参数依赖动力系统初值问题的机器学习
Machine Learning for Initial Value Problems of Parameter-Dependent Dynamical Systems
摘要：
本文研究一类含有物理参数的非线性动力系统的初值问题。观察到取决于溶液的感兴趣的量。离散化产生在许多时间点的感兴趣的量的轨迹。我们研究的映射从一组参数的离散值的轨迹。这个映射的评估需要解决一个初始值问题。或者，我们使用机器学习的概念来确定近似，其中评估需要低计算工作。我们采用前馈神经网络，这是适合从样本的轨迹数据。数值计算的结果给出了一个测试例子模拟电路。
英文摘要：
We consider initial value problems of nonlinear dynamical systems, which include physical parameters. A quantity of interest depending on the solution is observed. A discretisation yields the trajectories of the quantity of interest in many time points. We examine the mapping from the set of parameters to the discrete values of the trajectories. An evaluation of this mapping requires to solve an initial value problem. Alternatively, we determine an approximation, where the evaluation requires low computation work, using a concept of machine learning. We employ feedforward neural networks, which are fitted to data from samples of the trajectories. Results of numerical computations are presented for a test example modelling an electric circuit.
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