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Operator regression provides a powerful means of constructing discretization-invariant emulators for partial-differential equations (PDEs) describing physical systems. Neural operators specifically employ deep neural networks to approximate…

Machine Learning · Computer Science 2023-04-18 Katiana Kontolati , Somdatta Goswami , George Em Karniadakis , Michael D. Shields

This focused review explores a range of neural operator architectures for approximating solutions to parametric partial differential equations (PDEs), emphasizing high-level concepts and practical implementation strategies. The study covers…

Computational Engineering, Finance, and Science · Computer Science 2025-03-10 Prashant K. Jha

Neural networks are universal approximators that traditionally have been used to learn a map between function inputs and outputs. However, recent research has demonstrated that deep neural networks can be used to approximate operators,…

In the present work, we introduce a novel approach to enhance the precision of reduced order models by exploiting a multi-fidelity perspective and DeepONets. Reduced models provide a real-time numerical approximation by simplifying the…

Numerical Analysis · Mathematics 2023-11-21 Nicola Demo , Marco Tezzele , Gianluigi Rozza

Sparse Mixture-of-Experts (SMoE) architectures are widely used in large language models (LLMs) due to their computational efficiency. However, though only a few experts are activated for each token, SMoE still requires loading all expert…

Computation and Language · Computer Science 2025-09-15 Yixiao Zhou , Ziyu Zhao , Dongzhou Cheng , zhiliang wu , Jie Gui , Yi Yang , Fei Wu , Yu Cheng , Hehe Fan

In recent years, Mixture-of-Experts (MoE) has emerged as an effective approach for enhancing the capacity of deep neural network (DNN) with sub-linear computational costs. However, storing all experts on GPUs incurs significant memory…

Machine Learning · Computer Science 2025-03-11 Suraiya Tairin , Shohaib Mahmud , Haiying Shen , Anand Iyer

Accurately modeling and inferring solutions to time-dependent partial differential equations (PDEs) over extended horizons remains a core challenge in scientific machine learning. Traditional full rollout (FR) methods, which predict entire…

Machine Learning · Computer Science 2026-03-18 Luis Mandl , Dibyajyoti Nayak , Tim Ricken , Somdatta Goswami

Nonlinear physical phenomena often show complex multiscale interactions; motivated by the principles of multiscale modeling in scientific computing, we propose PAS-Net, a physics-informed Adaptive-Scale Deep Operator Network for learning…

Computational Physics · Physics 2025-11-20 Changhong Mou , Yeyu Zhang , Xuewen Zhu , Qiao Zhuang

The Mixture of Experts (MoE) architecture is an important method for scaling Large Language Models (LLMs). It increases model capacity while keeping computation cost low. However, the ultra-large MoE models still have hundreds of billions…

Artificial Intelligence · Computer Science 2025-10-01 Yixiao Chen , Yanyue Xie , Ruining Yang , Wei Jiang , Wei Wang , Yong He , Yue Chen , Pu Zhao , Yanzhi Wang

Human education system trains one student by multiple experts. Mixture-of-experts (MoE) is a powerful sparse architecture including multiple experts. However, sparse MoE model is easy to overfit, hard to deploy, and not hardware-friendly…

Machine Learning · Computer Science 2022-10-26 Fuzhao Xue , Xiaoxin He , Xiaozhe Ren , Yuxuan Lou , Yang You

Considering deep neural networks as manifold mappers, the pretrain-then-fine-tune paradigm can be interpreted as a two-stage process: pretrain establishes a broad knowledge base, and fine-tune adjusts the model parameters to activate…

This work demonstrates that neural operator learning provides a powerful and flexible framework for building fast, accurate emulators of moving boundary systems, enabling their integration into digital twin platforms. To this end, a Deep…

Machine Learning · Computer Science 2025-12-24 Marco A. Iglesias , Michael. E. Causon , Mikhail Y. Matveev , Andreas Endruweit , Michael . V. Tretyakov

Recently, Mixture-of-Experts (short as MoE) architecture has achieved remarkable success in increasing the model capacity of large-scale language models. However, MoE requires incorporating significantly more parameters than the base model…

Computation and Language · Computer Science 2022-10-14 Ze-Feng Gao , Peiyu Liu , Wayne Xin Zhao , Zhong-Yi Lu , Ji-Rong Wen

Sparse Mixture-of-Experts (MoE) is a neural architecture design that can be utilized to add learnable parameters to Large Language Models (LLMs) without increasing inference cost. Instruction tuning is a technique for training LLMs to…

Mixture-of-Experts (MoE) layers activate a subset of model weights, dubbed experts, to improve model performance. MoE is particularly promising for deployment on process-in-memory (PIM) architectures, because PIM can naturally fit experts…

Hardware Architecture · Computer Science 2026-02-12 Hanyuan Gao , Xiaoxuan Yang

Mixture-of-Experts (MoE) models mostly use a router to assign tokens to specific expert modules, activating only partial parameters and often outperforming dense models. We argue that the separation between the router's decision-making and…

Computation and Language · Computer Science 2025-06-02 Ang Lv , Ruobing Xie , Yining Qian , Songhao Wu , Xingwu Sun , Zhanhui Kang , Di Wang , Rui Yan

Particle-in-Cell (PIC) simulations are widely used for modeling plasma kinetics by tracking discrete particle dynamics. However, their computational cost remains prohibitively high, due to the need to simulate large numbers of particles to…

Computational Physics · Physics 2025-04-29 Jianhua Lv , Linlin Zhong

In this paper, we evaluate the effectiveness of deep operator networks (DeepONets) in solving both forward and inverse problems of partial differential equations (PDEs) on unknown manifolds. By unknown manifolds, we identify the manifold by…

Numerical Analysis · Mathematics 2024-07-09 Anran Jiao , Qile Yan , Jhn Harlim , Lu Lu

Recent advances in deep learning and large language models (LLMs) have facilitated the deployment of the mixture-of-experts (MoE) mechanism in the stock investment domain. While these models have demonstrated promising trading performance,…

Machine Learning · Computer Science 2025-01-20 Kuan-Ming Liu , Ming-Chih Lo

Mixture-of-Expert (MoE) models have obtained state-of-the-art performance in Neural Machine Translation (NMT) tasks. Existing works in MoE mostly consider a homogeneous design where the same number of experts of the same size are placed…