Interval and fuzzy physics-informed neural networks for uncertain fields

Temporally and spatially dependent uncertain parameters are regularly encountered in engineering applications. Commonly these uncertainties accounted for using random fields processes, which require knowledge about the appearing probability distributions functions that is not readily available. In cases non-probabilistic approaches such as interval analysis fuzzy set theory helpful to analyze uncertainty. Partial differential equations involving traditionally solved finite element method where input sampled some basis function expansion methods. This approach however relies on information spatial correlation of fields, always obtainable. this work we utilize physics-informed neural networks (PINNs) solve partial equations. The resulting network structures termed (iPINNs) (fPINNs) show promising results obtaining bounded solutions and/or temporally parameter fields. contrast approaches, no length specification well Monte-Carlo simulations necessary. fact, obtained directly a byproduct presented solution scheme. Furthermore, all major advantages PINNs retained, i.e. meshfree nature scheme, ease inverse problem set-up. • Fuzzy measures useful uncertainty measures. (fPINN iPINN) proposed. fPINN iPINN able PDEs No specification/ Information field proposed