Related papers: OPESCI-FD: Automatic Code Generation Package for F…
A novel recovery-based error indicator for high-order Finite Difference Methods, based on post-processing of the Finite Difference values is presented. The values obtained on the Finite Difference grid are interpolated into a suitable…
Developing efficient numerical algorithms for the solution of high dimensional random Partial Differential Equations (PDEs) has been a challenging task due to the well-known curse of dimensionality. We present a new solution framework for…
Diffusion (score-based) generative models have been widely used for modeling various types of complex data, including images, audios, and point clouds. Recently, the deep connection between forward-backward stochastic differential equations…
Procedural synthetic data generation has received increasing attention in computer vision. Procedural signed distance functions (SDFs) are a powerful tool for modeling large-scale detailed scenes, but existing mesh extraction methods have…
Shape-constrained nonparametric regression is a growing area in econometrics, statistics, operations research, machine learning and related fields. In the field of productivity and efficiency analysis, recent developments in the…
The computational efficiency of the Finite-Difference Time-Domain (FDTD) method can be significantly reduced by the presence of complex objects with fine features. Small geometrical details impose a fine mesh and a reduced time step,…
Recently, the joint design of optical systems and downstream algorithms is showing significant potential. However, existing rays-described methods are limited to optimizing geometric degradation, making it difficult to fully represent the…
The solution of optimization problems constrained by partial differential equations (PDEs) plays an important role in many areas of science and industry. In this work we present cashocs, a new software package written in Python, which…
In today's modern wide-field galaxy surveys, there is the necessity for parametric surface brightness decomposition codes characterised by accuracy, small degree of user intervention, and high degree of parallelisation. We try to address…
The end-to-end image communication system has been widely studied in the academic community. The escalating demands on image communication systems in terms of data volume, environmental complexity, and task precision require enhanced…
Exascale computing will feature novel and potentially disruptive hardware architectures. Exploiting these to their full potential is non-trivial. Numerical modelling frameworks involving finite difference methods are currently limited by…
Depth completion is a pivotal challenge in computer vision, aiming at reconstructing the dense depth map from a sparse one, typically with a paired RGB image. Existing learning based models rely on carefully prepared but limited data,…
The physics-informed neural network (PINN) is effective in solving the partial differential equation (PDE) by capturing the physics constraints as a part of the training loss function through the Automatic Differentiation (AD). This study…
Synthetic datasets are important for evaluating and testing machine learning models. When evaluating real-life recommender systems, high-dimensional categorical (and sparse) datasets are often considered. Unfortunately, there are not many…
We present a system for the automatic differentiation of a higher-order functional array-processing language. The core functional language underlying this system simultaneously supports both source-to-source automatic differentiation and…
UnDiFi-2D, an open source (free software) Unstructured-grid, Discontinuity Fitting code, is presented. The aim of UnDiFi-2D is to model gas-dynamic discontinuities in two-dimensional (2D) flows as if they were true discontinuities of null…
This paper introduces PDEformer-1, a versatile neural solver capable of simultaneously addressing various partial differential equations (PDEs). With the PDE represented as a computational graph, we facilitate the seamless integration of…
PYSCF is a Python-based general-purpose electronic structure platform that both supports first-principles simulations of molecules and solids, as well as accelerates the development of new methodology and complex computational workflows.…
We present a convergence analysis of a finite difference scheme for the time dependent partial different equation called gradient flow associated with the Rudin-Osher-Fatemi model. We devise an iterative algorithm to compute the solution of…
Predictive systems, in particular machine learning algorithms, can take important, and sometimes legally binding, decisions about our everyday life. In most cases, however, these systems and decisions are neither regulated nor certified.…