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In a previous article we have shown how one can employ Artificial Neural Networks (ANNs) in order to solve non-homogeneous ordinary and partial differential equations. In the present work we consider the solution of eigenvalue problems for…

Quantum Physics · Physics 2009-10-30 I. E. Lagaris , A. Likas , D. I. Fotiadis

The quadratic complexity of dot-product attention introduced in Transformer remains a fundamental bottleneck impeding the progress of foundation models toward unbounded context lengths. Addressing this challenge, we introduce the Deep…

Machine Learning · Computer Science 2025-09-03 Yifan Zhang

We introduce $\Sigma$-Attention, a Transformer-based operator-learning framework to address a key computational challenge in correlated materials. Our approach utilizes an Encoder-Only Transformer as an ansatz to approximate the self-energy…

Strongly Correlated Electrons · Physics 2025-06-02 Yuanran Zhu , Peter Rosenberg , Zhen Huang , Hardeep Bassi , Chao Yang , Shiwei Zhang

Accurately solving the Schr\"odinger equation remains a central challenge in computational physics, chemistry, and materials science. Here, we propose an alternative eigenvalue problem based on a system's autocorrelation function, avoiding…

Quantum Physics · Physics 2025-07-22 Timothy Stroschein , Davide Castaldo , Markus Reiher

Neural network quantum state (NNQS) has emerged as a promising candidate for quantum many-body problems, but its practical applications are often hindered by the high cost of sampling and local energy calculation. We develop a…

Quantum Physics · Physics 2023-11-02 Yangjun Wu , Chu Guo , Yi Fan , Pengyu Zhou , Honghui Shang

In recent years, neural network quantum states (NNQS) have emerged as powerful tools for the study of quantum many-body systems. Electronic structure calculations are one such canonical many-body problem that have attracted significant…

Chemical Physics · Physics 2022-01-27 Thomas D. Barrett , Aleksei Malyshev , A. I. Lvovsky

Data-driven learning of partial differential equations' solution operators has recently emerged as a promising paradigm for approximating the underlying solutions. The solution operators are usually parameterized by deep learning models…

Machine Learning · Computer Science 2023-05-01 Zijie Li , Kazem Meidani , Amir Barati Farimani

Machine learning has enabled the prediction of quantum chemical properties with high accuracy and efficiency, allowing to bypass computationally costly ab initio calculations. Instead of training on a fixed set of properties, more recent…

Relying entirely on an attention mechanism, the Transformer introduced by Vaswani et al. (2017) achieves state-of-the-art results for machine translation. In contrast to recurrent and convolutional neural networks, it does not explicitly…

Computation and Language · Computer Science 2018-04-16 Peter Shaw , Jakob Uszkoreit , Ashish Vaswani

Quantum theory has been remarkably successful in providing an understanding of physical systems at foundational scales. Solving the Schr\"odinger equation provides full knowledge of all dynamical quantities of the physical system. However…

Quantum Physics · Physics 2020-11-24 Cesar Lema , Anna Choromanska

We present JefiAtten, a novel neural network model employing the attention mechanism to solve Maxwell's equations efficiently. JefiAtten uses self-attention and cross-attention modules to understand the interplay between charge density,…

Computational Physics · Physics 2024-02-28 Ming-Yan Sun , Peng Xu , Jun-Jie Zhang , Tai-Jiao Du , Jian-Guo Wang

The point cloud learning community witnesses a modeling shift from CNNs to Transformers, where pure Transformer architectures have achieved top accuracy on the major learning benchmarks. However, existing point Transformers are…

Computer Vision and Pattern Recognition · Computer Science 2022-03-25 Zhang Cheng , Haocheng Wan , Xinyi Shen , Zizhao Wu

Designing a single neural network architecture that performs competitively across a range of molecule property prediction tasks remains largely an open challenge, and its solution may unlock a widespread use of deep learning in the drug…

Machine Learning · Computer Science 2021-02-10 Łukasz Maziarka , Tomasz Danel , Sławomir Mucha , Krzysztof Rataj , Jacek Tabor , Stanisław Jastrzębski

Despite their widespread success in various domains, Transformer networks have yet to perform well across datasets in the domain of 3D atomistic graphs such as molecules even when 3D-related inductive biases like translational invariance…

Machine Learning · Computer Science 2023-03-01 Yi-Lun Liao , Tess Smidt

Spiking neural networks (SNNs) have made great progress on both performance and efficiency over the last few years,but their unique working pattern makes it hard to train a high-performance low-latency SNN.Thus the development of SNNs still…

Neural and Evolutionary Computing · Computer Science 2022-11-22 Yudong Li , Yunlin Lei , Xu Yang

Physics-Informed Neural Networks (PINNs) have emerged as a promising deep learning framework for approximating numerical solutions to partial differential equations (PDEs). However, conventional PINNs, relying on multilayer perceptrons…

Computational Engineering, Finance, and Science · Computer Science 2024-05-08 Zhiyuan Zhao , Xueying Ding , B. Aditya Prakash

Atomistic modeling of energetic disorder in organic semiconductors (OSCs) and its effects on the optoelectronic properties of OSCs requires a large number of excited-state electronic-structure calculations, a computationally daunting task…

Chemical Physics · Physics 2021-05-10 Chengqiang Lu , Qi Liu , Qiming Sun , Chang-Yu Hsieh , Shengyu Zhang , Liang Shi , Chee-Kong Lee

Schr\"odinger's equation serves as a fundamental component in characterizing quantum systems, wherein both quantum state tomography and Hamiltonian learning are instrumental in comprehending and interpreting quantum systems. While numerous…

Quantum Physics · Physics 2024-01-25 Zheng An , Jiahui Wu , Muchun Yang , D. L. Zhou , Bei Zeng

Although Transformer models such as Google's BERT and OpenAI's GPT-3 are successful in many natural language processing tasks, training and deploying these models are costly and inefficient.Even if pre-trained models are used, deploying…

Machine Learning · Computer Science 2021-01-26 Madhusudan Verma

We present \textsc{dm-PhiSNet}, a physically constrained \textsc{PhiSNet}-based equivariant model that predicts one-electron reduced density matrices (1-RDMs) directly from molecular geometries in an atomic-orbital (AO) basis for…

Chemical Physics · Physics 2026-05-01 Zuriel Y. Yescas-Ramos , Andrés Álvarez-García , Huziel E. Sauceda