联合科学机器学习用于近似函数和用数据异质性解决微分方程.
联合学习与科学机器学习 (SciML) 结合,在分布式,私有数据上训练模型,用于解决微分方程. 新的联合模型 (FedPINNs,FedDeepONets) 与集中式方法相比,显示出具有竞争力的准确性.
科学领域:
- 科学机器学习 (SciML) 是指科学机器学习.
- 联合学习 (FL)
- 数字分析 数字分析
背景情况:
- 由部分微分方程 (PDEs) 控制的复杂问题通常涉及分布式或私有数据,阻碍了传统的机器学习方法.
- 联合学习 (FL) 为协作模式培训提供了去中心化的解决方案,同时保护数据隐私,解决数据孤岛和传输限制的挑战.
研究的目的:
- 探索FL和SciML的集成,以近似复杂函数和解决微分方程.
- 提出新的联合模型,联合物理信息神经网络 (FedPINNs) 和联合深层运营商网络 (FedDeepONets).
- 调查数据异质性对联合模型性能的影响,并为权重差异制定理论界限.
主要方法:
- 开发了两个新的联合模式:FedPINNs和FedDeepONets.
- 实施数据生成方法来控制非i.i.d. 数据和利用1瓦斯斯坦距离来量化数据异质性.
- 关于加权差异测量和FL增长边界理论框架的建议.
主要成果:
- 与仅在本地数据上训练的模型相比,联合方法显示出更高的性能.
- 拟议的FedPINNs和FedDeepONets实现了相对于所有可用数据上训练的集中模型的竞争性准确性.
- 系统调查揭示了数据异质性与联合模型性能之间的关系.
结论:
- FL和SciML的整合为解决分布式和私有数据的复杂问题提供了有效的框架.
- 新的FedPINNs和FedDeepONets模型为函数近似和PDE解决的集中训练提供了一种保护隐私和高效的替代方案.
- 该研究提供了对FL重量差异及其对模型性能影响的理论理解.
更多相关视频
08:51Author Spotlight: Integrated Multi-Omics Analysis for Unveiling Multicellular Immune Signatures in Clinical Heart Attack Cohorts
Published on: September 20, 2024
09:20Lumped-Parameter and Finite Element Modeling of Heart Failure with Preserved Ejection Fraction
Published on: February 13, 2021
相关概念视频
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
Linear Approximation in Time Domain
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
Linear Approximation in Frequency Domain
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
Model Approaches for Pharmacokinetic Data: Distributed Parameter Models
The distributed parameter models are specifically designed to account for variations and differences in some drug classes. This model is particularly useful for assessing regional concentrations of anticancer or...
Mechanistic Models: Compartment Models in Individual and Population Analysis
Ampere-Maxwell's Law: Problem-Solving
To solve the problem, we can use the equations from the analysis of an RC circuit and Maxwell's version of Ampère's law.
For the first part of...
