Burzawa Lukasz, Li Linlin, Wang Xu, Buganza-Tepole Adrian, Umulis David M
Weldon School of Biomedical Engineering, Purdue University, West Lafayette, IN 47907.
School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47907.
Curr Pathobiol Rep. 2020 Dec;8(4):121-131. doi: 10.1007/s40139-020-00216-8. Epub 2020 Nov 6.
Partial differential equation (PDE) mathematical models of biological systems and the simulation approaches used to solve them are widely used to test hypotheses and infer regulatory interactions based on optimization of the PDE model against the observed data. In this review, we discuss the ability of powerful machine learning methods to accelerate the parametric screening of biophysical informed- PDE systems.
A major shortcoming in more broad adaptation of PDE-based models is the high computational complexity required to solve and optimize the models and it requires many simulations to traverse the very high-dimensional parameter spaces during model calibration and inference tasks. For instance, when scaling up to tens of millions of simulations for optimization and sensitivity analysis of the PDE models, compute times quickly extend from months to years for sufficient coverage to solve the problems. For many systems, this brute-force approach is simply not feasible. Recently, neural network metamodels have been shown to be an efficient way to accelerate PDE model calibration and here we look at the benefits and limitations in extending the PDE acceleration methods to improve optimization and sensitivity analysis.
We use an example simulation to quantitatively and qualitatively show how neural network metamodels can be accurate and fast and demonstrate their potential for optimization of complex spatiotemporal problems in biology. We expect these approaches will be broadly applied to speed up scientific research and discovery in biology and other systems that can be described by complex PDE systems.
生物系统的偏微分方程（PDE）数学模型以及用于求解这些模型的模拟方法被广泛用于检验假设，并基于PDE模型针对观测数据的优化来推断调控相互作用。在本综述中，我们讨论了强大的机器学习方法加速生物物理信息PDE系统参数筛选的能力。
基于PDE的模型更广泛应用的一个主要缺点是求解和优化模型所需的高计算复杂性，并且在模型校准和推理任务期间需要进行许多模拟来遍历非常高维的参数空间。例如，在将PDE模型的优化和敏感性分析扩展到数千万次模拟时，计算时间会迅速从数月延长到数年才能获得足够的覆盖范围来解决问题。对于许多系统而言，这种暴力方法根本不可行。最近，神经网络元模型已被证明是加速PDE模型校准的有效方法，在此我们探讨扩展PDE加速方法以改进优化和敏感性分析的优点和局限性。
我们通过一个示例模拟定量和定性地展示了神经网络元模型如何既准确又快速，并证明了它们对生物学中复杂时空问题进行优化的潜力。我们预计这些方法将被广泛应用于加速生物学以及其他可以用复杂PDE系统描述的系统中的科学研究和发现。
