Learning-informed parameter identification in nonlinear time-dependent PDEs
Applied Mathematics & Optimization, 2023•Springer
We introduce and analyze a method of learning-informed parameter identification for partial
differential equations (PDEs) in an all-at-once framework. The underlying PDE model is
formulated in a rather general setting with three unknowns: physical parameter, state and
nonlinearity. Inspired by advances in machine learning, we approximate the nonlinearity via
a neural network, whose parameters are learned from measurement data. The latter is
assumed to be given as noisy observations of the unknown state, and both the state and the …
differential equations (PDEs) in an all-at-once framework. The underlying PDE model is
formulated in a rather general setting with three unknowns: physical parameter, state and
nonlinearity. Inspired by advances in machine learning, we approximate the nonlinearity via
a neural network, whose parameters are learned from measurement data. The latter is
assumed to be given as noisy observations of the unknown state, and both the state and the …
Abstract
We introduce and analyze a method of learning-informed parameter identification for partial differential equations (PDEs) in an all-at-once framework. The underlying PDE model is formulated in a rather general setting with three unknowns: physical parameter, state and nonlinearity. Inspired by advances in machine learning, we approximate the nonlinearity via a neural network, whose parameters are learned from measurement data. The latter is assumed to be given as noisy observations of the unknown state, and both the state and the physical parameters are identified simultaneously with the parameters of the neural network. Moreover, diverging from the classical approach, the proposed all-at-once setting avoids constructing the parameter-to-state map by explicitly handling the state as additional variable. The practical feasibility of the proposed method is confirmed with experiments using two different algorithmic settings: A function-space algorithm based on analytic adjoints as well as a purely discretized setting using standard machine learning algorithms.
Springer
以上显示的是最相近的搜索结果。 查看全部搜索结果