Simit: A Language for Physical Simulation by Fredrik Kjolstad, et al.
Abstract:
With existing programming tools, writing high-performance simulation code is labor intensive and requires sacrificing readability and portability. The alternative is to prototype simulations in a high-level language like Matlab, thereby sacrificing performance. The Matlab programming model naturally describes the behavior of an entire physical system using the language of linear algebra. However, simulations also manipulate individual geometric elements, which are best represented using linked data structures like meshes. Translating between the linked data structures and linear algebra comes at significant cost, both to the programmer and to the machine. High-performance implementations avoid the cost by rephrasing the computation in terms of linked or index data structures, leaving the code complicated and monolithic, often increasing its size by an order of magnitude.
In this article, we present Simit, a new language for physical simulations that lets the programmer view the system both as a linked data structure in the form of a hypergraph and as a set of global vectors, matrices, and tensors depending on what is convenient at any given time. Simit provides a novel assembly construct that makes it conceptually easy and computationally efficient to move between the two abstractions. Using the information provided by the assembly construct, the compiler generates efficient in-place computation on the graph. We demonstrate that Simit is easy to use: a Simit program is typically shorter than a Matlab program; that it is high performance: a Simit program running sequentially on a CPU performs comparably to hand-optimized simulations; and that it is portable: Simit programs can be compiled for GPUs with no change to the program, delivering 4 to 20× speedups over our optimized CPU code.
Very deep sledding ahead but consider the contributions:
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Simit is the first system that allows the development of physics code that is simultaneously:Concise. The Simit language has Matlab-like syntax that lets algorithms be implemented in a compact, readable form that closely mirrors their mathematical expression. In addition, Simit matrices assembled from hypergraphs are indexed by hypergraph elements like vertices and edges rather than by raw integers, significantly simplifying indexing code and eliminating bugs.
Expressive. The Simit language consists of linear algebra operations augmented with control flow that let developers implement a wide range of algorithms ranging from finite elements for deformable bodies to cloth simulations and more. Moreover, the powerful hypergraph abstraction allows easy specification of complex geometric data structures.
Fast. The Simit compiler produces high-performance executable code comparable to that of hand-optimized end-to-end libraries and tools, as validated against the state-of-the-art SOFA [Faure et al. 2007] and Vega [Sin et al. 2013] real-time simulation frameworks. Simulations can now be written as easily as a traditional prototype and yet run as fast as a high-performance implementation without manual optimization.
Performance Portable. A Simit program can be compiled to both CPUs and GPUs with no additional programmer effort, while generating efficient code for each architecture. Where Simit delivers performance comparable to hand-optimized CPU code on the same processor, the same simple Simit program delivers roughly an order of magnitude higher performance on a modern GPU in our benchmarks, with no changes to the program.
Interoperable. Simit hypergraphs and program execution are exposed as C++ APIs, so developers can seamlessly integrate with existing C++ programs, algorithms, and libraries.
(emphasis in original)
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Additional resources:
Source code (MIT license)
Enjoy!