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Within the framework of sea-level rise projections, there is a strong need for hindcast validation of the evolution of polar ice sheets in a way that tightly matches observational records (from radar, gravity, and altimetry observations mainly). However, the computational requirements for making hindcast reconstructions possible are severe and rely mainly on the evaluation of the adjoint state of transient iceflow models. Here, we look at the computation of adjoints in the context of the NASA/JPL/UCI Ice Sheet System Model (ISSM), written in C++ and designed for parallel execution with MPI.We present the adaptations required in the way the software is designed and written, but also generic adaptations in the tools facilitating the adjoint computations.We concentrate on the use of operator overloading coupled with the AdjoinableMPI library to achieve the adjoint computation of the ISSM.We present a comprehensive approach to (1) carry out type changing through the ISSM, hence facilitating operator overloading, (2) bind to external solvers such as MUMPS and GSL-LU, and (3) handle MPI-based parallelism to scale the capability. We demonstrate the success of the approach by computing sensitivities of hindcast metrics such as the misfit to observed records of surface altimetry on the northeastern Greenland Ice Stream, or the misfit to observed records of surface velocities on Upernavik Glacier, central West Greenland. We also provide metrics for the scalability of the approach, and the expected performance. This approach has the potential to enable a new generation of hindcast-validated projections that make full use of the wealth of datasets currently being collected, or already collected, in Greenland and Antarctica. [ABSTRACT FROM AUTHOR]

The computation of gradients via the reverse mode of algorithmic differentiation is a valuable technique in modelling many science and engineering applications. This technique is particularly efficient when implemented as a source transformation, as it may use static data-flow analysis. However, some features of the major programming languages are detrimental to the efficiency of the transformed source code. This paper provides an overview of the most common problem scenarios and estimates the cost overhead incurred by using the respective language feature or employing certain common patterns. An understanding of these topics is crucial for the efficiency or even feasibility of adjoint computations, particularly for large-scale numerical simulations, for example, in geosciences. While one cannot hope to cover all effects observable with a given programming language in a given run time environment, the paper aims at providing a reasonable guide for the users of C/C++ and Fortran source transformation tools for algorithmic differentiation. [ABSTRACT FROM AUTHOR]

Within the framework of sea-level rise projections, there is a strong need for hindcast validation of the evolution of polar ice sheets in a way that tightly matches observational records (from radar and altimetry observations mainly). However, the computational requirements for making hindcast reconstructions possible are severe and rely mainly on the evaluation of the adjoint state of transient ice-flow models. Here, we look at the computation of adjoints in the context of the NASA/JPL/UCI Ice Sheet System Model, written in C++ and designed for parallel execution with MPI. We present the adaptations required in the way the software is designed and written but also generic adaptations in the tools facilitating the adjoint computations. We concentrate on the use of operator overloading coupled with the AdjoinableMPI library to achieve the adjoint computation of ISSM. We present a comprehensive approach to 1) carry out type changing through ISSM, hence facilitating operator overloading, 2) bind to external solvers such as MUMPS and GSL-LU and 3) handle MPI-based parallelism to scale the capability. We demonstrate the success of the approach by computing sensitivities of hindcast metrics such as the misfit to observed records of surface altimetry on the North-East Greenland Ice Stream, or the misfit to observed records of surface velocities on Upernavik Glacier, Central West Greenland. We also provide metrics for the scalability of the approach, and the expected performance. This approach has the potential of enabling a new generation of hindcast-validated projections that make full use of the wealth of datasets currently being collected, or already collected in Greenland and Antarctica, such as surface altimetry, surface velocities, and/or gravity measurements. [ABSTRACT FROM AUTHOR]

The OpenAD/F tool allows the evaluation of derivatives of functions defined by a Fortran program. The derivative evaluation is performed by a Fortran code resulting from the analysis and transformation of the original program that defines the function of interest. OpenAD/F has been designed with a particular emphasis on modularity, flexibility, and the use of open source components. While the code transformation follows the basic principles of automatic differentiation, the tool implements new algorithmic approaches at various levels, for example, for basic block preaccumulation and call graph reversal. Unlike most other automatic differentiation tools, OpenAD/F uses components provided by the OpenAD framework, which supports a comparatively easy extension of the code transformations in a language-independent fashion. It uses code analysis results implemented in the OpenAnalysis component. The interface to the language-independent transformation engine is an XML-based format, specified through an XML schema. The implemented transformation algorithms allow efficient derivative computations using locally optimized cross-country sequences of vertex, edge, and face elimination steps. Specifically, for the generation of adjoint codes, OpenAD/F supports various code reversal schemes with hierarchical checkpointing at the subroutine level. As an example from geophysical fluid dynamics, a nonlinear time-dependent scalable, yet simple, barotropic ocean model is considered. OpenAD/F's reverse mode is applied to compute sensitivities of some of the model's transport properties with respect to gridded fields such as bottom topography as independent (control) variables. [ABSTRACT FROM AUTHOR]

Most recent machine learning research focuses on developing new classifiers for the sake of improving classification accuracy. With many well-performing state-of-the-art classifiers available, there is a growing need for understanding interpretability of a classifier necessitated by practical purposes such as to find the best diet recommendation for a diabetes patient. Inverse classification is a post modeling process to find changes in input features of samples to alter the initially predicted class. It is useful in many business applications to determine how to adjust a sample input data such that the classifier predicts it to be in a desired class. In real world applications, a budget on perturbations of samples corresponding to customers or patients is usually considered, and in this setting, the number of successfully perturbed samples is key to increase benefits. In this study, we propose a new framework to solve inverse classification that maximizes the number of perturbed samples subject to a per-feature-budget limits and favorable classification classes of the perturbed samples. We design algorithms to solve this optimization problem based on gradient methods, stochastic processes, Lagrangian relaxations, and the Gumbel trick. In experiments, we find that our algorithms based on stochastic processes exhibit an excellent performance in different budget settings and they scale well. The relative improvement of the proposed stochastic algorithms over an existing method with a traditional formulation is 15% in the real-world dataset and 21% in two public datasets on average. • A new framework to solve inverse classification is developed. • It obtains successfully perturbed samples within a per-feature budget. • Algorithms are designed based on a gradient method and the Gumbel trick. • Real data from an industrial partner and two healthcare public datasets are used. • The stochastic approaches perform great on various budget scenarios, and they scale. [ABSTRACT FROM AUTHOR]

In this paper, we describe a code transformation technique that, given a code for a vector function F, produces a code suitable for computing collections of Jacobian-vector products F′(x)x˙ or Jacobian-transpose-vector products F′(x)T y¯. Exploitation of scarcity – a measure of the degrees of freedom in the Jacobian matrix – requires solving a combinatorial optimization problem that is believed to be hard. Our heuristics transform the computational graph for F, producing, in the form of a transformed graph G′, a representation of the Jacobian F′(x) that is both concise and suitable for evaluating large collections of the Jacobian-vector products or the Jacobian-transpose-vector products. Our heuristics are randomized and compare favourably in all cases with the best known heuristics. [ABSTRACT FROM AUTHOR]

We apply an optimized method to the adjoint generation of a time-evolving land ice model through algorithmic differentiation (AD). The optimization involves a special treatment of the fixed-point iteration required to solve the nonlinear stress balance, which differs from a straight-forward application of AD software, and leads to smaller memory requirements and in some cases shorter computation times of the adjoint. The optimization is done via implementation of the algorithm of Christianson (1994) for reverse accumulation of fixed-point problems, with the AD tool OpenAD. For test problems, the optimized adjoint is shown to have far lower memory requirements, potentially enabling larger problem sizes on memory-limited machines. In the case of the land ice model, implementation of the algorithm allows further optimization by having the adjoint model solve a sequence of linear systems with identical (as opposed to varying) matrices, greatly improving performance. The methods introduced here will be of value to other efforts applying AD tools to ice models, particularly ones which solve a hybrid shallow ice/shallow shelf approximation to the Stokes equations. [ABSTRACT FROM AUTHOR]

We apply an optimized method to the adjoint generation of a time-evolving land ice model through algorithmic differentiation (AD). The optimization involves a special treatment of the fixedpoint iteration required to solve the nonlinear stress balance, which differs from a straightforward application of AD software, and leads to smaller memory requirements and in some cases shorter computation times of the adjoint. The optimization is done via implementation of the algorithm of Christianson [1994] for reverse accumulation of fixed-point problems, with the AD tool OpenAD. For test problems, the optimized adjoint is shown to have far lower memory requirements, potentially enabling larger problem sizes on memory-limited machines. In the case of the land ice model, implementation of the algorithm allows further optimization by having the adjoint model solve a sequence of linear systems with identical (as opposed to varying) matrices, greatly improving performance. The methods introduced here will be of value to other efforts applying AD tools to ice models, particularly ones which solve a "hybrid" shallow ice / shallow shelf approximation to the Stokes equations. [ABSTRACT FROM AUTHOR]

Abstract: A dual (adjoint) model is used to explore elements of the oceanic state influencing the meridional volume and heat transports (MVT and MHT) in the sub-tropical North Atlantic so as to understand their variability and to provide the elements of useful observational program design. Focus is on the effect of temperature (and salinity) perturbations. On short timescales (months), as expected, the greatest sensitivities are to local disturbances, but as the timescales extend back to a decade and longer, the region of influence expands to occupy much of the Atlantic basin and significant areas of the global ocean, although the influence of any specific point or small area tends to be quite weak. The propagation of information in the dual solution is a clear manifestation of oceanic teleconnections. It takes place through identifiable “dual” Kelvin, Rossby, and continental shelf-waves with an interpretable physics, in particular in terms of dual expressions of barotropic and baroclinic adjustment processes. Among the notable features are the relatively fast timescales of influence (albeit weak in amplitude) between 26°N and the tropical Pacific and Indian Ocean, the absence of dominance of the sub-polar North Atlantic, significant connections to the Agulhas leakage region in the southeast Atlantic on timescales of 5–10 years, and the marked sensitivity propagation of Doppler-shifted Rossby waves in the Southern Ocean on timescales of a decade and beyond. Regional, as well as time-dependent, differences between MVT and MHT sensitivities highlight the lack of a simple correspondence between their variability. Some implications for observing systems for the purpose of climate science are discussed. [Copyright &y& Elsevier]