P3D: Scalable Neural Surrogates for High-Resolution 3D Physics Simulations with Global Context

2025-09-12

AI Summary

This work addresses the challenges of modeling global dependencies and high computational cost in high-resolution 3D physical field simulation. Methodologically, we propose a scalable CNN-Transformer hybrid neural surrogate model featuring a local pretraining + global solution fusion architecture, incorporating sequence-to-sequence modeling and diffusion-based priors to jointly enable deterministic prediction and uncertainty quantification; the model supports 512³ ultra-resolution simulations and captures long-range physical dependencies. Contributions: (i) First systematic generalization evaluation of neural surrogates across 14 classes of 3D partial differential equations; (ii) Significant improvements over state-of-the-art baselines—accurately reproducing key statistical properties in isotropic turbulence and multi-Reynolds-number 3D channel flow; (iii) Establishing an efficient, scalable, end-to-end modeling paradigm for large-scale scientific computing.

Technology Category

• Machine Learning: Large Multimodal Models (LMMs)
• Search and Optimization: Sampling/Simulation-based Search
• Computer Vision: 3D Computer Vision

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

We present a scalable framework for learning deterministic and probabilistic neural surrogates for high-resolution 3D physics simulations. We introduce a hybrid CNN-Transformer backbone architecture targeted for 3D physics simulations, which significantly outperforms existing architectures in terms of speed and accuracy. Our proposed network can be pretrained on small patches of the simulation domain, which can be fused to obtain a global solution, optionally guided via a fast and scalable sequence-to-sequence model to include long-range dependencies. This setup allows for training large-scale models with reduced memory and compute requirements for high-resolution datasets. We evaluate our backbone architecture against a large set of baseline methods with the objective to simultaneously learn the dynamics of 14 different types of PDEs in 3D. We demonstrate how to scale our model to high-resolution isotropic turbulence with spatial resolutions of up to $512^3$. Finally, we demonstrate the versatility of our network by training it as a diffusion model to produce probabilistic samples of highly turbulent 3D channel flows across varying Reynolds numbers, accurately capturing the underlying flow statistics.

Problem

• Develop scalable neural surrogates for high-resolution 3D physics simulations
• Learn dynamics of 14 different PDE types in 3D simultaneously
• Capture turbulent flow statistics across varying Reynolds numbers

Innovation

• Hybrid CNN-Transformer architecture for 3D physics
• Patch-based pretraining with global fusion
• Scalable diffusion model for turbulent flows