Specialized Interior-Point Algorithm for Stable Nonlinear System Identification
TL;DR: In this article, a path-following interior-point algorithm is proposed to estimate nonlinear dynamic models from data, which takes advantage of the structure of the data and reduces computational complexity from cubic to linear growth.
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Abstract: Estimation of nonlinear dynamic models from data poses many challenges, including model instability and nonconvexity of long-term simulation fidelity. Recently Lagrangian relaxation has been proposed as a method to approximate simulation fidelity and guarantee stability via semidefinite programming (SDP); however, the resulting SDPs have large dimension, limiting their utility in practical problems. In this paper, we develop a path-following interior-point algorithm that takes advantage of special structure in the problem and reduces computational complexity from cubic to linear growth with the length of the dataset. The new algorithm enables empirical comparisons to established methods including nonlinear autoregressive models with exogenous inputs, and we demonstrate superior generalization to new data. We also explore the “regularizing” effect of stability constraints as an alternative to regressor subset selection.
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Figures
TABLE I: Parameter values for Algorithm 1. 
Fig. 5: Comparison of proposed method (LR) to various nonlinear ARX models; c.f. Section VI-C for a complete description of the models and methods. The percentages at infinite error denote the proportion of trials for which the simulated model diverged. 
TABLE VI: Frequency with which certain nonlinear regressors were chosen by Matlab’s subset selection algorithm (i.e. nlreg set to search) during the 30 experimental trials depicted in Figure 5. 
Fig. 6: Simulated performance on validation data for one of the trials in Figure 5. LR denotes a 4th order state-space model fit with our proposed algorithm. Sigmoid∗ denotes a nonlinear ARX model with sigmoid net nonlinearity and regressors chosen automatically by Matlab’s subset selection algorithm; see Section VI-C for details. Normalized simulation error for LR and Sigmoid∗ are 2.02× 10−2 and 3.71× 10−2, respectively. 
TABLE V: Computation times (in seconds, to 3 sig. fig.) for the methods applied in the 30 experimental trials depicted in Figure 5. 
TABLE II: Normalized difference between solutions from our specialized algorithm, θs, and a primal-dual IPM (Mosek), θpd, i.e., (Ĵλ(θpd) − Ĵλ(θ s))/Ĵλ(θ pd). Model refers to the degree of the polynomials (e, f, g). The first column denotes the dataset length T . Five trials were conducted per configuration; the worst (i.e. lowest/most negative) result is recorded.
Citations
Design of neuro-swarming-based heuristics to solve the third-order nonlinear multi-singular Emden–Fowler equation
Zulqurnain Sabir,Muhammad Asif Zahoor Raja,Muhammad Asif Zahoor Raja,Muhammad Umar,Muhammad Shoaib +4 more
TL;DR: The proposed ANN-PSO-IPS is implemented for four variants of TONMS-EFEs, and comparison with exact solutions relieved its robustness, correctness and effectiveness, which is further authenticated through statistical explorations.
134
A Neuro-Swarming Intelligence-Based Computing for Second Order Singular Periodic Non-linear Boundary Value Problems
Zulqurnain Sabir,Muhammad Asif Zahoor Raja,Muhammad Asif Zahoor Raja,Juan Luis García Guirao,Muhammad Shoaib +4 more
TL;DR: A novel neuro-swarming intelligence-based numerical computing solver is developed for solving second order non-linear singular periodic (NSP) boundary value problems (BVPs), i.e., ANN-PSO-IPS, which is compared with the available exact solutions to establish the worth of the solver in terms of accuracy and convergence.
Integrated neuro-swarm heuristic with interior-point for nonlinear SITR model for dynamics of novel COVID-19
Muhammad Umar,Zulqurnain Sabir,Muhammad Asif Zahoor Raja,Muhammad Asif Zahoor Raja,Fazli Amin,Tareq Saeed,Yolanda Guerrero-Sánchez +6 more
TL;DR: In this paper, the authors presented a novel design of intelligent solvers with a neuro-swarm heuristic integrated with interior-point algorithm (IPA) for the numerical investigations of the nonlinear SITR fractal system based on the dynamics of a novel coronavirus (COVID-19).
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Neuro-swarm intelligent computing paradigm for nonlinear HIV infection model with CD4+ T-cells
Muhammad Umar,Zulqurnain Sabir,Muhammad Asif Zahoor Raja,Muhammad Asif Zahoor Raja,J. F. Gómez Aguilar,Fazli Amin,Muhammad Shoaib +6 more
TL;DR: In this article, an efficient computing approach is applied to solve Human Immunodeficiency Virus (HIV) infection spread, which involves CD4+ T-cells by feed-forward artificial neural networks (FF-ANNs) trained with particle swarm optimization (PSO) and interior point method (IPM).
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A Convex Parameterization of Robust Recurrent Neural Networks
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TL;DR: In this paper, convex sets of RNNs with stability and robustness guarantees are derived using incremental quadratic constraints and can ensure global exponential stability of all solutions, and bounds on incremental Lipschitz constant of the learned sequence-to-sequence mapping.
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