arXiv subjects

Muhammad Abid

Publications and source records attributed to Muhammad Abid.

11 recordsLinked to original sources

arXiv2026

Hybrid Semantic Context-Enhanced Ensemble Learning for Wind Power Ramp-Event Forecasting and Uncertainty-Aware Evaluation

Wind power ramp events which are sudden, large swings in turbine output over short windows are difficult to estimate, and standard models often miss them. Hybrid forecasting approach is built which augments semantic context to ramp-event forecast. Rather than applying an extensive language model directly to predict turbine operating data, we have implemented a pipeline where turbine operating data is converted to simplified text, which is then converted to dense embeddings to be used as inputs for ensemble models incorporated with other features. Testing runs are performed at multiple intervals within the SDWPF dataset, including 10-minute, 30-minute, and 60- minute horizons, with ramp events constituting the highest change in future power output. We check robustness against autoregressive, LSTM, and GRU baselines plus several ensemble configurations, using Diebold-Mariano tests and bootstrap confidence intervals, and we vary the ramp threshold, compress the embeddings with PCA, and validate externally on Kaggle SCADA and NREL data with uncertainty-aware scoring. The semantic-context features produce negligible yet statistically significant gains over the baselines in multiple paired ensemble runs, most clearly at the 30- and 60-minute horizons where these gains hold across different ramp-threshold definitions, and PCA compression helps in some longer-horizon cases. The best context- augmented ensembles rank near the top overall, though the GRU model still posts the lowest ramp-event RMSE at 30 and 60 minutes. External tests confirm the error reduction generalizes across datasets, but the size of the gain depends on both model and dataset. Prediction intervals cover most test cases well but weaken during ramp events, pointing to a localized shift in the data distribution.

cs.LG↗

arXiv2026

Spectral-Embedded Operator Learning for Three-Phase Interfacial Flow: A Ternary Cahn-Hilliard-Navier-Stokes Benchmark

Operator-learning surrogates have been benchmarked largely on single-field, single-interface problems, leaving unclear whether architectural choices validated in those settings transfer to constrained, multiphase flows. We introduce a three-phase interfacial-flow benchmark to examine whether the trunk coordinate representation matters for a multi-channel, interface-dominated target. The configuration consists of an air bubble rising through water, piercing a water-oil interface, and entraining a water plume into the oil within a bounded, wall-confined domain. Reference data are generated using a structure-preserving ternary Cahn-Hilliard-Navier-Stokes solver that algebraically preserves the simplex constraint. From 1,024 Sobol-sampled simulations spanning a nine-dimensional parameter space, we learn the mapping from physical parameters to five-channel space-time fields. We compare three parameter-matched DeepONet variants differing only in trunk representation: raw coordinates (DeepONet), random Fourier features (FEDONet), and a fixed tensor-product Chebyshev dictionary (SEDONet). SEDONet reduces the test relative L2 error by 16.8% compared with FEDONet and by 24.0% compared with DeepONet, while improving all five output channels. Spatial and temporal error analyses localize the principal gains near the diffuse interfaces and after bubble breakthrough. The results indicate that the Chebyshev representation is particularly effective for the strongly non-periodic wall-normal and temporal structure of this three-phase flow.

physics.flu-dyn↗

arXiv2026

Quantum SEDONet: Spectrally-Embedded Quantum Deep Operator Networks for Partial Differential Equations

Quantum DeepONet accelerates neural-operator inference by evaluating an orthogonally parameterized network on a quantum computer, reproducing in ideal simulation the accuracy of its classical counterpart at asymptotically lower inference cost. Its trunk network, however, receives query coordinates with limited spectral structure, requiring the network to learn oscillatory features through its nonlinearities. We propose Quantum SEDONet (Spectral-Embedded Deep Operator Network), which assigns each trunk coordinate a spectral basis according to its boundary condition: Fourier features for periodic coordinates and Chebyshev features for bounded, non-periodic coordinates. The basis is selected per coordinate rather than per problem, allowing both representations within a single problem. Under unary amplitude encoding, the embedding incurs no additional qubits or circuit depth when its dimension remains within the network width, while increasing the parameter count by only a few percent. Across four benchmarks, Quantum SEDONet reduces the mean relative L2 error by 54.1% for the antiderivative, 49.6% for advection, 36.0% for Burgers, and 36.2% for a mixed-boundary channel Poisson problem. Quantum and classical evaluation paths agree to within 10^-8 throughout. The channel Poisson problem simultaneously uses Fourier features in the periodic direction and Chebyshev features in the bounded direction, demonstrating coordinate-wise boundary-matched spectral embedding without additional quantum-resource cost.

quant-ph↗

arXiv2026

WLNO: Wavelet-Laplace Neural Operator for Solving Partial Differential Equations

This work introduces the Wavelet-Laplace Neural Operator (WLNO), a novel neural operator that fuses Haar wavelet multi-scale spatial decomposition with the Laplace-domain pole-residue formulation of the Laplace Neural Operator (LNO). While LNO captures transient and steady-state dynamics through learnable system poles and residues, it lacks an explicit mechanism for extracting spatially localized multi-scale features inherent in complex PDE solutions. WLNO addresses this by augmenting the LNO core with a parallel single-level Haar discrete wavelet transform (DWT) branch that decomposes the lifted feature map into four frequency subbands: approximation (LL), horizontal detail (LH), vertical detail (HL), and diagonal detail (HH) and applies independent learned $1\times1$ convolutions to each subband before reconstruction via the inverse DWT. The two branches are fused through a learnable sigmoid-gated weight $\alpha_\mathrm{wav}$, initialized to give a small initial contribution to the wavelet branch, allowing the model to adaptively balance Laplace-domain dynamics against spatial multi-scale features throughout training. WLNO is evaluated against LNO on five benchmark PDE problems using identical hyperparameters, training data, and evaluation protocols: the diffusion equation, the Burgers equation, the reaction-diffusion system, Darcy flow, and the two-dimensional Navier-Stokes equation. WLNO consistently outperforms LNO on all five problems, with the most pronounced improvement on problems with strong spatial multi-scale structure, such as the Burgers equation with sharp shock fronts and the Navier-Stokes equation with coherent vortical structures, while remaining consistent across smoother and elliptic problems. These results demonstrate that wavelet-based multi-scale spatial decomposition is a principled and effective complement to Laplace-domain operator learning.

cs.LG↗

arXiv2026

The impact of observation density on Bayesian inversion of latent dynamics in shock-dominated flows

Inferring unknown initial states in shock-dominated compressible flows from sparse and noisy measurements is a challenging ill-posed inverse problem due to nonlinear wave interactions and limited sensing. In this work, we develop a non-intrusive reduced-order modeling framework for efficient Bayesian initial-state inversion with uncertainty quantification. The framework combines a convolutional autoencoder with a learned latent-space forward operator. The autoencoder compresses high-dimensional flow fields into a compact nonlinear latent representation, while the forward operator predicts final-time latent states from encoded initial conditions. This AE-ROM surrogate enables rapid forward evaluations and is embedded within a No-U-Turn Sampler (NUTS) for posterior exploration. The framework is demonstrated using 500 high-fidelity Sod shock tube simulations generated through Latin hypercube sampling and solved using a fifth-order WENO scheme. The inverse problem seeks to recover unknown left and right density and pressure states from sparse noisy observations of final-time density and pressure fields. Results show that the AE-ROM accurately reconstructs key shock-tube structures, including the rarefaction wave, contact discontinuity, and shock front. A latent dimension of 32 provides an effective balance between reconstruction accuracy and reduced-space compactness, while 250 training simulations are sufficient for accurate reconstruction. Increasing observation density significantly contracts posterior uncertainty, reducing the mean posterior standard deviation by approximately 78% for density and 76% for pressure. Overall, the proposed framework provides a computationally efficient and uncertainty-aware approach for inverse analysis of shock-dominated flows, with potential extensions to multidimensional compressible-flow and digital-twin applications.

cs.LG↗

arXiv2026

SIMR-NO: A Spectrally-Informed Multi-Resolution Neural Operator for Turbulent Flow Super-Resolution

Reconstructing high-resolution turbulent flow fields from severely under-resolved observations is a fundamental inverse problem in computational fluid dynamics and scientific machine learning. Classical interpolation methods fail to recover missing fine-scale structures, while existing deep learning approaches rely on convolutional architectures that lack the spectral and multiscale inductive biases necessary for physically faithful reconstruction at large upscaling factors. We introduce the Spectrally-Informed Multi-Resolution Neural Operator (SIMR-NO), a hierarchical operator learning framework that factorizes the ill-posed inverse mapping across intermediate spatial resolutions, combines deterministic interpolation priors with spectrally gated Fourier residual corrections at each stage, and incorporates local refinement modules to recover fine-scale spatial features beyond the truncated Fourier basis. The proposed method is evaluated on Kolmogorov-forced two-dimensional turbulence, where $128\times128$ vorticity fields are reconstructed from extremely coarse $8\times8$ observations representing a $16\times$ downsampling factor. Across 201 independent test realizations, SIMR-NO achieves a mean relative $\ell_2$ error of $26.04\%$ with the lowest error variance among all methods, reducing reconstruction error by $31.7\%$ over FNO, $26.0\%$ over EDSR, and $9.3\%$ over LapSRN. Beyond pointwise accuracy, SIMR-NO is the only method that faithfully reproduces the ground-truth energy and enstrophy spectra across the full resolved wavenumber range, demonstrating physically consistent super-resolution of turbulent flow fields.

cs.LG↗

arXiv2025

Neuro-Symbolic Control with Large Language Models for Language-Guided Spatial Tasks

Although large language models (LLMs) have recently become effective tools for language-conditioned control in embodied systems, instability, slow convergence, and hallucinated actions continue to limit their direct application to continuous control. A modular neuro-symbolic control framework that clearly distinguishes between low-level motion execution and high-level semantic reasoning is proposed in this work. While a lightweight neural delta controller performs bounded, incremental actions in continuous space, a locally deployed LLM interprets symbolic tasks. We assess the suggested method in a planar manipulation setting with spatial relations between objects specified by language. Numerous tasks and local language models, such as Mistral, Phi, and LLaMA-3.2, are used in extensive experiments to compare LLM-only control, neural-only control, and the suggested LLM+DL framework. In comparison to LLM-only baselines, the results show that the neuro-symbolic integration consistently increases both success rate and efficiency, achieving average step reductions exceeding 70% and speedups of up to 8.83x while remaining robust to language model quality. The suggested framework enhances interpretability, stability, and generalization without any need of reinforcement learning or costly rollouts by controlling the LLM to symbolic outputs and allocating uninterpreted execution to a neural controller trained on artificial geometric data. These outputs show empirically that neuro-symbolic decomposition offers a scalable and principled way to integrate language understanding with ongoing control, this approach promotes the creation of dependable and effective language-guided embodied systems.

cs.RO↗

arXiv2025

Spectral Embedding via Chebyshev Bases for Robust DeepONet Approximation

Deep Operator Networks (DeepONets) have emerged as a powerful framework for data-driven operator learning, providing flexible surrogates for nonlinear mappings arising in partial differential equations (PDEs). However, the standard trunk network, which operates directly on raw spatial or spatiotemporal coordinates through fully connected layers, often struggles to represent sharp gradients, boundary layers, and other non-periodic solution structures on bounded domains. To address these limitations, we introduce the Spectral-Embedded Deep Operator Network (SEDONet), a novel DeepONet architecture in which the trunk is driven by a fixed Chebyshev spectral dictionary instead of coordinate inputs. This non-periodic spectral embedding provides a principled inductive bias for bounded domains, enabling the learned operator to capture fine-scale features that are difficult for Fourier-based or MLP-only trunks to represent. SEDONet is evaluated on the 2-D Poisson equation, 1-D Burgers' equation, 1-D advection-diffusion equation, Allen-Cahn equation, Lorenz-96 chaotic system, and Darcy flow, covering elliptic, hyperbolic, parabolic, chaotic, and multiscale problems. Across all benchmarks, SEDONet consistently achieves the lowest or statistically comparable relative $L^2$ errors among DeepONet, FEDONet, and SEDONet, with improvements of up to 54% over the baseline DeepONet and consistent gains over Fourier-embedded variants on bounded, non-periodic problems. Energy spectrum analyses further demonstrate that SEDONet more accurately preserves intermediate- and high-frequency solution structures. The proposed framework provides a simple, parameter-neutral modification to DeepONets, offering a robust and computationally efficient spectral approach for surrogate modeling of nonlinear operators in scientific computing.

cs.LG↗

arXiv2021

An Empirical Study of Compression-friendly Community Detection Methods

Real-world graphs are massive in size and we need a huge amount of space to store them. Graph compression allows us to compress a graph so that we need a lesser number of bits per link to store it. Of many techniques to compress a graph, a typical approach is to find clique-like caveman or traditional communities in a graph and encode those cliques to compress the graph. On the other side, an alternative approach is to consider graphs as a collection of hubs connecting spokes and exploit it to arrange the nodes such that the resulting adjacency matrix of the graph can be compressed more efficiently. We perform an empirical comparison of these two approaches and show that both methods can yield good results under favorable conditions. We perform our experiments on ten real-world graphs and define two cost functions to present our findings.

cs.SI↗

arXiv2019

Analysis of a Model for Generating Weakly Scale-free Networks

It is commonly believed that real networks are scale-free and fraction of nodes $P(k)$ with degree $k$ satisfies the power law $P(k) \propto k^{-\gamma} \text{ for } k > k_{min} > 0$. Preferential attachment is the mechanism that has been considered responsible for such organization of these networks. In many real networks, degree distribution before the $k_{min}$ varies very slowly to the extent of being uniform as compared with the degree distribution for $k > k_{min}$ . In this paper, we proposed a model that describe this particular degree distribution for the whole range of $k>0$. We adopt a two step approach. In the first step, at every time stamp we add a new node to the network and attach it with an existing node using preferential attachment method. In the second step, we add edges between existing pairs of nodes with the node selection based on the uniform probability distribution. Our approach generates weakly scale-free networks that closely follow the degree distribution of real-world networks. We perform comprehensive mathematical analysis of the model in the discrete domain and compare the degree distribution generated by these models with that of real-world networks.

cs.DS↗

arXiv2019

High Impedance Fault Detection and Isolation in Power Distribution Networks using Support Vector Machines

This paper proposes an accurate High Impedance Fault (HIF) detection and isolation scheme in a power distribution network. The proposed schemes utilize the data available from voltage and current sensors. The technique employs multiple algorithms consisting of Principal Component Analysis, Fisher Discriminant Analysis, Binary and Multiclass Support Vector Machine for detection and identification of the high impedance fault. These data driven techniques have been tested on IEEE 13-node distribution network for detection and identification of high impedance faults with broken and unbroken conductor. Further, the robustness of machine learning techniques has also been analysed by examining their performance with variation in loads for different faults. Simulation results for different faults at various locations have shown that proposed methods are fast and accurate in diagnosing high impedance faults. Multiclass Support Vector Machine gives the best result to detect and locate High Impedance Fault accurately. It ensures reliability, security and dependability of the distribution network.

eess.SY↗