State-space models are accurate and efficient neural operators for dynamical systems

• URL: http://arxiv.org/abs/2409.03231v1
• Date: Thu, 5 Sep 2024 03:57:28 GMT
• Title: State-space models are accurate and efficient neural operators for dynamical systems
• Authors: Zheyuan Hu, Nazanin Ahmadi Daryakenari, Qianli Shen, Kenji Kawaguchi, George Em Karniadakis,
• Abstract summary: Physics-informed machine learning (PIML) has emerged as a promising alternative to classical methods for predicting dynamical systems. Existing models, including recurrent neural networks (RNNs), transformers, and neural operators, face challenges such as long-time integration, long-range dependencies, chaotic dynamics, and extrapolation. This paper introduces state-space models implemented in Mamba for accurate and efficient dynamical system operator learning.
• Score: 23.59679792068364
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Physics-informed machine learning (PIML) has emerged as a promising alternative to classical methods for predicting dynamical systems, offering faster and more generalizable solutions. However, existing models, including recurrent neural networks (RNNs), transformers, and neural operators, face challenges such as long-time integration, long-range dependencies, chaotic dynamics, and extrapolation, to name a few. To this end, this paper introduces state-space models implemented in Mamba for accurate and efficient dynamical system operator learning. Mamba addresses the limitations of existing architectures by dynamically capturing long-range dependencies and enhancing computational efficiency through reparameterization techniques. To extensively test Mamba and compare against another 11 baselines, we introduce several strict extrapolation testbeds that go beyond the standard interpolation benchmarks. We demonstrate Mamba's superior performance in both interpolation and challenging extrapolation tasks. Mamba consistently ranks among the top models while maintaining the lowest computational cost and exceptional extrapolation capabilities. Moreover, we demonstrate the good performance of Mamba for a real-world application in quantitative systems pharmacology for assessing the efficacy of drugs in tumor growth under limited data scenarios. Taken together, our findings highlight Mamba's potential as a powerful tool for advancing scientific machine learning in dynamical systems modeling. (The code will be available at https://github.com/zheyuanhu01/State_Space_Model_Neural_Operator upon acceptance.)

Related papers

• MobileMamba: Lightweight Multi-Receptive Visual Mamba Network [51.33486891724516]
  Previous research on lightweight models has primarily focused on CNNs and Transformer-based designs. We propose the MobileMamba framework, which balances efficiency and performance. MobileMamba achieves up to 83.6% on Top-1, surpassing existing state-of-the-art methods.
  arXiv  Detail & Related papers  (2024-11-24T18:01:05Z)
• Mamba Policy: Towards Efficient 3D Diffusion Policy with Hybrid Selective State Models [20.956716048789474]
  Mamba model has emerged as a promising solution for efficient modeling. We propose the Mamba Policy, which reduces the parameter count by over 80% compared to the original policy network. Extensive experiments demonstrate that the Mamba Policy excels on the Adroit, Dexart, and MetaWorld datasets.
  arXiv  Detail & Related papers  (2024-09-11T10:21:21Z)
• Bidirectional Gated Mamba for Sequential Recommendation [56.85338055215429]
  Mamba, a recent advancement, has exhibited exceptional performance in time series prediction. We introduce a new framework named Selective Gated Mamba ( SIGMA) for Sequential Recommendation. Our results indicate that SIGMA outperforms current models on five real-world datasets.
  arXiv  Detail & Related papers  (2024-08-21T09:12:59Z)
• MambaVT: Spatio-Temporal Contextual Modeling for robust RGB-T Tracking [51.28485682954006]
  We propose a pure Mamba-based framework (MambaVT) to fully exploit intrinsic-temporal contextual modeling for robust visible-thermal tracking. Specifically, we devise the long-range cross-frame integration component to globally adapt to target appearance variations. Experiments show the significant potential of vision Mamba for RGB-T tracking, with MambaVT achieving state-of-the-art performance on four mainstream benchmarks.
  arXiv  Detail & Related papers  (2024-08-15T02:29:00Z)
• Mamba-Spike: Enhancing the Mamba Architecture with a Spiking Front-End for Efficient Temporal Data Processing [4.673285689826945]
  Mamba-Spike is a novel neuromorphic architecture that integrates a spiking front-end with the Mamba backbone to achieve efficient temporal data processing. The architecture consistently outperforms state-of-the-art baselines, achieving higher accuracy, lower latency, and improved energy efficiency.
  arXiv  Detail & Related papers  (2024-08-04T14:10:33Z)
• DeciMamba: Exploring the Length Extrapolation Potential of Mamba [89.07242846058023]
  We introduce DeciMamba, a context-extension method specifically designed for Mamba. We show that DeciMamba can extrapolate context lengths 25x longer than the ones seen during training, and does so without utilizing additional computational resources.
  arXiv  Detail & Related papers  (2024-06-20T17:40:18Z)
• Vision Mamba: A Comprehensive Survey and Taxonomy [11.025533218561284]
  State Space Model (SSM) is a mathematical model used to describe and analyze the behavior of dynamic systems. Based on the latest state-space models, Mamba merges time-varying parameters into SSMs and formulates a hardware-aware algorithm for efficient training and inference. Mamba is expected to become a new AI architecture that may outperform Transformer.
  arXiv  Detail & Related papers  (2024-05-07T15:30:14Z)
• MedMamba: Vision Mamba for Medical Image Classification [0.0]
  Vision transformers (ViTs) and convolutional neural networks (CNNs) have been extensively studied and widely used in medical image classification tasks. Recent studies have shown that state space models (SSMs) represented by Mamba can effectively model long-range dependencies. We propose MedMamba, the first Vision Mamba for generalized medical image classification.
  arXiv  Detail & Related papers  (2024-03-06T16:49:33Z)
• Swin-UMamba: Mamba-based UNet with ImageNet-based pretraining [85.08169822181685]
  This paper introduces a novel Mamba-based model, Swin-UMamba, designed specifically for medical image segmentation tasks. Swin-UMamba demonstrates superior performance with a large margin compared to CNNs, ViTs, and latest Mamba-based models.
  arXiv  Detail & Related papers  (2024-02-05T18:58:11Z)
• CoDBench: A Critical Evaluation of Data-driven Models for Continuous Dynamical Systems [8.410938527671341]
  We introduce CodBench, an exhaustive benchmarking suite comprising 11 state-of-the-art data-driven models for solving differential equations. Specifically, we evaluate 4 distinct categories of models, viz., feed forward neural networks, deep operator regression models, frequency-based neural operators, and transformer architectures. We conduct extensive experiments, assessing the operators' capabilities in learning, zero-shot super-resolution, data efficiency, robustness to noise, and computational efficiency.
  arXiv  Detail & Related papers  (2023-10-02T21:27:54Z)
• Gone Fishing: Neural Active Learning with Fisher Embeddings [55.08537975896764]
  There is an increasing need for active learning algorithms that are compatible with deep neural networks. This article introduces BAIT, a practical representation of tractable, and high-performing active learning algorithm for neural networks.
  arXiv  Detail & Related papers  (2021-06-17T17:26:31Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.