Scientific machine learning for model-form uncertainties in nonlinear computational mechanics

What is it about?

A novel probabilistic approach is presented for taking into account model uncertainties induced by modeling errors in parameterized high-fidelity computational models of nonlinear dynamical systems for which a parameterized reduced-order model has to be constructed in order to be in capability to solve the problem. Since the classical parametric-uncertainties methodology is not adapted and cannot be used, a nonparametric probabilistic approach is proposed, involving a non-Gaussian probability model of the reduced-order basis, which depends on hyperparameters, which are identified by solving a nonconvex optimization problem in high dimension. A novel approach is proposed for solving this optimization problem using a probabilistic learning recently proposed in the framework of scientific machine learning. A validation is presented in the area of nonlinear structural dynamics for a MEMS device.

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Why is it important?

Taking into account model-form uncertainties in high-fidelity comptational modeL. This problem cannot be solved with classical methods and numerical algorithms.