线性/岭展开：通过岭函数增强线性逼近
Linear/Ridge expansions: Enhancing linear approximations by ridge functions
摘要：
我们考虑由脊函数增强的给定函数的线性组合的和形成的近似-线性/脊扩展。对于一个显式或隐式给定的函数，我们重新制定寻找一个最佳的线性/岭展开的最优化问题。我们介绍了一种粒子网格算法的解决方案。一些数值结果强调的灵活性，鲁棒性和效率的算法。一个特定的动机来源是参数化的传输或波动方程的模型简化。我们表明，粒子网格算法是能够产生一个线性/脊扩展作为一个有效的非线性模型减少。
英文摘要：
We consider approximations formed by the sum of a linear combination of given functions enhanced by ridge functions -- a Linear/Ridge expansion. For an explicitly or implicitly given function, we reformulate finding a best Linear/Ridge expansion in terms of an optimization problem. We introduce a particle grid algorithm for its solution. Several numerical results underline the flexibility, robustness and efficiency of the algorithm. One particular source of motivation is model reduction of parameterized transport or wave equations. We show that the particle grid algorithm is able to produce a Linear/Ridge expansion as an efficient nonlinear model reduction.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
