arXiv subjects

Owais Ahmad

Publications and source records attributed to Owais Ahmad.

16 recordsLinked to original sources

arXiv2026

Bridging Phase-Field Model and Deep Learning for Predicting 2D and 3D Microstructure Evolution in Ternary Alloys

We develop a hybrid framework that integrates a phase-field model (PFM) with an attention-enhanced deep learning (DL) architecture to study ternary spinodal dealloying, a sophisticated self-organization approach used to fabricate three-dimensional bicontinuous, hierarchical nanoporous materials. The study captures three distinct phase-separation mechanisms that emerge during the early stages of spinodal decomposition in both two and three dimensions. The DL workflow consists of three key components: (i) a dimensionality-reducing autoencoder that provides compact representations of high-resolution microstructure images (256x256x3), (ii) an attention-augmented convolutional long short-term memory (ConvLSTM) network that learns complex spatiotemporal correlations governing microstructure evolution, and (iii) a novel slice-by-slice strategy that enables extension of the model to three-dimensional systems (128x128x128x3). We further demonstrate a hybrid simulation strategy in which PFM accurately captures rapid early-stage microstructure evolution, while the DL model efficiently predicts late-stage coarsening dynamics. The trained DL model achieves remarkable predictive accuracy, maintaining fidelity up to 400 timesteps ahead and generalizing to compositions outside the training distribution. By bridging the physical fidelity of PFM with the computational efficiency of DL, this framework establishes a robust platform for predictive modeling of microstructure evolution in complex multicomponent systems.

cond-mat.mtrl-sci↗

arXiv2026

Nonuniform Periodic Wavelet Frames on Non-Archimedean Fields

In real life application all signals are not obtained from uniform shifts; so there is a natural question regarding analysis and decompositions of these types of signals by a stable mathematical tool. Gabardo and Nashed and Gabardo and Yu filled this gap by the concept of nonuniform multiresolution analysis and nonuniform wavelets based on the theory of spectral pairs for which the associated translation set $\Lambda =\left\{ 0,r/N\right\}+2\,\mathbb Z$ is no longer a discrete subgroup of $\mathbb R$ but a spectrum associated with a certain one-dimensional spectral pair and the associated dilation is an even positive integer related to the given spectral pair. In this paper, we introduce a notion of nonuniform periodic wavelet frame on non-Archimedean field. Using Fourier transform technique and the unitary extension principle, we propose an approach for the construction of nonuniform periodic wavelet frames on non-Archimedean fields.

math.FA↗

arXiv2026

Construction of Nonuniform Wavelet Frames on Non-Archimedean Fields

A constructive algorithm based on the theory of spectral pairs for constructing nonuniform wavelet basis in $L^2(\mathbb R)$ was considered by Gabardo and Nashed (J Funct. Anal. 158:209-241, 1998). In this setting, the associated translation set $\Lambda =\left\{ 0,r/N\right\}+2\,\mathbb Z$ is no longer a discrete subgroup of $\mathbb R$ but a spectrum associated with a certain one-dimensional spectral pair and the associated dilation is an even positive integer related to the given spectral pair. The main objective of this paper is to develop oblique and unitary extension principles for the construction nonuniform wavelet frames over non-Archimedean Local fields of positive characteristic. An example and some potential applications are also presented.

math.FA↗

arXiv2026

The Quaternion Boostlet Transform: Definition, Properties and Uncertainty Principles

In this article, we introduce the notion of Quaternion Boostlet Transform (QBT), a hypercomplex framework designed to unify the analysis of multi-component wavefields by merging the algebraic richness of quaternions with the relativistic, hyperbolic geometry of the boostlet system. By treating coupled physical phenomena such as acoustic pressure with particle velocity or orthogonally polarized elastic displacements as single quaternion-valued entities, the QBT preserves intrinsic geometric correlations that are typically lost in component-wise processing. We also establish a rigorous mathematical foundation for the transform, including the admissibility condition, a convolution-based representation, a Plancherel theorem for energy conservation, and an explicit inversion formula ensuring perfect signal reconstruction. Furthermore, the work derives a comprehensive set of uncertainty principles namely Heisenberg, logarithmic, and Pitt's inequalities that define the precise localization constraints of QBT coefficients in the augmented phase space. The theoretical development is substantiated with illustrative examples, wherein the QBT is applied to a quaternion-valued plane wave featuring coupled pressure-velocity components and to a Gaussian-modulated circularly polarized elastic wave packet. These examples demonstrate how the transform naturally encodes wavefront orientation and polarization state through quaternion phase, offering a physically coherent and sparse dictionary for vector-valued wavefield analysis in acoustics and seismology.

math.FA↗

arXiv2025

DETNO: A Diffusion-Enhanced Transformer Neural Operator for Long-Term Traffic Forecasting

Accurate long-term traffic forecasting remains a critical challenge in intelligent transportation systems, particularly when predicting high-frequency traffic phenomena such as shock waves and congestion boundaries over extended rollout horizons. Neural operators have recently gained attention as promising tools for modeling traffic flow. While effective at learning function space mappings, they inherently produce smooth predictions that fail to reconstruct high-frequency features such as sharp density gradients which results in rapid error accumulation during multi-step rollout predictions essential for real-time traffic management. To address these fundamental limitations, we introduce a unified Diffusion-Enhanced Transformer Neural Operator (DETNO) architecture. DETNO leverages a transformer neural operator with cross-attention mechanisms, providing model expressivity and super-resolution, coupled with a diffusion-based refinement component that iteratively reconstructs high-frequency traffic details through progressive denoising. This overcomes the inherent smoothing limitations and rollout instability of standard neural operators. Through comprehensive evaluation on chaotic traffic datasets, our method demonstrates superior performance in extended rollout predictions compared to traditional and transformer-based neural operators, preserving high-frequency components and improving stability over long prediction horizons.

cs.LG↗

arXiv2025

Deep Learning-Driven Prediction of Microstructure Evolution via Latent Space Interpolation

Phase-field models accurately simulate microstructure evolution, but their dependence on solving complex differential equations makes them computationally expensive. This work achieves a significant acceleration via a novel deep learning-based framework, utilizing a Conditional Variational Autoencoder (CVAE) coupled with Cubic Spline Interpolation and Spherical Linear Interpolation (SLERP). We demonstrate the method for binary spinodal decomposition by predicting microstructure evolution for intermediate alloy compositions from a limited set of training compositions. First, using microstructures from phase-field simulations of binary spinodal decomposition, we train the CVAE, which learns compact latent representations that encode essential morphological features. Next, we use cubic spline interpolation in the latent space to predict microstructures for any unknown composition. Finally, SLERP ensures smooth morphological evolution with time that closely resembles coarsening. The predicted microstructures exhibit high visual and statistical similarity to phase-field simulations. This framework offers a scalable and efficient surrogate model for microstructure evolution, enabling accelerated materials design and composition optimization.

cond-mat.mtrl-sci↗

arXiv2025

Deep Learning Assisted Denoising of Experimental Micrographs

Microstructure imaging is crucial in materials science, but experimental images often introduce noise that obscures critical structural details. This study presents a novel deep learning approach for robust microstructure image denoising, combining phase-field simulations, Fourier transform techniques, and an attention-based neural network. The innovative framework addresses dataset limitations by synthetically generating training data by combining computational phase-field microstructures with experimental optical micrographs. The neural network architecture features an attention mechanism that dynamically focuses on important microstructural features while systematically eliminating noise types like scratches and surface imperfections. Testing on a FeMnNi alloy system demonstrated the model's exceptional performance across multiple magnifications. By successfully removing diverse noise patterns while maintaining grain boundary integrity, the research provides a generalizable deep-learning framework for microstructure image enhancement with broad applicability in materials science.

cond-mat.mtrl-sci↗

arXiv2025

Microstructural Studies Using Generative Adversarial Network (GAN): a Case Study

The generative adversarial network (GAN) is one of the most widely used deep generative models for synthesizing high-quality images with the same statistics as the training set. Finite element method (FEM) based property prediction often relies on synthetically generated microstructures. The phase-field model is a computational method of generating realistic microstructures considering the underlying thermodynamics and kinetics of the material. Due to the expensive nature of the simulations, it is not always feasible to use phase-field for synthetic microstructure generation. In this work, we train a GAN with microstructures generated from the phase-field simulations. Mechanical properties calculated using the finite element method on synthetic and actual phase field microstructures show excellent agreement. Since the GAN model generates thousands of images within seconds, it has the potential to improve the quality of synthetic microstructures needed for FEM calculations or any other applications requiring a large number of realistic synthetic images at minimal computational cost.

cond-mat.mtrl-sci↗

arXiv2025

Continuous Boostlet Transform and Associated Uncertainty Principles

The Continuous Boostlet Transform (CBT) is introduced as a powerful tool for analyzing spatiotemporal signals, particularly acoustic wavefields. Overcoming the limitations of classical wavelets, the CBT leverages the Poincar\'e group and isotropic dilations to capture sparse features of natural acoustic fields. This paper presents the mathematical framework of the CBT, including its definition, fundamental properties, and associated uncertainty principles, such as Heisenberg's, logarithmic, Pitt's, and Nazarov's inequalities. These results illuminate the trade-offs between time and frequency localization in the boostlet domain. Practical examples with constant and exponential functions highlight the CBT's adaptability. With applications in radar, communications, audio processing, and seismic analysis, the CBT offers flexible time-frequency resolution, making it ideal for non-stationary and transient signals, and a valuable tool for modern signal processing.

eess.SP↗

arXiv2024

Biquaternion Windowed Linear Canonical Transform

In this paper, we introduce the notion of windowed linear canonical transform in biquaternion setting namely Biquaternion Windowed Linear Canonical Transform (BiQWLCT) and various properties of BiQWLCT, such as linearity, shift, parity, orthogonality relation, inversion formula, Plancherel theorem are established. Heisenberg uncertainty principle associated with the Biquaternion Windowed Linear Canonical Transform is also derived. Towards the culmination, an example and some potential applications are presented.

math.FA↗

arXiv2023

Accelerating microstructure modelling via machine learning: a new method combining Autoencoder and ConvLSTM

Phase-field modeling is an elegant and versatile computation tool to predict microstructure evolution in materials in the mesoscale regime. However, these simulations require rigorous numerical solutions of differential equations, which are accurate but computationally expensive. To overcome this difficulty, we combine two popular machine learning techniques, autoencoder and convolutional long short-term memory (ConvLSTM), to accelerate the study of microstructural evolution without compromising the resolution of the microstructural representation. After training with phase-field generated microstructures of ten known compositions, the model can accurately predict the microstructure for the future nth frames based on previous m frames for an unknown composition. Replacing n phase-field steps with machine-learned microstructures can significantly accelerate the in silico study of microstructure evolution.

cond-mat.mtrl-sci↗

arXiv2020

Novel Special Affine Wavelet Transform and Associated Uncertainity Inequalities

{.2in} {\small {\bf Abstract.} Due to the extra degrees of freedom, special affine Fourier transform (SAFT) has achieved a respectable status within a short span and got versatile applicability in the areas of signal processing, image processing,sampling theory, quantum mechanics. However, due to its global kernel, SAFT fails to obtain local information of non-transient signals. To overcome this, we in this paper introduce the concept of novel special affine wavelet transform (NSAWT) and extend key harmonic analysis results to NSAWT analogous to those for the wavelet transform. We first establish some fundamental properties including Moyal's principle, Inversion formula and the range theorem. Some Heisenberg type inequalities and Pitt's inequality are established for SAFT and consequently Heisenberg uncertainity principle is derived for NSAWT.

math.FA↗

arXiv2020

Fractional Biorthogonal wavelets in $L^2(\mathbb R)$

The fractional Fourier transform (FrFT), which is a generalization of the Fourier transform, has become the focus of many research papers in recent years because of its applications in electrical engineering and optics. In this paper, we introduce the notion of fractional biorthogonal wavelets on $\mathbb{R}$ and obtain the necessary and sufficient conditions for the translates of a single function to form the fractional Riesz bases for their closed linear span. We also provide a complete characterization for the fractional biorthogonality of the translates of fractional scaling functions of two fractional MRAs and the associated fractional biorthogonal wavelet families. Moreover, under mild assumptions on the fractional scaling functions and the corresponding fractional wavelets, we show that the fractional wavelets can generate Reisz bases for $L^2(\mathbb R).$.

math.FA↗

arXiv2020

Fractional Multiresolution Analysis and Associated Scaling Functions in $L^2(\mathbb R)$

In this paper, we show how to construct an orthonormal basis from Riesz basis by assuming that the fractional translates of a single function in the core subspace of the fractional multiresolution analysis form a Riesz basis instead of an orthonormal basis. In the definition of fractional multiresolution analysis, we show that the intersection triviality condition follows from the other conditions. Furthermore, we show that the union density condition also follows under the assumption that the fractional Fourier transform of the scaling function is continuous at $0$. At the culmination, we provide the complete characterization of the scaling functions associated with fractional multiresolutrion analysis.

math.FA↗

arXiv2018

Construction of $J^{\text{th}}$-stage Nonuniform Wavelets on Local Fields

Shah and Abdullah [Complex Analysis Operator Theory, 9 (2015), 1589-1608] have introduced a generalized notion of nonuniform multiresolution analysis (NUMRA) on local field $K$ of positive characteristic in which the translation set $Λ$ acting on the scaling function to generate the core space $V_{0}$ is no longer a group, but is the union of ${\mathcal Z}$ and a translate of ${\mathcal Z}$, given by $Λ=\left\{0,u(r)/N \right\}+{\mathcal Z}$, where $N \ge 1$ is an integer and $r$ is an odd integer such that $r$ and $N$ are relatively prime, and ${\mathcal Z}=\{u(n): n\in\mathbb N_{0}\}$ is a complete list of distinct cosets of the unit disc $\mathfrak D$ in $K^+.$ In this paper, we focus on the extension of nonuniform continuous wavelets to the construction of $J^{\text{th}}$-stage nonuniform discrete wavelets on local fields. We establish some general characterizations for the $J^{\text{th}}$-stage nonuniform discrete wavelet systems to be orthornormal bases in $L^2(Λ)$. Moreover, we establish a relation between the continuous wavelets of $L^2(K)$ and their discrete counterparts of $l^2(Λ)$.

math.FA↗

arXiv2017

Biorthogonal Wavelets on the Spectrum

A generalization of Mallat's classic theory of multiresolution analysis based on the theory of spectral pairs was considered by Gabardo and Nashed (J. Funct. Anal. 158, 209-241, 1998). In this article, we introduce the notion of biorthgonoal nonuniform multiresolution analysis on the spectrum $Λ=\left\{0, r/N\right\}+2\mathbb Z$, where $N\ge 1$ is an integer and $r$ is an odd integer with $1\le r\le 2N-1$ such that $r$ and $N$ are relatively prime. We first establish the necessary and sufficient conditions for the translates of a single function to form the Riesz bases for their closed linear span. We provide the complete characterization for the biorthogonality of the translates of scaling functions of two nonuniform multiresolution analysis and the associated biorthogonal wavelet families. Furthermore, under the mild assumptions on the scaling functions and the corresponding wavelets associated with nonuniform multiresolution analysis, we show that the wavelets can generate Reisz bases.

math.FA↗