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In this paper, we propose a stochastic-dimension frozen sampled neural network (SD-FSNN) for solving a class of high-dimensional Gross-Pitaevskii equations (GPEs) on unbounded domains. SD-FSNN is unbiased across all dimensions, and its…

Time series forecasting often demands a trade-off between accuracy and efficiency. While recent Transformer models have improved forecasting capabilities, they come with high computational costs. Linear-based models have shown better…

There has been an arising trend of adopting deep learning methods to study partial differential equations (PDEs). In this paper, we introduce a deep recurrent framework for solving time-dependent PDEs without generating large scale data…

Spatiotemporal datasets, which consist of spatially-referenced time series, are ubiquitous in diverse applications, such as air pollution monitoring, disease tracking, and cloud-demand forecasting. As the scale of modern datasets increases,…

We propose a versatile framework for survival analysis that combines advanced concepts from statistics with deep learning. The presented framework is based on piecewise exponential models and thereby supports various survival tasks, such as…

How to improve generative modeling by better exploiting spatial regularities and coherence in images? We introduce a novel neural network for building image generators (decoders) and apply it to variational autoencoders (VAEs). In our…

We propose STANE (Shared and Time-specific Adaptive Network Embedding), a new joint embedding framework for dynamic networks that captures both stable global structures and localized temporal variations. To further improve the model's…

Unsupervised structure learning in high-dimensional time series data has attracted a lot of research interests. For example, segmenting and labelling high dimensional time series can be helpful in behavior understanding and medical…

Solving partial differential equations (PDEs) is the canonical approach for understanding the behavior of physical systems. However, large scale solutions of PDEs using state of the art discretization techniques remains an expensive…

We introduce Neural Parameter Regression (NPR), a novel framework specifically developed for learning solution operators in Partial Differential Equations (PDEs). Tailored for operator learning, this approach surpasses traditional DeepONets…

We present an approach to numerical homogenization of the elastic response of microstructures. Our work uses deep neural network representations trained on data obtained from direct numerical simulation (DNS) of martensitic phase…

Discovering the underlying relationships among variables from temporal observations has been a longstanding challenge in numerous scientific disciplines, including biology, finance, and climate science. The dynamics of such systems are…

Machine learning models can be used to predict physical quantities like homogenized elasticity stiffness tensors, which must always be symmetric positive definite (SPD) based on conservation arguments. Two datasets of homogenized elasticity…

Combining additive models and neural networks allows to broaden the scope of statistical regression and extend deep learning-based approaches by interpretable structured additive predictors at the same time. Existing attempts uniting the…

In this paper, we present SSDNet, a novel deep learning approach for time series forecasting. SSDNet combines the Transformer architecture with state space models to provide probabilistic and interpretable forecasts, including trend and…

Deep neural network (DNN) models have achieved state-of-the-art predictive accuracy in a wide range of supervised learning applications. However, accurately quantifying the uncertainty in DNN predictions remains a challenging task. For…

This work presents a two-stage adaptive framework for progressively developing deep neural network (DNN) architectures that generalize well for a given training data set. In the first stage, a layerwise training approach is adopted where a…

Stochastic Petri Nets (SPNs) are an increasingly popular tool of choice for modeling discrete-event dynamics in areas such as epidemiology and systems biology, yet their parameter estimation remains challenging in general and in particular…

In this paper, we propose the Deep Structured self-Driving Network (DSDNet), which performs object detection, motion prediction, and motion planning with a single neural network. Towards this goal, we develop a deep structured energy based…

Neural network-based solvers for partial differential equations (PDEs) have attracted considerable attention, yet they often face challenges in accuracy and computational efficiency. In this work, we focus on time-dependent PDEs and observe…