We implemented the 2D, and 3D customized CUDA kernel of the triple backward grid sampler that supports cosine, linear, and smoothstep kernel (Thomas Müller) and third-order gradients $u_{xxc}, u_{yyc}$ with second-order gradients (Tymoteusz Bleja). As a result, the runtime and the memory requirement were significantly reduced. It is used in https://github.com/NamGyuKang/PIXEL
The code is tested with Python3 environment (3.8, 3.9, 3.10) and PyTorch (1.11, 1.12, 2.7.1) with CUDA (11.3, 11.8). Please make sure PyTorch is installed before installing CosineSampler. Please run the following command to install it.
pip install . --no-build-isolationor
pip install git+https://github.com/NamGyuKang/CosineSampler.gitPlease make sure that ninja-build and gcc are installed. Errors may occur otherwise.
You can choose the kernel (cosine, linear, smoothstep), and the multicell (True, False). The multicell is used in PIXEL (Physics-Informed Cell Representation), and if you set the multicell False, and linear kernel, it is the same with Pytorch grid_sample and our CosineSampler support triple backpropagation of kernel.
Second-order PDE (Helmholtz equation)
If you use this code for research, please consider citing:
@article{kang2023pixel,
title={PIXEL: Physics-Informed Cell Representations for Fast and Accurate PDE Solvers},
author={Kang, Namgyu and Lee, Byeonghyeon and Hong, Youngjoon and Yun, Seok-Bae and Park, Eunbyung},
journal={Proceedings of the AAAI Conference on Artificial Intelligence},
year={2023}}