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Neural closure models have recently been proposed as a method for efficiently approximating small scales in multiscale systems with neural networks. The choice of loss function and associated training procedure has a large effect on the…
We provide tight finite-time convergence bounds for gradient descent and stochastic gradient descent on quadratic functions, when the gradients are delayed and reflect iterates from $\tau$ rounds ago. First, we show that without stochastic…
Dynamic optimisation occurs in a variety of real-world problems. To tackle these problems, evolutionary algorithms have been extensively used due to their effectiveness and minimum design effort. However, for dynamic problems, extra…
Performance optimization is the art of continuous seeking a harmonious mapping between the application domain and hardware. Recent years have witnessed a surge of deep learning (DL) applications in industry. Conventional wisdom for…
The multiscale complexity of modern problems in computational science and engineering can prohibit the use of traditional numerical methods in multi-dimensional simulations. Therefore, novel algorithms are required in these situations to…
Partial differential equation (PDE) solvers are extensively utilized across numerous scientific and engineering fields. However, achieving high performance and scalability often necessitates intricate and low-level programming, particularly…
In this paper, we address a way to reduce the total computational cost of meshless approximation by reducing the required stencil size through spatially varying computational node regularity. Rather than covering the entire domain with…
The Finite Difference Time Domain (FDTD) method is a widely used numerical technique for solving Maxwell's equations, particularly in computational electromagnetics and photonics. It enables accurate modeling of wave propagation in complex…
In this work, we propose a numerical approach for simulations of large deformations of interfaces in a level set framework. To obtain a fast and viable numerical solution in both time and space, temporal discretization is based on the…
Neural ordinary differential equations (NODE) have been proposed as a continuous depth generalization to popular deep learning models such as Residual networks (ResNets). They provide parameter efficiency and automate the model selection…
Stochastic programming can be applied to consider uncertainties in energy system optimization models for capacity expansion planning. However, these models become increasingly large and time-consuming to solve, even without considering…
We present RETA (Relative Timing Analysis), a differential timing analysis technique to verify the impact of an update on the execution time of embedded software. Timing analysis is computationally expensive and labor intensive. Software…
Immersed boundary methods have attracted substantial interest in the last decades due to their potential for computations involving complex geometries. Often these cannot be efficiently discretized using boundary-fitted finite elements.…
Time-dependent partial differential equations (PDEs) are ubiquitous in science and engineering. Recently, mostly due to the high computational cost of traditional solution techniques, deep neural network based surrogates have gained…
We consider large linear and nonlinear fixed point problems, and solution with proximal algorithms. We show that there is a close connection between two seemingly different types of methods from distinct fields: 1) Proximal iterations for…
The Devito DSL is a code generation tool for the solution of partial differential equations using the finite difference method specifically aimed at seismic inversion problems. In this work we investigate the integration of OPS, an API to…
We present a hybrid a-priori/a-posteriori goal oriented error estimator for a combination of dynamic iteration-based solution of ordinary differential equations discretized by finite elements. Our novel error estimator combines estimates…
We overview a series of recent works addressing numerical simulations of partial differential equations in the presence of some elements of randomness. The specific equations manipulated are linear elliptic, and arise in the context of…
This paper is concerned with the adaptive numerical treatment of stochastic partial differential equations. Our method of choice is Rothe's method. We use the implicit Euler scheme for the time discretization. Consequently, in each step, an…
PET is a functional imaging method that visualizes metabolic processes. TOF information can be derived from coincident detector signals and incorporated into image reconstruction to enhance the SNR. PET detectors are typically assessed by…