Cubature Kalman Filter Based Training of Hybrid Differential Equation Recurrent Neural Network Physiological Dynamic Models.
Cubature Kalman Filter Based Training of Hybrid Differential Equation Recurrent Neural Network Physiological Dynamic Models.
复制标题
基于Cuature卡尔曼滤波器的混合微分方程递归神经网络生理动态模型的训练。
DOI：
10.1109/embc46164.2021.9631038
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Erdogmus,Deniz
中科院分区：
文献类型：
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作者：
Demirkaya,Ahmet;Imbiriba,Tales;Lockwood,Kyle;Rampersad,Sumientra;Alhajjar,Elie;Guidoboni,Giovanna;Danziger,Zachary;Erdogmus,Deniz
生物动力学系统的建模是具有挑战性的，由于不同的系统组件的相互依赖性，其中一些还没有完全理解。为了填补现有的差距，我们的能力，机械建模生理系统，我们建议将联合收割机神经网络与基于物理的模型。具体来说，我们演示了如何使用贝叶斯滤波技术来训练模型参数并同时估计动态状态变量，从而近似缺失的常微分方程（ODE）与已知的ODE。作为一个研究案例，我们利用一个很好理解的人类视网膜血液循环模型，并用神经网络近似代替其核心常微分方程之一，代表我们对生理状态动力学不完全了解的情况。结果表明，状态动态对应于丢失的常微分方程可以很好地近似使用递归贝叶斯滤波方法训练的神经网络的时尚加上已知的状态动态微分方程。这表明，动态和丢失的状态变量的影响，可以通过联合状态估计和模型参数估计递归贝叶斯状态估计（RBSE）框架内捕获。结果还表明，这种RBSE方法来训练NN参数产生更好的结果（测量/状态估计精度）比在相同的设置下通过时间反向传播训练神经网络。
Modeling biological dynamical systems is challenging due to the interdependence of different system components, some of which are not fully understood. To fill existing gaps in our ability to mechanistically model physiological systems, we propose to combine neural networks with physics-based models. Specifically, we demonstrate how we can approximate missing ordinary differential equations (ODEs) coupled with known ODEs using Bayesian filtering techniques to train the model parameters and simultaneously estimate dynamic state variables. As a study case we leverage a well-understood model for blood circulation in the human retina and replace one of its core ODEs with a neural network approximation, representing the case where we have incomplete knowledge of the physiological state dynamics. Results demonstrate that state dynamics corresponding to the missing ODEs can be approximated well using a neural network trained using a recursive Bayesian filtering approach in a fashion coupled with the known state dynamic differential equations. This demonstrates that dynamics and impact of missing state variables can be captured through joint state estimation and model parameter estimation within a recursive Bayesian state estimation (RBSE) framework. Results also indicate that this RBSE approach to training the NN parameters yields better outcomes (measurement/state estimation accuracy) than training the neural network with backpropagation through time in the same setting.