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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…
Extension and neural operator approximation of the electrical impedance tomography inverse map
Maarten V. de Hoop, Nikola B. Kovachki, Matti Lassas +1
This paper considers the problem of noise-robust neural operator approximation for the solution map of Calderón's inverse conductivity problem. In this continuum model of electrica…
Geometric Operator Learning with Optimal Transport
Xinyi Li, Zongyi Li, Nikola Kovachki +1
We propose integrating optimal transport (OT) into operator learning for partial differential equations (PDEs) on complex geometries. Classical geometric learning methods typically…
InverseBench: Benchmarking Plug-and-Play Diffusion Priors for Inverse Problems in Physical Sciences
Hongkai Zheng, Wenda Chu, Bingliang Zhang +9
Plug-and-play diffusion priors (PnPDP) have emerged as a promising research direction for solving inverse problems. However, current studies primarily focus on natural image restor…
Memorization and Regularization in Generative Diffusion Models
Ricardo Baptista, Agnimitra Dasgupta, Nikola B. Kovachki +2
Diffusion models have emerged as a powerful framework for generative modeling. At the heart of the methodology is score matching: learning gradients of families of log-densities fo…