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Incorporating symmetries can lead to highly data-efficient and generalizable models by defining equivalence classes of data samples related by transformations. However, characterizing how transformations act on input data is often…

Neural networks (NNs) are inherently multidimensional classifiers that learn complex, non-linear relationships among input observables. While their flexibility enables unprecedented performance in high-energy physics (HEP) analyses, it also…

Understanding the dynamic processes of the glassy system continues to be challenging. Recent advances have shown the power of graph neural networks (GNNs) for determining the correlation between structure and dynamics in the glassy system.…

Stochastic gradient descent (SGD) is a standard optimization method to minimize a training error with respect to network parameters in modern neural network learning. However, it typically suffers from proliferation of saddle points in the…

Network data are ubiquitous in modern machine learning, with tasks of interest including node classification, node clustering and link prediction. A frequent approach begins by learning an Euclidean embedding of the network, to which…

The Synthetic Nervous System (SNS) is a biologically inspired neural network (NN). Due to its capability of capturing complex mechanisms underlying neural computation, an SNS model is a candidate for building compact and interpretable NN…

In this paper, we introduces a Pseudo-Symplectic Neural Network (PSNN) for learning general Hamiltonian systems (both separable and non-separable) from data. To address the limitations of existing structure-preserving methods (e.g.,…

Accurately predicting the elastic properties of crystalline solids is vital for computational materials science. However, traditional atomistic scale ab initio approaches are computationally intensive, especially for studying complex…

The fast and accurate prediction of unsteady flow becomes a serious challenge in fluid dynamics, due to the high-dimensional and nonlinear characteristics. A novel hybrid deep neural network (DNN) architecture was designed to capture the…

A key aspect of human intelligence is the ability to infer abstract rules directly from high-dimensional sensory data, and to do so given only a limited amount of training experience. Deep neural network algorithms have proven to be a…

Neural networks are powerful function estimators, leading to their status as a paradigm of choice for modeling structured data. However, unlike other structured representations that emphasize the modularity of the problem -- e.g., factor…

Recently, learning-based image compression methods that utilize convolutional neural layers have been developed rapidly. Rescaling modules such as batch normalization which are often used in convolutional neural networks do not operate…

A physics-constrained neural network is presented for predicting the optical response of metasurfaces. Our approach incorporates physical laws directly into the neural network architecture and loss function, addressing critical challenges…

Soft biological tissues often have complex mechanical properties due to variation in structural components. In this paper, we develop a novel UNet-based neural network model for inversion in elasticity (El-UNet) to infer the spatial…

Graph Neural Networks (GNN) can capture the geometric properties of neural representations in EEG data. Here we utilise those to study how reinforcement-based motor learning affects neural activity patterns during motor planning, leveraging…

In many cases, the computing resources are limited without the benefit from GPU, especially in the edge devices of IoT enabled systems. It may not be easy to implement complex AI models in edge devices. The Universal Approximation Theorem…

Due to its geometric properties, hyperbolic space can support high-fidelity embeddings of tree- and graph-structured data, upon which various hyperbolic networks have been developed. Existing hyperbolic networks encode geometric priors not…

Many supervised learning tasks have intrinsic symmetries, such as translational and rotational symmetry in image classifications. These symmetries can be exploited to enhance performance. We formulate the symmetry constraints into a concise…

Graph representation learning resurges as a trending research subject owing to the widespread use of deep learning for Euclidean data, which inspire various creative designs of neural networks in the non-Euclidean domain, particularly…

Graph neural networks excel at modeling pairwise interactions, but they cannot flexibly accommodate higher-order interactions and features. Topological deep learning (TDL) has emerged recently as a promising tool for addressing this issue.…