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In this paper, we propose a numerical scheme for structured population models defined on a separable and complete metric space. In particular, we consider a generalized version of a transport equation with additional growth and non-local…
The constant increase in parallelism available on large-scale distributed computers poses major scalability challenges to many scientific applications. A common strategy to improve scalability is to express the algorithm in terms of…
In recent years, simulation methods based on the scaling of atomic potential functions, such as quasi-coarse-grained dynamics and coarse-grained dynamics, have shown promising results for modeling crystalline systems at multiple scales.…
Stochastic equations play an important role in computational science, due to their ability to treat a wide variety of complex statistical problems. However, current algorithms are strongly limited by their sampling variance, which scales…
Current AMR simulations require algorithms that are highly parallelized and manage memory efficiently. As compute engines grow larger, AMR simulations will require algorithms that achieve new levels of efficient parallelization and memory…
Large-scale deep learning models contribute to significant performance improvements on varieties of downstream tasks. Current data and model parallelism approaches utilize model replication and partition techniques to support the…
Recent work has shown a variety of ways in which machine learning can be used to accelerate the solution of constrained optimization problems. Increasing demand for real-time decision-making capabilities in applications such as artificial…
Biochemical networks play a crucial role in biological systems, implementing a broad range of vital functions. They normally operate at low copy numbers and in spatial settings, but this is often ignored and well-stirred conditions are…
Design of next generation computer systems should be supported by simulation infrastructure that must achieve a few contradictory goals such as fast execution time, high accuracy, and enough flexibility to allow comparison between large…
Particle-In-Cell codes are widely used for plasma physics simulations. It is often the case that particles within a computational cell need to be split to improve the statistics or, in the case of non-uniform meshes, to avoid the…
Collisional and stochastic wave-particle dynamics in plasmas far from equilibrium are complex, temporally evolving, stochastic processes which are challenging to model. In this work, we extend previous methods coupling differentiable…
The probability distribution describing the state of a Stochastic Reaction Network evolves according to the Chemical Master Equation (CME). It is common to estimated its solution using Monte Carlo methods such as the Stochastic Simulation…
A random recursive cell splitting scheme of the $2$-dimensional unit sphere is considered, which is the spherical analogue of the STIT tessellation process from Euclidean stochastic geometry. First-order moments are computed for a large…
This article describes algorithms for the hybrid parallelization and SIMD vectorization of molecular dynamics simulations with short-range forces. The parallelization method combines domain decomposition with a thread-based parallelization…
Molecular dynamics simulations produce data with complex nonlinear dynamics. If the timestep behavior of such a dynamic system can be represented by a linear operator, future states can be inferred directly without expensive simulations.…
We present GridFF, an efficient method for simulating molecules on rigid substrates, derived from techniques used in protein-ligand docking in biochemistry. By projecting molecule-substrate interactions onto precomputed spatial grids with…
This paper proposes a general formulation for temporal parallelisation of dynamic programming for optimal control problems. We derive the elements and associative operators to be able to use parallel scans to solve these problems with…
Kernel embeddings of distributions have recently gained significant attention in the machine learning community as a data-driven technique for representing probability distributions. Broadly, these techniques enable efficient computation of…
Parallelization is a popular strategy for improving the performance of iterative algorithms. Optimization methods are no exception: design of efficient parallel optimization methods and tight analysis of their theoretical properties are…
In view of the existing limitations of sequential computing, parallelization has emerged as an alternative in order to improve the speedup of numerical simulations. In the framework of evolutionary problems, space-time parallel methods…