Estimating the temperature field of a building envelope could be a time-consuming task. The use of a reduced-order method is then proposed: the Proper Generalized Decomposition method. The solution of the transient heat equation is then re-written as a function of its parameters: the boundary conditions, the initial condition, etc. To avoid a tremendous number of parameters, the initial condition is parameterized. This is usually done by using the Proper Orthogonal Decomposition method to provide an optimal basis. Building this basis requires data and a learning strategy. As an alternative, the use of orthogonal polynomials (Chebyshev, Legendre) is here proposed.

翻译：估计建筑物信封的温度场可能是一项耗时的工作。 然后提议使用减序法: 适当的通用分解法。 然后, 瞬时热方程式的解决方案将重新写成其参数的函数: 边界条件、 初始条件等。 为了避免参数数量之多, 初始条件将参数化。 通常通过使用正正正正正正的分解法来提供最佳基础来完成。 建立这一基础需要数据和学习策略。 作为替代, 在此提议使用正向多面的多面体( Chebyshev、 Tultre) 。