Gaussian processes regression is applied to augment experimental data of transfer-path analysis (TPA) by known information about the underlying physical properties of the system under investigation. The approach can be used as an alternative to model updating and is also applicable if no detailed simulation model of the system exists. For vibro-acoustic systems at least three features are known. Firstly, observable quantities fulfill a wave equation or a Helmholtz-like equation in the frequency domain. Secondly, the relation between pressure/stress and displacement/velocity/acceleration are known via constitutive relations involving mass density and elastic constants of the material. The latter also determine the propagation speed of waves. Thirdly, the geometry of the system is often known up to a certain accuracy. Here it is demonstrated that taking into account this information can potentially enhance TPA results and quantify their uncertainties at the same time. In particular this is the case for noisy measurement data and if material parameters and source distributions are (partly) unknown. Due to the probabilistic nature of the procedure unknown parameters can be estimated, making the method also applicable to material characterization as an inverse problem.
Physics-informed Gaussian Process Regression in Solving Eigenvalue Problem of Linear Operators
School of AI and Advanced Computing（人工智能与高级计算学院）；Xi’an Jiaotong Liverpool University（西安交通大学利物浦大学）；School of Physics, Engineering and Technology（物理、工程与技术学院）；University of York（约克大学）
Operator-Informed Gaussian Processes for Complex Helmholtz Wavefields: From Synthetic Benchmarks to In Vivo Brain Elastography
Department of Civil and Systems Engineering, Johns Hopkins University（约翰霍普金斯大学土木与系统工程系）；Department of Aerospace Engineering and Mechanics, University of Minnesota（明尼苏达大学航空航天工程与力学系）
