Generative learning of the solution of parametric partial differential equations using guided diffusion models and virtual observations
We introduce a generative learning framework to model high-dimensional parametric
systems using gradient guidance and virtual observations. We consider systems described …
systems using gradient guidance and virtual observations. We consider systems described …
Semi-supervised invertible neural operators for Bayesian inverse problems
S Kaltenbach, P Perdikaris… - Computational Mechanics, 2023 - Springer
Neural Operators offer a powerful, data-driven tool for solving parametric PDEs as they can
represent maps between infinite-dimensional function spaces. In this work, we employ …
represent maps between infinite-dimensional function spaces. In this work, we employ …
STENCIL-NET for equation-free forecasting from data
We present an artificial neural network architecture, termed STENCIL-NET, for equation-free
forecasting of spatiotemporal dynamics from data. STENCIL-NET works by learning a …
forecasting of spatiotemporal dynamics from data. STENCIL-NET works by learning a …
Fractional rheology-informed neural networks for data-driven identification of viscoelastic constitutive models
Developing constitutive models that can describe a complex fluid's response to an applied
stimulus has been one of the critical pursuits of rheologists. The complexity of the models …
stimulus has been one of the critical pursuits of rheologists. The complexity of the models …
Personalized predictions of Glioblastoma infiltration: Mathematical models, Physics-Informed Neural Networks and multimodal scans
Predicting the infiltration of Glioblastoma (GBM) from medical MRI scans is crucial for
understanding tumor growth dynamics and designing personalized radiotherapy treatment …
understanding tumor growth dynamics and designing personalized radiotherapy treatment …
Physics-informed neural networks for incompressible flows with moving boundaries
Physics-informed neural networks (PINNs) employed in fluid mechanics deal primarily with
stationary boundaries. This hinders the capability to address a wide range of flow problems …
stationary boundaries. This hinders the capability to address a wide range of flow problems …
Bilo: Bilevel local operator learning for pde inverse problems
RZ Zhang, X Xie, JS Lowengrub - arXiv preprint arXiv:2404.17789, 2024 - arxiv.org
We propose a new neural network based method for solving inverse problems for partial
differential equations (PDEs) by formulating the PDE inverse problem as a bilevel …
differential equations (PDEs) by formulating the PDE inverse problem as a bilevel …
Neural functional a posteriori error estimates
We propose a new loss function for supervised and physics-informed training of neural
networks and operators that incorporates a posteriori error estimate. More specifically …
networks and operators that incorporates a posteriori error estimate. More specifically …
Flow reconstruction by multiresolution optimization of a discrete loss with automatic differentiation
We present a potent computational method for the solution of inverse problems in fluid
mechanics. We consider inverse problems formulated in terms of a deterministic loss …
mechanics. We consider inverse problems formulated in terms of a deterministic loss …
Electromagnetic-thermal analysis with FDTD and physics-informed neural networks
This article presents the coupling of the finite-difference time-domain (FDTD) method for
electromagnetic field simulation, with a physics-informed neural network based solver for the …
electromagnetic field simulation, with a physics-informed neural network based solver for the …