TY - M-10422
AU - Gotur, Goutam
AU - S, Chaitrashree
AU - Saravana Kumar, Dr.
TI - A Linear Algebra–Based Mathematical Model of Digital System Performance Using Neural Networks as Predictive Approximators
T2 - Scientific Research Journal of Science, Engineering and Technology

PY - 2026
VL - 4
IS - 1
SN - 2584-0584

AB - Modern digital systems exhibit complex performance characteristics, throughput, and tail latency that depend nonlinearly on workload features and resource constraints. Traditional linear models 𝐴𝑥 provide computational efficiency and interpretability but systematically underfit nonlinear phenomena such as cache thrashing, queueing saturation, and inter-resource contention, while black-box neural networks achieve superior accuracy through universal approximation but sacrifice causal interpretability and increase inference latency. This paper develops a hybrid framework decomposing performance prediction into an interpretable linear baseline plus compact neural residual: 𝑦(𝑥) = 𝐴𝑥 + 𝑓 (𝑥; 𝜃), where matrix 𝐴 ∈ ℝ𝑚×𝑛 encodes resource-to-metric contributions and feedforward network 𝑓 (1-3 layers, 32-256 neurons) learns systematic residuals 𝑟(𝑥) = 𝑓(𝑥) − 𝐴𝑥. Construction employs ridge regression or sparse optimization for 𝐴, staged training alternating between baseline initialization and residual learning, and complexity analysis showing 𝑂(nnz(𝐴)) + 𝑂(∑𝑑ℓ−1𝑑ℓ) inference cost. Across CPU scheduling and bandwidth prediction case studies, the hybrid achieves near-black-box accuracy (MSE: 0.014, MAE: 0.05) with linear efficiency (8.5k parameters, 0.18 ms inference) versus linear-only (MSE: 0.045) or large NN (200k parameters, 1.8 ms), supported by theoretical error bounds ∥ 𝐸(𝑥) ∥≤∥𝑓(𝑥) − 𝐴𝑥 ∥ +𝜖 and ablation studies confirming optimal interpretability-accuracy trade-offs. The linear-neural hybrid resolves fundamental modeling trade-offs, providing production-ready performance prediction with guaranteed error decomposition, staged training algorithms, and deployment strategies including sparsity constraints and online adaptation.

KW - Performance Modeling
KW - Linear Algebra
KW - Neural Networks
KW - Hybrid Models
KW - Predictive Approximators
KW - Digital Systems
KW - Machine Learning
KW - System Optimization
DO -