A data‐free, support vector machine‐based physics‐driven estimator for dynamic response computation

• Published in: Computer-aided civil and infrastructure engineering Vol. 38; no. 1; pp. 26 - 48
• Main Authors: Luo, Huan, Paal, Stephanie German
• Format: Journal Article
• Language: English
• Published: Hoboken Wiley Subscription Services, Inc 01.01.2023
• Subjects: Accuracy; Computation; Constraint modelling; Dynamic response; Dynamical systems; Equilibrium equations; Hyperplanes; Initial conditions; Machine learning; Nonlinear dynamics; Nonlinear response; Optimization; Physics; Regression models; Support vector machines; Training
• DOI: 10.1111/mice.12823
• ISSN: 1093-9687

Direct integration methods are widely used for dynamic response computation. However, the performance of their computational accuracy significantly degrades with increasing the time step. Although machine learning methods can address this shortcoming, they require training data for dynamic response computation. This paper proposes a novel computational method to overcome these shortcomings. The proposed approach is a data‐free physics‐driven estimator, which minimizes the objective function of multi‐output least squares support vector machines for regression to model parameters subject to physical constraints introduced by the multi‐degree of freedom system's dynamic equilibrium equations and initial conditions in the feature space, bypassing the need for training data (due to the coupled physics) and for satisfying the requirement of the time step due to the built‐in optimization procedure. A new efficient step‐by‐step solver is developed to solve the optimization problem, and the solution is equivalent to a hyperplane satisfying the physical constraints in the feature space. The extension of the proposed approach for nonlinear dynamic response computation is also analyzed theoretically. The numerical results demonstrate that the proposed approach provides the solution with higher accuracy and efficiency and achieves the best performance for large time steps over classical integration methods.