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We present MAGNET (Model Autonomously Growing Network), a decentralized system for autonomous generation, training, and serving of domain-expert language models across commodity hardware. MAGNET integrates four components: (1) autoresearch,…

We propose MESA and DMESA as novel feature matching methods, which utilize Segment Anything Model (SAM) to effectively mitigate matching redundancy. The key insight of our methods is to establish implicit-semantic area matching prior to…

Isogeometric analysis (IGA) has become one of the most popular methods for the discretization of partial differential equations motivated by the use of NURBS for geometric representations in industry and science. A crucial challenge lies in…

Dynamic mode decomposition (DMD) is a recently developed tool for the analysis of the behavior of complex dynamical systems. In this paper, we will propose an extension of DMD that exploits low-rank tensor decompositions of potentially…

In this work, we propose a machine learning-based approach to address a specific aspect of the Quantum Marginal Problem: reconstructing a global density matrix compatible with a given set of quantum marginals. Our method integrates a…

The tensor decomposition addressed in this paper may be seen as a generalisation of Singular Value Decomposition of matrices. We consider general multilinear and multihomogeneous tensors. We show how to reduce the problem to a truncated…

We present the marginal unbiased score expansion (MUSE) method, an algorithm for generic high-dimensional hierarchical Bayesian inference. MUSE performs approximate marginalization over arbitrary non-Gaussian latent parameter spaces,…

Originally, tangles were invented as an abstract tool in mathematical graph theory to prove the famous graph minor theorem. In this paper, we showcase the practical potential of tangles in machine learning applications. Given a collection…

In order to comprehensively investigate the multiphysics coupling in spintronic devices, it is essential to parallelize and utilize GPU-acceleration to address the spatial and temporal disparities inherent in the relevant physics.…

To respond to the need of efficient training and inference of deep neural networks, a plethora of domain-specific hardware architectures have been introduced, such as Google Tensor Processing Units and NVIDIA Tensor Cores. A common feature…

The computational complexity of classical numerical methods for solving Partial Differential Equations (PDE) scales significantly as the resolution increases. As an important example, climate predictions require fine spatio-temporal…

In this paper, we propose a multi-resolution deep-learning architecture to semantically segment dense large-scale pointclouds. Dense pointcloud data require a computationally expensive feature encoding process before semantic segmentation.…

The prediction of the quasi-static response of industrial laminate structures requires to use fine descriptions of the material, especially when debonding is involved. Even when modeled at the mesoscale, the computation of these structures…

A common optimization problem in the areas of magnetized plasmas and fusion energy is the design of magnets to produce a given three-dimensional magnetic field distribution to high precision. When designing arrays of permanent magnets for…

Optimizing over the set of orthogonal matrices is a central component in problems like sparse-PCA or tensor decomposition. Unfortunately, such optimization is hard since simple operations on orthogonal matrices easily break orthogonality,…

Since its introduction by Gauss, Matrix Algebra has facilitated understanding of scientific problems, hiding distracting details and finding more elegant and efficient ways of computational solving. Today's largest problems, which often…

We develop a new spatial semidiscrete multiscale method based upon the edge multiscale methods to solve semilinear parabolic problems with heterogeneous coefficients and smooth initial data. This method allows for a cheap spatial…

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…

The calculation of the demagnetization field is crucial in various disciplines, including magnetic resonance imaging (MRI) and micromagnetics. A standard method involves discretizing the spatial domain into finite difference cells and using…

This study proposes an automated data mining framework based on autoencoders and experimentally verifies its effectiveness in feature extraction and data dimensionality reduction. Through the encoding-decoding structure, the autoencoder can…