earlier multimodal baselines. Targeted ablations show its advantage depends specifically on confidence-aware fusion and structured local depth interaction rather than model complexity alone. Cross-well analyses confirm this performance is broadly stable. These results establish a practical, scalable framework for annotation-free segmentation, showing multimodal improvement is maximized when auxiliary logs are incorporated selectively and depth-aware.

cs.CV↗

arXiv2025

Hybrid Context-Fusion Attention (CFA) U-Net and Clustering for Robust Seismic Horizon Interpretation

Interpreting seismic horizons is a critical task for characterizing subsurface structures in hydrocarbon exploration. Recent advances in deep learning, particularly U-Net-based architectures, have significantly improved automated horizon tracking. However, challenges remain in accurately segmenting complex geological features and interpolating horizons from sparse annotations. To address these issues, a hybrid framework is presented that integrates advanced U-Net variants with spatial clustering to enhance horizon continuity and geometric fidelity. The core contribution is the Context Fusion Attention (CFA) U-Net, a novel architecture that fuses spatial and Sobel-derived geometric features within attention gates to improve both precision and surface completeness. The performance of five architectures, the U-Net (Standard and compressed), U-Net++, Attention U-Net, and CFA U-Net, was systematically evaluated across various data sparsity regimes (10-, 20-, and 40-line spacing). This approach outperformed existing baselines, achieving state-of-the-art results on the Mexilhao field (Santos Basin, Brazil) dataset with a validation IoU of 0.881 and MAE of 2.49ms, and excellent surface coverage of 97.6% on the F3 Block of the North Sea dataset under sparse conditions. The framework further refines merged horizon predictions (inline and cross-line) using Density-Based Spatial Clustering of Applications with Noise (DBSCAN) to produce geologically plausible surfaces. The results demonstrate the advantages of hybrid methodologies and attention-based architectures enhanced with geometric context, providing a robust and generalizable solution for seismic interpretation in structurally complex and data-scarce environments.

cs.LG↗

arXiv2025

Optimizing Information Asset Investment Strategies in the Exploratory Phase of the Oil and Gas Industry: A Reinforcement Learning Approach

Our work investigates the economic efficiency of the prevailing "ladder-step" investment strategy in oil and gas exploration, which advocates for the incremental acquisition of geological information throughout the project lifecycle. By employing a multi-agent Deep Reinforcement Learning (DRL) framework, we model an alternative strategy that prioritizes the early acquisition of high-quality information assets. We simulate the entire upstream value chain-comprising competitive bidding, exploration, and development phases-to evaluate the economic impact of this approach relative to traditional methods. Our results demonstrate that front-loading information investment significantly reduces the costs associated with redundant data acquisition and enhances the precision of reserve valuation. Specifically, we find that the alternative strategy outperforms traditional methods in highly competitive environments by mitigating the "winner's curse" through more accurate bidding. Furthermore, the economic benefits are most pronounced during the development phase, where superior data quality minimizes capital misallocation. These findings suggest that optimal investment timing is structurally dependent on market competition rather than solely on price volatility, offering a new paradigm for capital allocation in extractive industries.

econ.TH↗