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We present an autotuning approach for compile-time optimization of numerical discretization methods in simulations of partial differential equations. Our approach is based on data-driven regression of performance models for numerical methods. We use these models at compile time to automatically determine the parameters (e.g., resolution, time step size, etc.) of numerical simulations of continuum spatio-temporal models in order to optimize the tradeoff between simulation accuracy and runtime. The resulting autotuner is developed for the compiler of a Domain-Specific Language (DSL) for numerical simulations. The abstractions in the DSL enable the compiler to automatically determine the performance models and know which discretization parameters to tune. We demonstrate that this high-level approach can explore a large space of possible simulations, with simulation runtimes spanning multiple orders of magnitude. We evaluate our approach in two test cases: the linear diffusion equation and the nonlinear Gray-Scott reaction–diffusion equation. The results show that our model-based autotuner consistently finds configurations that outperform those found by state-of-the-art general-purpose autotuners. Specifically, our autotuner yields simulations that are on average 4.2x faster than those found by the best generic exploration algorithms, while using 16x less tuning time. Compared to manual tuning by a group of researchers with varying levels of expertise, the autotuner was slower than the best users by not more than a factor of 2, whereas it was able to significantly outperform half of them.

Abstract We present a user-friendly and intuitive C++ expression system to implement numerical simulations of continuum biological hydrodynamics. The expression system allows writing simulation programs in near-mathematical notation and makes codes more readable, more compact, and less error-prone. It also cleanly separates the implementation of the partial differential equation model from the implementation of the numerical methods used to discretize it. This allows changing either of them with minimal changes to the source code. The presented expression system is implemented in the high-performance computing platform OpenFPM, supporting simulations that transparently parallelize on multi-processor computer systems. We demonstrate that our expression system makes it easier to write scalable codes for simulating biological hydrodynamics in space and time. We showcase the present framework in numerical simulations of active polar fluids, as well as in classic simulations of fluid dynamics from the incompressible Navier–Stokes equations to Stokes flow in a ball. The presented expression system accelerates scalable simulations of spatio-temporal models that encode the physics and material properties of tissues in order to algorithmically study morphogenesis. Graphicabstract

Live in situ visualization of numerical simulations – interactive visualization while the simulation is running – can enable new modes of interaction, including computational steering. Designing easy-to-use distributed in situ architectures, with viewing latency low enough, and frame rate high enough, for interactive use, is challenging. Here, we propose a fully asynchronous, hybrid CPU–GPU in situ architecture that emphasizes interactivity. We also present a transparent implementation of this architecture embedded into the OpenFPM simulation framework. The benchmarks show that our architecture minimizes visual latencies, and achieves frame rates between 6 and 60 frames/second – depending on simulation data size and degree of parallelism – by changing only a few lines of an existing simulation code.

As computer simulations progress to increasingly complex, non-linear, and three-dimensional systems and phenomena, intuitive and immediate visualization of their results is becoming crucial. While Virtual Reality (VR) and Natural User Interfaces (NUIs) have been shown to improve understanding of complex 3D data, their application to live in situ visualization and computational steering is hampered by performance requirements. Here, we present the design of a software framework for interactive VR in situ visualization of parallel numerical simulations, as well as a working prototype implementation. Our design is targeted towards meeting the performance requirements for VR, and our work is packaged in a framework that allows for easy instrumentation of simulations. Our preliminary results inform about the technical feasibility of the architecture, as well as the challenges that remain., 2 pages, 2 figures, accepted at IEEE Large Data Analysis and Visualization (LDAV) 2019

Scalable and efficient numerical simulations continue to gain importance, as computation is firmly established as the third pillar of discovery, alongside theory and experiment. Meanwhile, the performance of computing hardware grows through increasing heterogeneous parallelism, enabling simulations of ever more complex models. However, efficiently implementing scalable codes on heterogeneous, distributed hardware systems becomes the bottleneck. This bottleneck can be alleviated by intermediate software layers that provide higher-level abstractions closer to the problem domain, hence allowing the computational scientist to focus on the simulation. Here, we present OpenFPM, an open and scalable framework that provides an abstraction layer for numerical simulations using particles and/or meshes. OpenFPM provides transparent and scalable infrastructure for shared-memory and distributed-memory implementations of particles-only and hybrid particle-mesh simulations of both discrete and continuous models, as well as non-simulation codes. This infrastructure is complemented with portable implementations of frequently used numerical routines, as well as interfaces to third-party libraries. We present the architecture and design of OpenFPM, detail the underlying abstractions, and benchmark the framework in applications ranging from Smoothed-Particle Hydrodynamics (SPH) to Molecular Dynamics (MD), Discrete Element Methods (DEM), Vortex Methods, stencil codes, high-dimensional Monte Carlo sampling (CMA-ES), and Reaction-Diffusion solvers, comparing it to the current state of the art and existing software frameworks., 32 pages, 12 figures

Detection and quantification of fluorescently labeled molecules in subcellular compartments is a key step in the analysis of many cell biological processes. Pixel-wise colocalization analyses, however, are not always suitable, because they do not provide object-specific information, and they are vulnerable to noise and background fluorescence. Here we present a versatile protocol for a method named 'Squassh' (segmentation and quantification of subcellular shapes), which is used for detecting, delineating and quantifying subcellular structures in fluorescence microscopy images. The workflow is implemented in freely available, user-friendly software. It works on both 2D and 3D images, accounts for the microscope optics and for uneven image background, computes cell masks and provides subpixel accuracy. The Squassh software enables both colocalization and shape analyses. The protocol can be applied in batch, on desktop computers or computer clusters, and it usually requires