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The thermal radiative transfer (TRT) equations form an integro-differential system that describes the propagation and collisional interactions of photons. Computing accurate and efficient numerical solutions TRT are challenging for several…

Recurrent neural networks (RNNs), particularly long short-term memory (LSTM), have gained much attention in automatic speech recognition (ASR). Although some successful stories have been reported, training RNNs remains highly challenging,…

Graph Transformers have recently attracted attention for molecular property prediction by combining the inductive biases of graph neural networks (GNNs) with the global receptive field of Transformers. However, many existing hybrid…

Partial Differential Equations (PDEs) are used to model a variety of dynamical systems in science and engineering. Recent advances in deep learning have enabled us to solve them in a higher dimension by addressing the curse of…

We propose an efficient framework that integrates distance-aware multi-hop message passing with dynamic topology refinement. Unlike standard GNNs that rely on shallow, fixed-hop aggregation, DRTR leverages both static preprocessing and…

The eigenvalue problem of quantum many-body systems is a fundamental and challenging subject in condensed matter physics, since the dimension of the Hilbert space (and hence the required computational memory and time) grows exponentially as…

Physics-Informed Neural Networks (PINNs) have emerged as a powerful, mesh-free paradigm for solving partial differential equations (PDEs). However, they notoriously struggle with stiff, multi-scale, and nonlinear systems due to the inherent…

Lane-Emden differential equations describe different physical and astrophysical phenomena that include forms of stellar structure, isothermal gas spheres, gas spherical cloud thermal history, and thermionic currents. This paper presents a…

Recurrent Neural Networks (RNNs) achieve state-of-the-art results in many sequence-to-sequence modeling tasks. However, RNNs are difficult to train and tend to suffer from overfitting. Motivated by the Data Processing Inequality (DPI), we…

This paper introduces a tensor neural network (TNN) to address nonparametric regression problems, leveraging its distinct sub-network structure to effectively facilitate variable separation and enhance the approximation of complex,…

Classical methods of solving spatiotemporal dynamical systems include statistical approaches such as autoregressive integrated moving average, which assume linear and stationary relationships between systems' previous outputs. Development…

Active researches are currently being performed to incorporate the wealth of scientific knowledge into data-driven approaches (e.g., neural networks) in order to improve the latter's effectiveness. In this study, the Theory-guided Neural…

Physics-Informed Neural Networks (PINNs) have emerged as a promising approach for solving Partial Differential Equations (PDEs) by incorporating physical constraints into deep learning models. However, standard PINNs often require a large…

The state-of-the-art deep neural networks (DNNs) have significant computational and data management requirements. The size of both training data and models continue to increase. Sparsification and pruning methods are shown to be effective…

We present a numerical framework for approximating unknown governing equations using observation data and deep neural networks (DNN). In particular, we propose to use residual network (ResNet) as the basic building block for equation…

This short note describes the concept of guided training of deep neural networks (DNNs) to learn physically reasonable solutions. DNNs are being widely used to predict phenomena in physics and mechanics. One of the issues of DNNs is that…

Autonomous robot exploration (ARE) is the process of a robot autonomously navigating and mapping an unknown environment. Recent Reinforcement Learning (RL)-based approaches typically formulate ARE as a sequential decision-making problem…

Recent advances in machine learning have demonstrated an enormous utility of deep learning approaches, particularly Graph Neural Networks (GNNs) for materials science. These methods have emerged as powerful tools for high-throughput…

Fast and accurate modeling of MR signal responses are typically required for various quantitative MRI applications, such as MR Fingerprinting and MR-STAT. This work uses a new EPG-Bloch model for accurate simulation of transient-state…

Graph Neural Networks (GNN) has demonstrated the superior performance in many challenging applications, including the few-shot learning tasks. Despite its powerful capacity to learn and generalize the model from few samples, GNN usually…