IN040-02
hIPPYlib: An Extensible Software Framework for Large-Scale Inverse Problems Governed by PDEs
hIPPYlib: An Extensible Software Framework for Large-Scale Inverse Problems Governed by PDEs
Tuesday, 15 December 2020: 19:03
Virtual
Abstract:
Recent years have seen tremendous growth in the volumes of observational and experimental data that are being collected, stored, processed, and analyzed. The central question that has emerged is how do we extract knowledge and insight from all of this data? When the data correspond to observations of (natural or engineered) systems, and these systems can be represented by mathematical models, this knowledge-from-data problem is fundamentally a mathematical inverse problem. That is, given noisy data and an uncertain model, infer parameters that characterize the model. Inverse problems can arise in a broad spectrum of geophysical models including those arising in meteorology, climate, seismology, geodynamics, subsurface flow, etc. As just a few examples of model-based inverse problems, we may infer: the ice sheet basal friction field from satellite observation of surface flow, the earth structure from reflected seismic waves, the ocean state from surface temperature observations, etc.
Bayesian inference has emerged as the most comprehensive and systematic framework for formulating and solving inverse problems with quantified uncertainties. However, the solution of Bayesian inverse problems is extremely challenging; when the forward model is complex and the parameter dimension is large, Bayesian inversion becomes prohibitive with standard methods. Recent years have seen intensive efforts to develop advanced algorithms aimed at this class of problems; however, due to the complexity of the algorithms and their requirement for gradient and Hessian sensitivity information from the forward model, often these remain inaccessible. In this talk, we present an extensible software framework, hIPPYlib, for solution of large-scale Bayesian inverse problems governed by partial differential equations (PDEs) with infinite-dimensional parameter fields. hIPPYlib overcomes the prohibitively expensive nature of Bayesian inversion by implementing state-of-the-art scalable algorithms for PDE-based inverse problems that exploit the structure of the underlying operators. hIPPYlib makes all of these advanced algorithms easily accessible to domain scientists, and provides an environment that expedites the development of new algorithms.
Bayesian inference has emerged as the most comprehensive and systematic framework for formulating and solving inverse problems with quantified uncertainties. However, the solution of Bayesian inverse problems is extremely challenging; when the forward model is complex and the parameter dimension is large, Bayesian inversion becomes prohibitive with standard methods. Recent years have seen intensive efforts to develop advanced algorithms aimed at this class of problems; however, due to the complexity of the algorithms and their requirement for gradient and Hessian sensitivity information from the forward model, often these remain inaccessible. In this talk, we present an extensible software framework, hIPPYlib, for solution of large-scale Bayesian inverse problems governed by partial differential equations (PDEs) with infinite-dimensional parameter fields. hIPPYlib overcomes the prohibitively expensive nature of Bayesian inversion by implementing state-of-the-art scalable algorithms for PDE-based inverse problems that exploit the structure of the underlying operators. hIPPYlib makes all of these advanced algorithms easily accessible to domain scientists, and provides an environment that expedites the development of new algorithms.