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We consider how a closed Riemannian manifold and its metric tensor can beapproximately reconstructed from local distance measurements. In the part 1 ofthe paper, we considered the construction of a smooth manifold in the case whenone is given the noisy distances $\tilde d(x,y)=d(x,y)+\varepsilon_{x,y}$ forall points $x,y\in X$, where $X$ is a $\delta$-dense subset of $M$ and$|\varepsilon_{x,y}|<\delta$. In this paper we consider a similar problem withpartial data, that is, the approximate construction of the manifold $(M,g)$when we are given $\tilde d(x,y)$ for $x\in X$ and $y \in U\cap X$, where $U$is an open subset of $M$. As an application, we consider the inverse problem ofdetermining the manifold $(M,g)$ with non-negative Ricci curvature from noisyobservations of the heat kernel $G(y,z,t)$ with separated observation points$y\in U$ and source points $z\in M\setminus \overline U$ on the time interval$0<t<1$.

Reconstruction and interpolation of manifolds II: Inverse problems for Riemannian manifolds with partial distance data