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The time evolution of physical systems is described by differential equations, which depend on abstract quantities like energy and force. Traditionally, these quantities are derived as functionals based on observables such as positions and…
The predictive learning of spatiotemporal sequences aims to generate future images by learning from the historical context, where the visual dynamics are believed to have modular structures that can be learned with compositional subsystems.…
We present a new model, Predictive State Recurrent Neural Networks (PSRNNs), for filtering and prediction in dynamical systems. PSRNNs draw on insights from both Recurrent Neural Networks (RNNs) and Predictive State Representations (PSRs),…
Data-driven models for predicting dynamic responses of linear and nonlinear systems are of great importance due to their wide application from probabilistic analysis to inverse problems such as system identification and damage diagnosis. In…
In this paper, we study novel neural network structures to better model long term dependency in sequential data. We propose to use more memory units to keep track of more preceding states in recurrent neural networks (RNNs), which are all…
We introduce Effective Field Neural Networks (EFNNs), a new architecture based on continued functions -- mathematical tools used in renormalization to handle divergent perturbative series. Our key insight is that neural networks can…
Many nonequilibrium systems, such as biochemical reactions and socioeconomic interactions, can be described by reaction-diffusion equations that demonstrate a wide variety of complex spatiotemporal patterns. The diversity of the morphology…
This paper presents a new algorithm, Evolutionary eXploration of Augmenting Memory Models (EXAMM), which is capable of evolving recurrent neural networks (RNNs) using a wide variety of memory structures, such as Delta-RNN, GRU, LSTM, MGU…
Recurrent neural networks are machine learning algorithms which are suited well to predict time series. Echo state networks are one specific implementation of such neural networks that can describe the evolution of dynamical systems by…
Attempts to apply Neural Networks (NN) to a wide range of research problems have been ubiquitous and plentiful in recent literature. Particularly, the use of deep NNs for understanding complex physical and chemical phenomena has opened a…
Recently, three dimensional (3D) convolutional neural networks (CNNs) have emerged as dominant methods to capture spatiotemporal representations in videos, by adding to pre-existing 2D CNNs a third, temporal dimension. Such 3D CNNs,…
Spatiotemporal forecasting has various applications in neuroscience, climate and transportation domain. Traffic forecasting is one canonical example of such learning task. The task is challenging due to (1) complex spatial dependency on…
Convolutional architectures have recently been shown to be competitive on many sequence modelling tasks when compared to the de-facto standard of recurrent neural networks (RNNs), while providing computational and modeling advantages due to…
The convolutional neural network (CNN) has become a basic model for solving many computer vision problems. In recent years, a new class of CNNs, recurrent convolution neural network (RCNN), inspired by abundant recurrent connections in the…
Graph-structured data commonly arise in many real-world applications, and this extends naturally into the quantum setting, where quantum data with inherent graph structures are frequently generated by typical quantum data sources. However,…
The era of data deluge has sparked the interest in graph-based learning methods in a number of disciplines such as sociology, biology, neuroscience, or engineering. In this paper, we introduce a graph recurrent neural network (GRNN) for…
We propose a hybrid meta-learning framework for forecasting and anomaly detection in nonlinear dynamical systems characterized by nonstationary and stochastic behavior. The approach integrates a physics-inspired simulator that captures…
Real-world time series data exhibit non-stationary behavior, regime shifts, and temporally varying noise (heteroscedastic) that degrade the robustness of standard regression models. We introduce the Variability-Aware Recursive Neural…
We investigate the use of discrete and continuous versions of physics-informed neural network methods for learning unknown dynamics or constitutive relations of a dynamical system. For the case of unknown dynamics, we represent all the…
In a number of disciplines, the data (e.g., graphs, manifolds) to be analyzed are non-Euclidean in nature. Geometric deep learning corresponds to techniques that generalize deep neural network models to such non-Euclidean spaces. Several…