6 papers
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…
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…
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…
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…
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…
LazyDINO: Fast, scalable, and efficiently amortized Bayesian inversion via structure-exploiting and surrogate-driven measure transport
Lianghao Cao, Joshua Chen, Michael Brennan +3
We present LazyDINO, a transport map variational inference method for fast, scalable, and efficiently amortized solutions of high-dimensional nonlinear Bayesian inverse problems wi…