Session: Recent Advances on PDE-constrained optimization packages and libraries: Part II
Chair: Umberto Villa
Cluster: Computational Software
Talk 1: hIPPYlib: An Extensible Software Framework for Large-Scale Inverse Problems Governed by PDEs
Speaker: Noemi Petra
Abstract: We present an extensible software framework, hIPPYlib, for solution of large-scale deterministic and Bayesian inverse problems governed by partial differential equations (PDEs) with infinite-dimensional parameter fields (which are high-dimensional after discretization). hIPPYlib overcomes the prohibitive nature of Bayesian inversion for this class of problems by implementing state-of-the-art scalable algorithms for PDE-based inverse problems that exploit the structure of the underlying operators, notably the Hessian of the log-posterior. The key property of the algorithms implemented in hIPPYlib is that the solution of the deterministic and linearized Bayesian inverse problem is computed at a cost, measured in linearized forward PDE solves, that is independent of the parameter dimension. The mean of the posterior is approximated by the MAP point, which is found by minimizing the negative log-posterior. This deterministic nonlinear least-squares optimization problem is solved with an inexact matrix-free Newton-CG method. The posterior covariance is approximated by the inverse of the Hessian of the negative log posterior evaluated at the MAP point. The construction of the posterior covariance is made tractable by invoking a low-rank approximation of the Hessian of the log-likelihood. hIPPYlib makes all of these advanced algorithms easily accessible to domain scientists and provides an environment that expedites the development of new algorithms. Authors: Umberto Villa (UT Austin), Noemi Petra (UC Merced), Omar Ghattas (UT Austin)
Talk 2: SimPEG: an open-source framework for simulation and parameter estimation in geophysics
Speaker: Lindsey Heagy
Abstract: Geophysical data can provide insights about the subsurface in a range of applications. A few examples include locating critical minerals, monitoring geologic storage of CO2, managing groundwater, and characterizing changes to permafrost. The geophysical inverse problem is posed as a PDE-constrained optimization problem where we aim to fit the observed data and incorporate additional information that may include petrophysical, geologic, and geochemical measurements, as well as additional geophysical data sets. We started the SimPEG project with the aim of accelerating research and education in geophysics and enabling researchers to build upon and contribute to a modular toolbox for solving problems in geophysics. At the core is a framework for finite volume forward simulations and gradient-based inversions. SimPEG currently supports simulation and inversion of gravity, magnetic, electrical and electromagnetic data. In this talk, I will provide an overview of how we have broken down inverse problems in geophysics into modular components and how working in an open-source paradigm has facilitated our research, collaborations with industry, and dissemination of educational resources in classrooms and for humanitarian projects.
Talk 3: TBA
Speaker: TBA TBA
Abstract: TBA
