SineNet: Learning Temporal Dynamics in Time-Dependent Partial Differential Equations

1 code implementation • 28 Mar 2024 • Xuan Zhang, Jacob Helwig, Yuchao Lin, Yaochen Xie, Cong Fu, Stephan Wojtowytsch, Shuiwang Ji

While the U-Net architecture with skip connections is commonly used by prior studies to enable multi-scale processing, our analysis shows that the need for features to evolve across layers results in temporally misaligned features in skip connections, which limits the model's performance.

Artificial Intelligence for Science in Quantum, Atomistic, and Continuum Systems

1 code implementation • 17 Jul 2023 • Xuan Zhang, Limei Wang, Jacob Helwig, Youzhi Luo, Cong Fu, Yaochen Xie, Meng Liu, Yuchao Lin, Zhao Xu, Keqiang Yan, Keir Adams, Maurice Weiler, Xiner Li, Tianfan Fu, Yucheng Wang, Haiyang Yu, Yuqing Xie, Xiang Fu, Alex Strasser, Shenglong Xu, Yi Liu, Yuanqi Du, Alexandra Saxton, Hongyi Ling, Hannah Lawrence, Hannes Stärk, Shurui Gui, Carl Edwards, Nicholas Gao, Adriana Ladera, Tailin Wu, Elyssa F. Hofgard, Aria Mansouri Tehrani, Rui Wang, Ameya Daigavane, Montgomery Bohde, Jerry Kurtin, Qian Huang, Tuong Phung, Minkai Xu, Chaitanya K. Joshi, Simon V. Mathis, Kamyar Azizzadenesheli, Ada Fang, Alán Aspuru-Guzik, Erik Bekkers, Michael Bronstein, Marinka Zitnik, Anima Anandkumar, Stefano Ermon, Pietro Liò, Rose Yu, Stephan Günnemann, Jure Leskovec, Heng Ji, Jimeng Sun, Regina Barzilay, Tommi Jaakkola, Connor W. Coley, Xiaoning Qian, Xiaofeng Qian, Tess Smidt, Shuiwang Ji

Advances in artificial intelligence (AI) are fueling a new paradigm of discoveries in natural sciences.

Out-of-Distribution Generalization Transfer Learning +1

Group Equivariant Fourier Neural Operators for Partial Differential Equations

1 code implementation • 9 Jun 2023 • Jacob Helwig, Xuan Zhang, Cong Fu, Jerry Kurtin, Stephan Wojtowytsch, Shuiwang Ji

We consider solving partial differential equations (PDEs) with Fourier neural operators (FNOs), which operate in the frequency domain.