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We present an extensible software framework, hIPPYlib, for solution oflarge-scale deterministic and Bayesian inverse problems governed by partialdifferential equations (PDEs) with infinite-dimensional parameter fields (whichare high-dimensional after discretization). hIPPYlib overcomes the prohibitivenature of Bayesian inversion for this class of problems by implementingstate-of-the-art scalable algorithms for PDE-based inverse problems thatexploit the structure of the underlying operators, notably the Hessian of thelog-posterior. The key property of the algorithms implemented in hIPPYlib isthat the solution of the deterministic and linearized Bayesian inverse problemis computed at a cost, measured in linearized forward PDE solves, that isindependent of the parameter dimension. The mean of the posterior isapproximated by the MAP point, which is found by minimizing the negativelog-posterior. This deterministic nonlinear least-squares optimization problemis solved with an inexact matrix-free Newton-CG method. The posteriorcovariance is approximated by the inverse of the Hessian of the negative logposterior evaluated at the MAP point. This Gaussian approximation is exact whenthe parameter-to-observable map is linear; otherwise, its logarithm agrees totwo derivatives with the log-posterior at the MAP point, and thus it can serveas a proposal for Hessian-based MCMC methods. The construction of the posteriorcovariance is made tractable by invoking a low-rank approximation of theHessian of the log-likelihood. Scalable tools for sample generation are alsoimplemented. hIPPYlib makes all of these advanced algorithms easily accessibleto domain scientists and provides an environment that expedites the developmentof new algorithms. hIPPYlib is also a teaching tool to educate researchers andpractitioners who are new to inverse problems and the Bayesian inferenceframework.

hIPPYlib: An Extensible Software Framework for Large-Scale Inverse  Problems Governed by PDEs; Part I: Deterministic Inversion and Linearized  Bayesian Inference