Branched Latent Neural Maps
Branched Latent Neural Maps
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分支潜在神经图
DOI：
10.1016/j.cma.2023.116499
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发表时间：
2024
影响因子：
7.2
通讯作者：
Marsden, Alison Lesley
中科院分区：
文献类型：
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作者：
Salvador, Matteo;Marsden, Alison Lesley
摘要引入分支潜伏神经映射(BLNMs)来学习编码复杂物理过程的有限维输入输出映射。BLNM是由一个简单而紧凑的前馈部分连接神经网络定义的，它在结构上将具有不同内在作用的输入(如时间变量)从微分方程的模型参数中分离出来，同时将它们转换到一个通用的感兴趣领域。BLNMS利用潜在输出来增强学习的动力学，并通过在单个处理器上以小的训练数据集和短的训练时间表现出良好的分布泛化特性来增强学习的动力学和打破维度诅咒。事实上，无论在测试阶段采用何种离散化方法，它们的分布内泛化误差仍然具有可比性。此外，部分连接取代了完全连接的结构，大大减少了可调参数的数量。我们在一个具有挑战性的测试案例中展示了BLNMs的能力，该测试案例包括在一个患有左心发育不良综合征的儿童患者的双室心脏模型中进行生物物理详细的电生理学模拟。该模型包括用于快速传导的1D Purkinje网络和3D心脏-躯干几何图形。具体地说，我们在150个BLNM上进行了硅胶生成12导联心电图(ECG)的培训，同时跨越了7个模型参数，涵盖了细胞尺度、器官水平和电不同步。虽然12导联的ECG表现出非常快的动态和陡峭的梯度，但经过自动超参数调整后，最优的BLNM在单CPU上训练不到3h，仅保留7个隐含层和每层19个神经元。在包含50个附加电生理模拟的独立测试数据集上，产生的均方误差约为1 0−4。在在线阶段，BLNM允许在单核标准计算机上以5000倍的速度实时模拟心脏电生理学，并且可以在几秒钟的计算时间内通过全局优化来解决逆问题。为在工程应用中建立可靠、高效的数字孪生模型提供了一种新的计算工具。Julia的实现在麻省理工学院的许可下可以在https://github.上公开获得Com/StanfordCBCL/BLNM。Jl.
Abstract We introduce Branched Latent Neural Maps (BLNMs) to learn finite dimensional input–output maps encoding complex physical processes. A BLNM is defined by a simple and compact feedforward partially-connected neural network that structurally disentangles inputs with different intrinsic roles, such as the time variable from model parameters of a differential equation, while transferring them into a generic field of interest. BLNMs leverage latent outputs to enhance the learned dynamics and break the curse of dimensionality by showing excellent in-distribution generalization properties with small training datasets and short training times on a single processor. Indeed, their in-distribution generalization error remains comparable regardless of the adopted discretization during the testing phase. Moreover, the partial connections, in place of a fully-connected structure, significantly reduce the number of tunable parameters. We show the capabilities of BLNMs in a challenging test case involving biophysically detailed electrophysiology simulations in a biventricular cardiac model of a pediatric patient with hypoplastic left heart syndrome. The model includes a 1D Purkinje network for fast conduction and a 3D heart-torso geometry. Specifically, we trained BLNMs on 150 in silico generated 12-lead electrocardiograms (ECGs) while spanning 7 model parameters, covering cell-scale, organ-level and electrical dyssynchrony. Although the 12-lead ECGs manifest very fast dynamics with sharp gradients, after automatic hyperparameter tuning the optimal BLNM, trained in less than 3 h on a single CPU, retains just 7 hidden layers and 19 neurons per layer. The resulting mean square error is on the order of 1 0− 4 on an independent test dataset comprised of 50 additional electrophysiology simulations. In the online phase, the BLNM allows for 5000x faster real-time simulations of cardiac electrophysiology on a single core standard computer and can be employed to solve inverse problems via global optimization in a few seconds of computational time. This paper provides a novel computational tool to build reliable and efficient reduced-order models for digital twinning in engineering applications. The Julia implementation is publicly available under MIT License at https://github. com/StanfordCBCL/BLNM. jl.