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Topology optimization is used for the design of high-performance structures but remains fundamentally limited by its iterative nature, requiring repeated finite element analyses that prevent real-time deployment and large-scale design…

Computational Engineering, Finance, and Science · Computer Science 2026-04-07 Aaron Lutheran , Srijan Das , Alireza Tabarraei

Partial differential equations (PDEs) are fundamental for modeling complex physical systems, yet classical numerical solvers face prohibitive computational costs in high-dimensional and multi-scale regimes. While Transformer-based neural…

Machine Learning · Computer Science 2026-03-04 Pengyu Lai , Yixiao Chen , Dewu Yang , Rui Wang , Feng Wang , Hui Xu

Partial differential equations (PDEs) are central to describing complex physical system simulations. Their expensive solution techniques have led to an increased interest in deep neural network based surrogates. However, the practical…

Machine Learning · Computer Science 2022-11-17 Jayesh K. Gupta , Johannes Brandstetter

Inspired by the performance and scalability of autoregressive large language models (LLMs), transformer-based models have seen recent success in the visual domain. This study investigates a transformer adaptation for video prediction with a…

Computer Vision and Pattern Recognition · Computer Science 2025-10-24 Dean L Slack , G Thomas Hudson , Thomas Winterbottom , Noura Al Moubayed

Fast and accurate simulation of dynamical systems is a fundamental challenge across scientific and engineering domains. Traditional numerical integrators often face a trade-off between accuracy and computational efficiency, while existing…

Computational Engineering, Finance, and Science · Computer Science 2026-03-06 Jiaxin Yuan , Haizhao Yang , Maria Cameron

Solving partial differential equations (PDEs) by numerical methods meet computational cost challenge for getting the accurate solution since fine grids and small time steps are required. Machine learning can accelerate this process, but…

Numerical Analysis · Mathematics 2025-01-28 Qi Wang , Yuan Mi , Haoyun Wang , Yi Zhang , Ruizhi Chengze , Hongsheng Liu , Ji-Rong Wen , Hao Sun

Transformer has shown state-of-the-art performance on various applications and has recently emerged as a promising tool for surrogate modeling of partial differential equations (PDEs). Despite the introduction of linear-complexity…

Machine Learning · Computer Science 2023-11-06 Zijie Li , Dule Shu , Amir Barati Farimani

We present a unified framework for solving partial differential equations (PDEs) using video-inpainting diffusion transformer models. Unlike existing methods that devise specialized strategies for either forward or inverse problems under…

Machine Learning · Computer Science 2025-06-18 Edward Li , Zichen Wang , Jiahe Huang , Jeong Joon Park

Transformers enable powerful content-based global routing via self-attention, but they lack an explicit local geometric prior along the sequence axis. As a result, the placement of locality-inducing modules in hybrid architectures has…

Machine Learning · Computer Science 2026-02-17 Yukun Zhang , Xueqing Zhou

Developing fast surrogates for Partial Differential Equations (PDEs) will accelerate design and optimization in almost all scientific and engineering applications. Neural networks have been receiving ever-increasing attention and…

Machine Learning · Computer Science 2024-11-21 AmirPouya Hemmasian , Amir Barati Farimani

We introduce dense vision transformers, an architecture that leverages vision transformers in place of convolutional networks as a backbone for dense prediction tasks. We assemble tokens from various stages of the vision transformer into…

Computer Vision and Pattern Recognition · Computer Science 2021-03-26 René Ranftl , Alexey Bochkovskiy , Vladlen Koltun

Pretraining for partial differential equation (PDE) modeling has recently shown promise in scaling neural operators across datasets to improve generalizability and performance. Despite these advances, our understanding of how pretraining…

Machine Learning · Computer Science 2024-10-03 Anthony Zhou , Cooper Lorsung , AmirPouya Hemmasian , Amir Barati Farimani

Deep learning has emerged as a transformative tool for the neural surrogate modeling of partial differential equations (PDEs), known as neural PDE solvers. However, scaling these solvers to industrial-scale geometries with over $10^8$ cells…

Machine Learning · Computer Science 2026-02-06 Hang Zhou , Haixu Wu , Haonan Shangguan , Yuezhou Ma , Huikun Weng , Jianmin Wang , Mingsheng Long

The spatiotemporal resolution of Partial Differential Equations (PDEs) plays important roles in the mathematical description of the world's physical phenomena. In general, scientists and engineers solve PDEs numerically by the use of…

Artificial Intelligence · Computer Science 2023-06-29 Lucas Meyer , Marc Schouler , Robert Alexander Caulk , Alejandro Ribés , Bruno Raffin

Accurate and efficient simulations of physical phenomena governed by partial differential equations (PDEs) are important for scientific and engineering progress. While traditional numerical solvers are powerful, they are often…

Machine Learning · Computer Science 2025-11-13 Can Yang , Zhenzhong Wang , Junyuan Liu , Yunpeng Gong , Min Jiang

In recent years, augmentation of differentiable PDE solvers with neural networks has shown promising results, particularly in fluid simulations. However, most approaches rely on convolutional neural networks and custom solvers operating on…

Machine Learning · Computer Science 2025-02-27 Matthias Schulz , Gwendal Jouan , Daniel Berger , Stefan Gavranovic , Dirk Hartmann

Transformer models have emerged as potent solutions to a wide array of multidisciplinary challenges. The deployment of Transformer architectures is significantly hindered by their extensive computational and memory requirements,…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-07-03 Zhengxian Lu , Fangyu Wang , Zhiwei Xu , Fei Yang , Tao Li

Physics-informed neural network architectures have emerged as a powerful tool for developing flexible PDE solvers which easily assimilate data, but face challenges related to the PDE discretization underpinning them. By instead adapting a…

Numerical Analysis · Mathematics 2020-12-11 Ravi G. Patel , Indu Manickam , Nathaniel A. Trask , Mitchell A. Wood , Myoungkyu Lee , Ignacio Tomas , Eric C. Cyr

Neural operators, serving as physics surrogate models, have recently gained increased interest. With ever increasing problem complexity, the natural question arises: what is an efficient way to scale neural operators to larger and more…

Machine Learning · Computer Science 2025-02-28 Benedikt Alkin , Andreas Fürst , Simon Schmid , Lukas Gruber , Markus Holzleitner , Johannes Brandstetter

This document is a hands-on, comprehensive guide to deep learning in the realm of physical simulations. Rather than just theory, we emphasize practical application: every concept is paired with interactive Jupyter notebooks to get you up…

Machine Learning · Computer Science 2025-03-28 N. Thuerey , B. Holzschuh , P. Holl , G. Kohl , M. Lino , Q. Liu , P. Schnell , F. Trost