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Hyperbolic geometry has emerged as a powerful tool for modeling complex, structured data, particularly where hierarchical or tree-like relationships are present. By enabling embeddings with lower distortion, hyperbolic neural networks offer…

A continual learning (CL) algorithm learns from a non-stationary data stream. The non-stationarity is modeled by some schedule that determines how data is presented over time. Most current methods make strong assumptions on the schedule and…

Much combinatorial optimisation problems constitute a non-polynomial (NP) hard optimisation problem, i.e., they can not be solved in polynomial time. One such problem is finding the shortest route between two nodes on a graph.…

Recurrent Neural Networks (RNN) are ubiquitous computing systems for sequences and multivariate time series data. While several robust architectures of RNN are known, it is unclear how to relate RNN initialization, architecture, and other…

Models with dominant advection always posed a difficult challenge for projection-based reduced order modelling. Many methodologies that have recently been proposed are based on the pre-processing of the full-order solutions to accelerate…

Across scientific domains, a fundamental challenge is to characterize and compute the mappings from underlying physical processes to observed signals and measurements. While nonlinear neural networks have achieved considerable success, they…

The design of recurrent neural networks (RNNs) to accurately process sequential inputs with long-time dependencies is very challenging on account of the exploding and vanishing gradient problem. To overcome this, we propose a novel RNN…

Deep neural networks (DNN) have shown great capacity of modeling a dynamical system; nevertheless, they usually do not obey physics constraints such as conservation laws. This paper proposes a new learning framework named ConCerNet to…

Modern IT system operation demands the integration of system software and hardware metrics. As a result, it generates a massive amount of data, which can be potentially used to make data-driven operational decisions. In the basic form, the…

To have a superior generalization, a deep learning neural network often involves a large size of training sample. With increase of hidden layers in order to increase learning ability, neural network has potential degradation in accuracy.…

Despite a lot of research efforts devoted in recent years, how to efficiently learn long-term dependencies from sequences still remains a pretty challenging task. As one of the key models for sequence learning, recurrent neural network…

Forecasting models are pivotal in a data-driven world with vast volumes of time series data that appear as a compound of vast Linear and Nonlinear patterns. Recent deep time series forecasting models struggle to utilize seasonal and trend…

In recent years residual neural networks (ResNets) as introduced by [He, K., Zhang, X., Ren, S., and Sun, J., Proceedings of the IEEE conference on computer vision and pattern recognition (2016), 770-778] have become very popular in a large…

Identifying reaction coordinates (RCs) is a key to understanding the mechanism of reactions in complex systems. Deep neural network (DNN) and machine learning approaches have become a powerful tool to find the RC. On the other hand, the…

Most real-world datasets consist of a natural hierarchy between classes or an inherent label structure that is either already available or can be constructed cheaply. However, most existing representation learning methods ignore this…

The ability to learn in dynamic, nonstationary environments without forgetting previous knowledge, also known as Continual Learning (CL), is a key enabler for scalable and trustworthy deployments of adaptive solutions. While the importance…

We consider the approximation of entropy solutions of nonlinear hyperbolic conservation laws using neural networks. We provide explicit computations that highlight why classical PINNs will not work for discontinuous solutions to nonlinear…

For hyperbolic conservation laws, traditional methods and physics-informed neural networks (PINNs) often encounter difficulties in capturing sharp discontinuities and maintaining temporal consistency. To address these challenges, we…

Proper orthogonal decomposition (POD) allows reduced-order modeling of complex dynamical systems at a substantial level, while maintaining a high degree of accuracy in modeling the underlying dynamical systems. Advances in machine learning…

We present a novel approach (DyNODE) that captures the underlying dynamics of a system by incorporating control in a neural ordinary differential equation framework. We conduct a systematic evaluation and comparison of our method and…