ICML 2023 Papers

Neural networks have shown great potential in accelerating the solution of partial differential equations (PDEs). Recently, there has been a growing interest in introducing physics constraints into training neural PDE solvers to reduce the use of costly data and improve the generalization ability. However, these physics constraints, based on certain finite dimensional approximations over the function space, must resolve the smallest scaled physics to ensure the accuracy and stability of the simulation, resulting in high computational costs from large input, output, and neural networks. This paper proposes a general acceleration methodology called NeuralStagger by spatially and temporally decomposing the original learning tasks into several coarser-resolution subtasks. We define a coarse-resolution neural solver for each subtask, which requires fewer computational resources, and jointly train them with the vanilla physics-constrained loss by simply arranging their outputs to reconstruct the original solution. Due to the perfect parallelism between them, the solution is achieved as fast as a coarse-resolution neural solver. In addition, the trained solvers bring the flexibility of simulating with multiple levels of resolution. We demonstrate the successful application of NeuralStagger on 2D and 3D fluid dynamics simulations, which leads to an additional $10\sim100\times$ speed-up. Moreover, the experiment also shows that the learned model could be well used for optimal control.

Fourier Neural Operators (FNOs) have proven to be an efficient and effective method for resolution-independent operator learning in a broad variety of application areas across scientific machine learning. A key reason for their success is their ability to accurately model long-range dependencies in spatio-temporal data by learning global convolutions in a computationally efficient manner. To this end, FNOs rely on the discrete Fourier transform (DFT), however, DFTs cause visual and spectral artifacts as well as pronounced dissipation when learning operators in spherical coordinates by incorrectly assuming flat geometry. To overcome this limitation, we generalize FNOs on the sphere, introducing Spherical FNOs (SFNOs) for learning operators on spherical geometries. We apply SFNOs to forecasting atmo- spheric dynamics, and demonstrate stable autoregressive rollouts for a year of simulated time (1,460 steps), while retaining physically plausible dynamics. The SFNO has important implications for machine learning-based simulation of climate dynamics that could eventually help accelerate our response to climate change.

Reasoning is the crux of intellectual thinking. While question answering (QA) tasks are prolific with various computational models and benchmark datasets, they mostly tackle factoid or shallow QA without asking deeper understanding. Dual process theory asserts that human reasoning consists of associative thinking to collect relevant pieces of knowledge and logical reasoning to consciously conclude grounding on evidential rationale. Based on our intensive think-aloud study that revealed the three types of questions: surface, testing, and deep questions, we first propose the QASA benchmark that consists of 1798 novel question answering pairs that require full-stack reasoning on scientific articles in AI and ML fields. Then we propose the QASA approach that tackles the full-stack reasoning with large language models via associative selection, evidential rationale-generation, and systematic composition. Our experimental results show that QASA's full-stack inference outperforms the state-of-the-art InstructGPT by a big margin. We also find that rationale-generation is critical for the performance gain, claiming how we should rethink advanced question answering. The dataset is available at https://github.com/lgresearch/QASA.