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Poster
Learning to Accelerate Partial Differential Equations via Latent Global Evolution
Tailin Wu · Takashi Maruyama · Jure Leskovec

Wed Nov 30 02:00 PM -- 04:00 PM (PST) @ Hall J #921
in Poster Session 4 »

Simulating the time evolution of Partial Differential Equations (PDEs) of large-scale systems is crucial in many scientific and engineering domains such as fluid dynamics, weather forecasting and their inverse optimization problems. However, both classical solvers and recent deep learning-based surrogate models are typically extremely computationally intensive, because of their local evolution: they need to update the state of each discretized cell at each time step during inference. Here we develop Latent Evolution of PDEs (LE-PDE), a simple, fast and scalable method to accelerate the simulation and inverse optimization of PDEs. LE-PDE learns a compact, global representation of the system and efficiently evolves it fully in the latent space with learned latent evolution models. LE-PDE achieves speedup by having a much smaller latent dimension to update during long rollout as compared to updating in the input space. We introduce new learning objectives to effectively learn such latent dynamics to ensure long-term stability. We further introduce techniques for speeding-up inverse optimization of boundary conditions for PDEs via backpropagation through time in latent space, and an annealing technique to address the non-differentiability and sparse interaction of boundary conditions. We test our method in a 1D benchmark of nonlinear PDEs, 2D Navier-Stokes flows into turbulent phase and an inverse optimization of boundary conditions in 2D Navier-Stokes flow. Compared to state-of-the-art deep learning-based surrogate models and other strong baselines, we demonstrate up to 128x reduction in the dimensions to update, and up to 15x improvement in speed, while achieving competitive accuracy.

Keywords: Partial Differential Equation · inverse optimization · accelerate · latent global evolution
[ Paper]  [ Slides]  [ Poster]  [ OpenReview] 

Author Information

Tailin Wu (Stanford)
Tailin Wu

Tailin Wu is a postdoc researcher in the Department of Computer Science at Stanford University, working with professor Jure Leskovec. His research interests lies in AI for large-scale simulations of complex systems, AI for scientific discovery, and representation learning

Takashi Maruyama (NEC Corporation)

Research engineer @ NEC Corporation Japan.

Jure Leskovec (Stanford University/Pinterest)

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