Active Learning for Neural PDE Solvers
Solving partial differential equations (PDEs) is a fundamental problem in engineering and
science. While neural PDE solvers can be more efficient than established numerical solvers …
science. While neural PDE solvers can be more efficient than established numerical solvers …
Zero-Shot Uncertainty Quantification using Diffusion Probabilistic Models
D Shu, AB Farimani - arXiv preprint arXiv:2408.04718, 2024 - arxiv.org
The success of diffusion probabilistic models in generative tasks, such as text-to-image
generation, has motivated the exploration of their application to regression problems …
generation, has motivated the exploration of their application to regression problems …
Generalization Error Estimates of Machine Learning Methods for Solving High Dimensional Schr\" odinger Eigenvalue Problems
H Yu, Y Guo, P Ming - arXiv preprint arXiv:2408.13511, 2024 - arxiv.org
We propose a machine learning method for computing eigenvalues and eigenfunctions of
the Schr\" odinger operator on a $ d $-dimensional hypercube with Dirichlet boundary …
the Schr\" odinger operator on a $ d $-dimensional hypercube with Dirichlet boundary …