7 papers
Real-time inverse solutions via neural matrix operators
Julie Pham, Thomas O'Leary-Roseberry, Omar Ghattas +1
Rapid data assimilation is required for real-time prediction and control in digital twins. For many physical systems, the data assimilation task requires the solution of a physics-…
Performance of Neural and Polynomial Operator Surrogates
Josephine Westermann, Benno Huber, Thomas O'Leary-Roseberry +1
We consider the problem of constructing surrogate operators for parameter-to-solution maps arising from parametric partial differential equations, where repeated forward model eval…
Derivative-Informed Fourier Neural Operator: Universal Approximation and Applications to PDE-Constrained Optimization
Boyuan Yao, Dingcheng Luo, Lianghao Cao +3
We present approximation theories and efficient training methods for derivative-informed Fourier neural operators (DIFNOs) with applications to PDE-constrained optimization. A DIFN…
Shape Derivative-Informed Neural Operators with Application to Risk-Averse Shape Optimization
Xindi Gong, Dingcheng Luo, Thomas O'Leary-Roseberry +2
Shape optimization under uncertainty (OUU) is computationally intensive for classical PDE-based methods due to the high cost of repeated sampling-based risk evaluation across many…
Verification and Validation for Trustworthy Scientific Machine Learning
John D. Jakeman, Lorena A. Barba, Joaquim R. R. A. Martins +1
Scientific machine learning (SciML) models are transforming many scientific disciplines. However, the development of good modeling practices to increase the trustworthiness of SciM…
Dimension reduction for derivative-informed operator learning: An analysis of approximation errors
Dingcheng Luo, Thomas O'Leary-Roseberry, Peng Chen +1
We study the derivative-informed learning of nonlinear operators between infinite-dimensional separable Hilbert spaces by neural networks. Such operators can arise from the solutio…