arXiv subjects

Munawar Ali

Publications and source records attributed to Munawar Ali.

4 recordsLinked to original sources

arXiv2026

Branched Signature Kernel Solvers for ODEs with rough Single-Trajectory signals

We develop a branched signature kernel solver for linear and nonlinear ordinary differential equations driven by a \emph{single observed trajectory} of a possibly rough forcing signal--a setting common within earthquake engineering, finance, biology, and structural health monitoring, where only one forcing realization is available, and the solver must respect the underlying physical law without an ensemble of realizations. We first introduce a count-sampling construction method to turn the single observation into a hierarchical family of $N+1$ nested training paths on which the branched signature kernel can be evaluated; this allows the signature kernel machinery, originally designed for multi-realization regression problems, to operate on a single-trajectory observation. Then we build a kernel-collocation framework, which places the ansatz either on the highest-order derivative of the solution or on the solution itself. We prove a universal approximation theorem for the branched signature kernel, leveraging the Hairer--Kelly morphism to express branched signature evaluations through geometric signatures of time-extended paths. The offline solver is extended to a streaming Test/Train/Retrain protocol with optional closed-form online updates in both linear and nonlinear cases. Numerical experiments on six benchmarks show accurate, stable predictions across all regimes.

math.NA↗

arXiv2025

Branched Signature Model

In this paper, we introduce the branched signature model, motivated by the branched rough path framework of [Gubinelli, Journal of Differential Equations, 248(4), 2010], which generalizes the classical geometric rough path. We establish a universal approximation theorem for the branched signature model and demonstrate that iterative compositions of lower-level signature maps can approximate higher-level signatures. Furthermore, building on the existence of the extension map proposed in [Hairer-Kelly. Annales de l'Institue Henri Poincar\'e, Probabilit\'es et Statistiques 51, no. 1 (2015)], we show how to explicitly construct the extension of the original paths into higher-dimensional spaces via a map $\Psi$, so that the branched signature can be realized as the classical geometric signature of the extended path. This framework not only provides an efficient computational scheme for branched signatures but also opens new avenues for data-driven modeling and applications.

math.NA↗

arXiv2025

Noise estimation of SDE from a single data trajectory

In this paper, we propose a data-driven framework for model discovery of stochastic differential equations (SDEs) from a single trajectory, without requiring the ergodicity or stationary assumption on the underlying continuous process. By combining (stochastic) Taylor expansions with Girsanov transformations, and using the drift function's initial value as input, we construct drift estimators while simultaneously recovering the model noise. This allows us to recover the underlying $\mathbb P$ Brownian motion increments. Building on these estimators, we introduce the first stochastic Sparse Identification of Stochastic Differential Equation (SSISDE) algorithm, capable of identifying the governing SDE dynamics from a single observed trajectory without requiring ergodicity or stationarity. To validate the proposed approach, we conduct numerical experiments with both linear and quadratic drift-diffusion functions. Among these, the Black-Scholes SDE is included as a representative case of a system that does not satisfy ergodicity or stationarity.

q-fin.ST↗

arXiv2023

Advanced Efficient Strategy for Detection of Dark Objects Based on Spiking Network with Multi-Box Detection

Several deep learning algorithms have shown amazing performance for existing object detection tasks, but recognizing darker objects is the largest challenge. Moreover, those techniques struggled to detect or had a slow recognition rate, resulting in significant performance losses. As a result, an improved and accurate detection approach is required to address the above difficulty. The whole study proposes a combination of spiked and normal convolution layers as an energy-efficient and reliable object detector model. The proposed model is split into two sections. The first section is developed as a feature extractor, which utilizes pre-trained VGG16, and the second section of the proposal structure is the combination of spiked and normal Convolutional layers to detect the bounding boxes of images. We drew a pre-trained model for classifying detected objects. With state of the art Python libraries, spike layers can be trained efficiently. The proposed spike convolutional object detector (SCOD) has been evaluated on VOC and Ex-Dark datasets. SCOD reached 66.01% and 41.25% mAP for detecting 20 different objects in the VOC-12 and 12 objects in the Ex-Dark dataset. SCOD uses 14 Giga FLOPS for its forward path calculations. Experimental results indicated superior performance compared to Tiny YOLO, Spike YOLO, YOLO-LITE, Tinier YOLO and Center of loc+Xception based on mAP for the VOC dataset.

cs.CV↗