Related papers: Automating the Design of Multigrid Methods with Ev…

This work studies a variational formulation and numerical solution of a regularized morphoelasticity problem of shape evolution. The foundation of our analysis is based on the governing equations of linear elasticity, extended to account…

Data-efficient image classification is a challenging task that aims to solve image classification using small training data. Neural network-based deep learning methods are effective for image classification, but they typically require…

Partial differential equations (PDEs) are typically used as models of physical processes but are also of great interest in PDE-based image processing. However, when it comes to their use in imaging, conventional numerical methods for…

The efficient generation of meshes is an important step in the numerical solution of various problems in physics and engineering. We are interested in situations where global mesh quality and tight coupling to the physical solution is…

The problem of finding the solution of Partial Differential Equations (PDEs) plays a central role in modeling real world problems. Over the past years, Multigrid solvers have showed their robustness over other techniques, due to its high…

Recent advances in generative artificial intelligence have had a significant impact on diverse domains spanning computer vision, natural language processing, and drug discovery. This work extends the reach of generative models into physical…

Recently, a lot of papers proposed to use neural networks to approximately solve partial differential equations (PDEs). Yet, there has been a lack of flexible framework for convenient experimentation. In an attempt to fill the gap, we…

Blended modeling is an emerging paradigm involving seamless interaction between multiple notations for the same underlying modeling language. We focus on a model-driven engineering (MDE) approach based on meta-models to develop textual…

We present a brief survey on the modern tensor numerical methods for multidimensional stationary and time-dependent partial differential equations (PDEs). The guiding principle of the tensor approach is the rank-structured separable…

In recent years, Deep Learning models have shown a great performance in complex optimization problems. They generally require large training datasets, which is a limitation in most practical cases. Transfer learning allows importing the…

Stencil computations are a key part of many high-performance computing applications, such as image processing, convolutional neural networks, and finite-difference solvers for partial differential equations. Devito is a framework capable of…

We present an iterative scheme, reminiscent of the Multigrid method, to solve large boundary value problems with Probabilistic Domain Decomposition (PDD). In it, increasingly accurate approximations to the solution are used as control…

While recent AI-for-math has made strides in pure mathematics, areas of applied mathematics, particularly PDEs, remain underexplored despite their significant real-world applications. We present PDE-Controller, a framework that enables…

Convolution-type integral equations commonly occur in signal processing and image processing. Discretizing these equations yields large and ill-conditioned linear systems. While the classic multigrid method is effective for solving linear…

Partial differential equations (PDEs) are often computationally challenging to solve, and in many settings many related PDEs must be be solved either at every timestep or for a variety of candidate boundary conditions, parameters, or…

Prompt engineering is a challenging and important task due to the high sensitivity of Large Language Models (LLMs) to the given prompt and the inherent ambiguity of a textual task instruction. Automatic prompt engineering is essential to…

Multigrid methods are well suited to large massively parallel computer architectures because they are mathematically optimal and display excellent parallelization properties. Since current architecture trends are favoring regular compute…

The performance of a syntax-guided synthesis algorithm is highly dependent on the provision of a good syntactic template, or grammar. Provision of such a template is often left to the user to do manually, though in the absence of such a…

We present in this paper a new approach for polyphonic music transcription using evolution strategies (ES). Automatic music transcription is a complex process that still remains an open challenge. Using an audio signal to be transcribed as…

Differentiable programming has revolutionised optimisation by enabling efficient gradient-based training of complex models, such as Deep Neural Networks (NNs) with billions and trillions of parameters. However, traditional Evolutionary…