Abstract We present an algorithm for the time-inversion of diffusion–advection equations, based on the adjoint methodology. Given a final state distribution our main aim is to recover sparse initial conditions, constituted by a finite combination of Kronecker deltas, identifying their location and mass. We discuss the strengths of the adjoint machinery and the difficulties that are to be faced, in particular when the diffusivity coefficient or the time horizon is large.

中文翻译：

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线性扩散-平流方程的稀疏源识别伴随方法

摘要 我们提出了一种基于伴随方法的扩散平流方程的时间反演算法。给定最终状态分布，我们的主要目标是恢复由 Kronecker deltas 的有限组合构成的稀疏初始条件，确定它们的位置和质量。我们讨论了伴随机制的优势和将面临的困难，特别是当扩散系数或时间范围很大时。