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Related papers: Autoregressive Renaissance in Neural PDE Solvers

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Physics-informed deep learning often faces optimization challenges due to the complexity of solving partial differential equations (PDEs), which involve exploring large solution spaces, require numerous iterations, and can lead to unstable…

Recent advances in deep learning have inspired numerous works on data-driven solutions to partial differential equation (PDE) problems. These neural PDE solvers can often be much faster than their numerical counterparts; however, each…

Machine Learning · Computer Science 2025-02-06 Anthony Zhou , Zijie Li , Michael Schneier , John R Buchanan , Amir Barati Farimani

We propose a conditional non-autoregressive neural sequence model based on iterative refinement. The proposed model is designed based on the principles of latent variable models and denoising autoencoders, and is generally applicable to any…

Machine Learning · Computer Science 2018-08-29 Jason Lee , Elman Mansimov , Kyunghyun Cho

We present a graph neural network model for solving graph-to-graph learning problems. Most deep learning on graphs considers ``simple'' problems such as graph classification or regressing real-valued graph properties. For such tasks, the…

Machine Learning · Computer Science 2021-06-08 Guan Wang , Francois Bernard Lauze , Aasa Feragen

Deep learning-based partial differential equation(PDE) solvers have received much attention in the past few years. Methods of this category can solve a wide range of PDEs with high accuracy, typically by transforming the problems into…

Numerical Analysis · Mathematics 2024-07-23 Ramesh Chandra Sau , Luowei Yin

We present Mechanistic PDE Networks -- a model for discovery of governing partial differential equations from data. Mechanistic PDE Networks represent spatiotemporal data as space-time dependent linear partial differential equations in…

Machine Learning · Computer Science 2025-06-12 Adeel Pervez , Efstratios Gavves , Francesco Locatello

Partial differential equations (PDEs) govern nearly every physical process in science and engineering, yet solving them at scale remains prohibitively expensive. Generative AI has transformed language, vision, and protein science, but…

Machine Learning · Computer Science 2026-04-10 Yilong Dai , Shengyu Chen , Xiaowei Jia , Runlong Yu

As an alternative to classical numerical solvers for partial differential equations (PDEs) subject to boundary value constraints, there has been a surge of interest in investigating neural networks that can solve such problems efficiently.…

Machine Learning · Computer Science 2023-08-21 Winfried Lötzsch , Simon Ohler , Johannes S. Otterbach

We present an approach based on feed-forward neural networks for learning the distribution of textual documents. This approach is inspired by the Neural Autoregressive Distribution Estimator(NADE) model, which has been shown to be a good…

Machine Learning · Computer Science 2016-03-21 Stanislas Lauly , Yin Zheng , Alexandre Allauzen , Hugo Larochelle

Several recent papers have proposed increasing the expressive power of graph neural networks by exploiting subgraphs or other topological structures. In parallel, researchers have investigated higher order permutation equivariant networks.…

Machine Learning · Statistics 2026-02-05 Andrew Hands , Tianyi Sun , Risi Kondor

Neural networks have emerged as promising tools for solving partial differential equations (PDEs), particularly through the application of neural operators. Training neural operators typically requires a large amount of training data to…

Machine Learning · Computer Science 2025-01-27 Chaoyu Liu , Chris Budd , Carola-Bibiane Schönlieb

Neural networks have shown promising potential in accelerating the numerical simulation of systems governed by partial differential equations (PDEs). Different from many existing neural network surrogates operating on high-dimensional…

Machine Learning · Computer Science 2025-01-09 Zijie Li , Saurabh Patil , Francis Ogoke , Dule Shu , Wilson Zhen , Michael Schneier , John R. Buchanan, , Amir Barati Farimani

Autoregressive and recurrent networks have achieved remarkable progress across various fields, from weather forecasting to molecular generation and Large Language Models. Despite their strong predictive capabilities, these models lack a…

Machine Learning · Computer Science 2025-07-22 Dario Coscia , Max Welling , Nicola Demo , Gianluigi Rozza

Solving partial differential equations (PDEs) serves as a cornerstone for modeling complex dynamical systems. Recent progresses have demonstrated grand benefits of data-driven neural-based models for predicting spatiotemporal dynamics…

Machine Learning · Computer Science 2025-03-04 Bocheng Zeng , Qi Wang , Mengtao Yan , Yang Liu , Ruizhi Chengze , Yi Zhang , Hongsheng Liu , Zidong Wang , Hao Sun

Deep autoregressive sequence-to-sequence models have demonstrated impressive performance across a wide variety of tasks in recent years. While common architecture classes such as recurrent, convolutional, and self-attention networks make…

Machine Learning · Computer Science 2018-11-09 Mitchell Stern , Noam Shazeer , Jakob Uszkoreit

We introduce the Autoregressive PDE Emulator Benchmark (APEBench), a comprehensive benchmark suite to evaluate autoregressive neural emulators for solving partial differential equations. APEBench is based on JAX and provides a seamlessly…

Machine Learning · Computer Science 2024-11-04 Felix Koehler , Simon Niedermayr , Rüdiger Westermann , Nils Thuerey

Finding accurate solutions to partial differential equations (PDEs) is a crucial task in all scientific and engineering disciplines. It has recently been shown that machine learning methods can improve the solution accuracy by correcting…

Computational Physics · Physics 2021-01-06 Kiwon Um , Robert Brand , Yun , Fei , Philipp Holl , Nils Thuerey

Recent advances in neural models have shown considerable promise in solving Traveling Salesman Problems (TSPs) without relying on much hand-crafted engineering. However, while non-autoregressive (NAR) approaches benefit from faster…

Machine Learning · Computer Science 2025-01-24 Mingzhao Wang , You Zhou , Zhiguang Cao , Yubin Xiao , Xuan Wu , Wei Pang , Yuan Jiang , Hui Yang , Peng Zhao , Yuanshu Li

Multiphysics problems such as multicomponent diffusion, phase transformations in multiphase systems and alloy solidification involve numerical solution of a coupled system of nonlinear partial differential equations (PDEs). Numerical…

Materials Science · Physics 2022-11-24 Vir Karan , A. Maruthi Indresh , Saswata Bhattacharyya

Large sparse symmetric linear systems appear in several branches of science and engineering thanks to the widespread use of the finite element method (FEM). The fastest sparse linear solvers available implement hybrid iterative methods.…

Machine Learning · Computer Science 2022-03-15 Luca Grementieri , Paolo Galeone