论文标题
部分可观测时空混沌系统的无模型预测
Solving the Schrodinger equation with genetic algorithms: a practical approach
论文作者
论文摘要
储层计算是预测湍流的有力工具，其简单的架构具有处理大型系统的计算效率。然而，其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间，然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用，该系统模拟了湍流的若干特征。我们表明，使用径向基函数作为非线性投影器，即使只有部分观测并且不知道控制方程，也能稳健地捕捉复杂的系统非线性。最后，我们表明，当测量稀疏、不完整且带有噪声，甚至控制方程变得不准确时，我们的网络仍然可以产生相当准确的预测，从而为实际湍流系统的无模型预测铺平了道路。
The Schrodinger equation is one of the most important equations in physics and chemistry and can be solved in the simplest cases by computer numerical methods. Since the beginning of the 70s of the last century the computer began to be used to solve this equation in elementary quantum systems, e.g. and in the most complex case a hydrogen-like system. Obtaining the solution means finding the wave function, which allows predicting the physical and chemical properties of the quantum system. However, when a quantum system is more complex than a hydrogen-like system then we must be satisfied with an approximate solution of the equation. During the last decade the application of algorithms and principles of quantum computation in disciplines other than physics and chemistry, such as biology and artificial intelligence, has led to the search for alternative techniques with which to obtain approximate solutions of the Schrodinger equation. In this paper, we review and illustrate the application of genetic algorithms, i.e. stochastic optimization procedures inspired by Darwinian evolution, in elementary quantum systems and in quantum models of artificial intelligence. In this last field, we illustrate with two toy models how to solve the Schrodinger equation in an elementary model of a quantum neuron and in the synthesis of quantum circuits controlling the behavior of a Braitenberg vehicle.
