Constructing a backward (P)DE which effectively gives us the gradients of the forward (P)DE. A trick in automatic differentiation which happens to be useful in differentiating likelihood (or other functions) of time-evolving systems. e.g. (Errico 1997; Kidger, Chen, and Lyons 2021; Kidger et al. 2020; Li et al. 2020; Rackauckas et al. 2018; Stapor, Fröhlich, and Hasenauer 2018; Cao et al. 2003).
References
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Errico, Ronald M. 1997. “What Is an Adjoint Model?” Bulletin of the American Meteorological Society 78 (11): 2577–92.
Gahungu, Paterne, Christopher W. Lanyon, Mauricio A. Álvarez, Engineer Bainomugisha, Michael Thomas Smith, and Richard David Wilkinson. 2022. “Adjoint-Aided Inference of Gaussian Process Driven Differential Equations.” In.
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