Taichi

Abstract

3D visual computing data are often spatially sparse. To exploit such sparsity, people have developed hierarchical sparse data structures, such as multi-level sparse voxel grids, particles, and 3D hash tables. However, developing and using these high-performance sparse data structures is challenging, due to their intrinsic complexity and overhead. We propose Taichi , a new data-oriented programming language for efficiently authoring, accessing, and maintaining such data structures. The language offers a high-level, data structure-agnostic interface for writing computation code. The user independently specifies the data structure. We provide several elementary components with different sparsity properties that can be arbitrarily composed to create a wide range of multi-level sparse data structures. This decoupling of data structures from computation makes it easy to experiment with different data structures without changing computation code, and allows users to write computation as if they are working with a dense array. Our compiler then uses the semantics of the data structure and index analysis to automatically optimize for locality, remove redundant operations for coherent accesses, maintain sparsity and memory allocations, and generate efficient parallel and vectorized instructions for CPUs and GPUs. Our approach yields competitive performance on common computational kernels such as stencil applications, neighbor lookups, and particle scattering. We demonstrate our language by implementing simulation, rendering, and vision tasks including a material point method simulation, finite element analysis, a multigrid Poisson solver for pressure projection, volumetric path tracing, and 3D convolution on sparse grids. Our computation-data structure decoupling allows us to quickly experiment with different data arrangements, and to develop high-performance data structures tailored for specific computational tasks. With 1 <u> 1 </u> 0 th as many lines of code, we achieve 4.55× higher performance on average, compared to hand-optimized reference implementations.

End-to-End Differentiable Modeling and Management of the Environment

“…This is unlike numerical differentiation, which requires a forward pass for each dimension of the input; it also improves upon symbolic differentiation by avoiding the exponential number of terms that result from naïve applications of the chain rule for derivatives. Additionally, examples of physical models (Hu et al, 2020;Schenck and Fox, 2018) are now implemented in autodiff-enabled programming frameworks. Because the composition of differentiable functions is also differentiable via the chain rule, these forms could be combined and composed to create novel systems amenable to the application of gradient descent or its stochastic counterpart.…”

A moving least square reproducing kernel particle method for unified multiphase continuum simulation

“…GPU optimized MPM simulator was developed in [Gao et al 2018b]. Hu et al [2019] proposed a domain specific programming language to efficiently implement and execute MPM algorithms.…”

“…Implementing P2G and G2P transfer for MPM is not an easy job, especially when spatial data structure is used. To simplify the implementation of MPM, the Taichi programming language [Hu et al 2019] with built-in support for sparse data structure is designed recently for programming with spatial sparsity.…”

“…Knowing this difference, comparison can be made with the same number of particles or DoFs. For a fair comparison, we implemented an MLSRK simulator with Taichi programming language [Hu et al 2019] and compared the performance with Taichi's MLS-MPM implementation. Using the same number of particles, MPM is faster than MLSRK but delivers less details, because the grid has significantly less DoFs.…”

An adaptive staggered-tilted grid for incompressible flow simulation

“…Multiple regular grids of different resolutions could also be grouped by rigidly translating and overlapping, forming a more descriptive grid structure (Chimera grid) [Cohen et al 2010;Dobashi et al 2008;English et al 2013;Golas et al 2012]. The spatially sparse nature of the fluid simulation task also drives researchers to propose more unified solutions, such as a high resolution sparse dynamic data structure (VDB) supporting O(1) data access [Museth 2013], a computational framework for sparsely populated grid [Liu et al 2018] and a data-oriented programming language for spatial sparse structure [Hu et al 2019].…”