arXiv subjects

Amirhossein Sadr

Publications and source records attributed to Amirhossein Sadr.

3 recordsLinked to original sources

arXiv2026

PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs

Physics-informed learning of partial differential equations (PDEs) has been dominated by multilayer perceptrons (MLPs), whose spectral bias and dense parameterization limit both accuracy and interpretability. Kolmogorov Arnold Networks (KANs) mitigate these limitations because their learnable spline activations are structurally aligned with the piecewise-polynomial bases of classical discretizations. However, the way a PDE is cast into a loss functional is as decisive as the choice of approximator: strong-form residual minimization requires high-order derivatives and heavily weighted losses, the energy (Bubnov-Galerkin) form is restricted to self-adjoint operators and, as we show, collapses to a trivial solution for parameter-identification problems, and boundary integral forms require a known fundamental solution. We propose PG-KINN, a physics-informed KAN built on a Petrov-Galerkin formulation in which the trial space is a KAN and the test space is an independent, compactly supported, piecewise-polynomial space evaluated with Gauss-Legendre quadrature. Integration by parts lowers the differentiation order while retaining applicability to general non-self-adjoint, nonlinear, and inverse problems; the localized test functions turn the global residual into a set of element-wise weak residuals with favorable conditioning. On a suite of benchmarks spanning crack singularities, stress concentration, Neo-Hookean hyperelasticity, inverse parameter identification in heterogeneous media, and complex geometries, PG-KINN consistently outperforms legacy MLP baselines and state-of-the-art KAN-based strong/energy/inverse formulations (PIKAN). These results position the Petrov-Galerkin coupling of KAN trial spaces and polynomial test spaces as a robust and accurate route for AI-based computational mechanics.

cs.LG↗

arXiv2026

A Generic Modulo-$(2^n\pmδ)$ RNS Multiplier Based on Twit Representation

Modular multiplication is a fundamental arithmetic primitive in Residue Number Systems (RNS) and is often the dominant source of delay, area, and energy consumption in RNS datapaths used in cryptography, signal processing, and machine-learning accelerators. Recent work introduced a twit-based residue representation for moduli of the form $2^n \pm δ$, with $0 \le δ\le 2^{n-1}-1$, and showed that it enables efficient generic modular addition and subtraction across the full admissible $δ$ range. However, an efficient modular multiplier compatible with the same representation has remained unavailable. This paper presents a generic twit-based modulo-$(2^n \pm δ)$ multiplier for RNS channels. The proposed architecture computes the product through operand splitting, modular partial-product generation, carry-save accumulation, overflow folding, and a twit-compatible final modular addition. By deferring carry propagation to the final stage, the resulting organization avoids the long critical paths characteristic of conventional multiply-then-reduce designs. To demonstrate the effectiveness of the proposed approach, we study a modulus set with 5-bit residue channels and show that, owing to the broad admissible range of $δ$, it can provide a sufficiently wide dynamic range. Moreover, additional 8-bit and 11-bit configurations are used to evaluate the proposed approach at larger channel widths. We implement and synthesize the proposed multiplier in a FreePDK 45\,nm flow, and the results show average reductions of 20.5\% in delay, 13.2\% in area, and 28.0\% in power relative to baseline designs. A system-level study further indicates that these circuit-level improvements translate into lower end-to-end latency over a broad range of modular multiplication and addition workloads.

cs.AR↗

arXiv2026

ITS-Mina: A Harris Hawks Optimization-Based All-MLP Framework with Iterative Refinement and External Attention for Multivariate Time Series Forecasting

Multivariate time series forecasting plays a pivotal role in numerous real-world applications, including financial analysis, energy management, and traffic planning. While Transformer-based architectures have gained popularity for this task, recent studies reveal that simpler MLP-based models can achieve competitive or superior performance with significantly reduced computational cost. In this paper, we propose ITS-Mina, a novel all-MLP framework for multivariate time series forecasting that integrates three key innovations: (1) an iterative refinement mechanism that progressively enhances temporal representations by repeatedly applying a shared-parameter residual mixer stack, effectively deepening the model's computational capacity without multiplying the number of distinct parameters; (2) an external attention module that replaces traditional self-attention with learnable memory units, capturing cross-sample global dependencies at linear computational complexity; and (3) a Harris Hawks Optimization (HHO) algorithm for automatic dropout rate tuning, enabling adaptive regularization tailored to each dataset. Extensive experiments on six widely-used benchmark datasets demonstrate that ITS-Mina achieves state-of-the-art or highly competitive performance compared to eleven baseline models across multiple forecasting horizons.

cs.LG↗