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Register a new userFunctional programming framework for GRworkbench
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The software tool GRworkbench is an ongoing project in visual, numerical General Relativity at The Australian National University. Recently, the numerical differential geometric engine of GRworkbench has been rewritten using functional programming techniques. By allowing functions to be directly represented as program variables in C++ code, the functional framework enables the mathematical formalism of Differential Geometry to be more closely reflected in GRworkbench . The powerful technique of `automatic differentiation has replaced numerical differentiation of the metric components, resulting in more accurate derivatives and an order-of-magnitude performance increase for operations relying on differentiation.
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The software tool GRworkbench is an ongoing project in visual, numerical General Relativity at The Australian National University. Recently, GRworkbench has been significantly extended to facilitate numerical experimentation in analytically-defined space-times. The numerical differential geometric engine has been rewritten using functional programming techniques, enabling objects which are normally defined as functions in the formalism of differential geometry and General Relativity to be directly represented as function variables in the C++ code of GRworkbench. The new functional differential geometric engine allows for more accurate and efficient visualisation of objects in space-times and makes new, efficient computational techniques available. Motivated by the desire to investigate a recent scientific claim using GRworkbench, new tools for numerical experimentation have been implemented, allowing for the simulation of complex physical situations.
The software tool GRworkbench is an ongoing project in visual, numerical General Relativity at The Australian National University. This year, GRworkbench has been significantly extended to facilitate numerical experimentation. The numerical differential geometric engine has been rewritten using functional programming techniques, enabling fundamental concepts to be directly represented as variables in the C++ code of GRworkbench. Sophisticated general numerical methods have replaced simpler specialised algorithms. Various tools for numerical experimentation have been implemented, allowing for the simulation of complex physical situations. A recent claim, that the mass of the Milky Way can be measured using a small interferometer located on the surface of the Earth, has been investigated, and found to be an artifact of the approximations employed in the analysis. This difficulty is symptomatic of the limitations of traditional pen-and-paper analysis in General Relativity, which was the motivation behind the original development of GRworkbench. The physical situation pertaining to the claim has been modelled in a numerical experiment in GRworkbench, without the necessity of making any simplifying assumptions, and an accurate estimate of the effect has been obtained.
It is a significant challenge to design probabilistic programming systems that can accommodate a wide variety of inference strategies within a unified framework. Noting that the versatility of modern automatic differentiation frameworks is based in large part on the unifying concept of tensors, we describe a software abstraction for integration --functional tensors-- that captures many of the benefits of tensors, while also being able to describe continuous probability distributions. Moreover, functional tensors are a natural candidate for generalized variable elimination and parallel-scan filtering algorithms that enable parallel exact inference for a large family of tractable modeling motifs. We demonstrate the versatility of functional tensors by integrating them into the modeling frontend and inference backend of the Pyro programming language. In experiments we show that the resulting framework enables a large variety of inference strategies, including those that mix exact and approximate inference.
A summary is given of recent exact results concerning the functional integration measure in Regge gravity.
An attempt at unifying logic and functional programming is reported. As a starting point, we take the view that logic programs are not about logic but constitute inductive definitions of sets and relations. A skeletal language design based on these considerations is sketched and a prototype implementation discussed.
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