Related papers: Renormalized density matrix downfolding: A rigorou…

We develop a combined machine learning (ML) and quantum mechanics approach that enables data-efficient reconstruction of flexible molecular force fields from high-level ab initio calculations, through the consideration of fundamental…

The Hadamard decomposition is a powerful technique for data analysis and matrix compression, which decomposes a given matrix into the element-wise product of two or more low-rank matrices. In this paper, we develop an efficient algorithm to…

Many applications, such as optimization, uncertainty quantification and inverse problems, require repeatedly performing simulations of large-dimensional physical systems for different choices of parameters. This can be prohibitively…

Multi-material design optimization problems can, after discretization, be solved by the iterative solution of simpler sub-problems which approximate the original problem at an expansion point to first order. In particular, models…

Data augmentation methods are commonly integrated into the training of anomaly detection models. Previous approaches have primarily focused on replicating real-world anomalies or enhancing diversity, without considering that the standard of…

We propose a new approach to implement the density matrix renormalization group (DMRG) in two dimensions. With this approach the initial blocks of a L by L lattice are built up directly from the matrix elements of a (L-1) by L-1) lattice…

Denoising diffusion models (DDMs) have recently attracted increasing attention by showing impressive synthesis quality. DDMs are built on a diffusion process that pushes data to the noise distribution and the models learn to denoise. In…

Interpolating scattered CFD datasets onto a uniform Cartesian grid can distort the true geometry, producing a convex-hull type envelope and activating nonphysical regions. This work presents a reconstruction framework that recovers…

We propose Comprehensive Robust Dynamic Mode Decomposition (CR-DMD), a novel framework that robustifies the entire DMD process - from mode extraction to dimensional reduction - against mixed noise. Although standard DMD widely used for…

Despite perfectly interpolating the training data, deep neural networks (DNNs) can often generalize fairly well, in part due to the "implicit regularization" induced by the learning algorithm. Nonetheless, various forms of regularization,…

We introduce a novel \abinitio many-body method designed to compute the properties of nuclei in the continuum. This approach combines well-established techniques, namely the Complex Scaling (CS) and Similarity Renormalization Group (SRG)…

We consider model order reduction of parameterized Hamiltonian systems describing nondissipative phenomena, like wave-type and transport dominated problems. The development of reduced basis methods for such models is challenged by two main…

We revisit the classical problem of 3D shape interpolation and propose a novel, physically plausible approach based on Hamiltonian dynamics. While most prior work focuses on synthetic input shapes, our formulation is designed to be…

Dynamic mode decomposition (DMD) has become a powerful data-driven method for analyzing the spatiotemporal dynamics of complex, high-dimensional systems. However, conventional DMD methods are limited to matrix-based formulations, which…

The Dynamic-Mode Decomposition (DMD) is a well established data-driven method of finding temporally evolving linear-mode decompositions of nonlinear time series. Traditionally, this method presumes that all relevant dimensions are sampled…

Deep unfolding methods---for example, the learned iterative shrinkage thresholding algorithm (LISTA)---design deep neural networks as learned variations of optimization methods. These networks have been shown to achieve faster convergence…

Part of the success of diffusion models stems from their ability to perform iterative refinement, i.e., repeatedly correcting outputs during generation. However, modern masked discrete diffusion lacks this capability: when a token is…

We present a scheme to controllably improve the accuracy of tight-binding Hamiltonian matrices derived by projecting the solutions of plane-wave ab initio calculations on atomic orbital basis sets. By systematically increasing the…

This paper presents a novel framework to recover detailed human body shapes from a single image. It is a challenging task due to factors such as variations in human shapes, body poses, and viewpoints. Prior methods typically attempt to…

A new density matrix renormalisation group (DMRG) approach is presented for quantum systems of two spatial dimensions. In particular, it is shown that it is possible to create a multi-chain-type 2D DMRG approach which utilises previously…