Related papers: Reconstructing a dynamical system and forecasting …
Ability of deep networks to extract high level features and of recurrent networks to perform time-series inference have been studied. In view of universality of one hidden layer network at approximating functions under weak constraints, the…
This script offers an implementation-oriented introduction to deep learning methods for solving and estimating high-dimensional dynamic stochastic models in economics and finance. Its starting point is the curse of dimensionality:…
Improving the interpretability of deep neural networks has recently gained increased attention, especially when the power of deep learning is leveraged to solve problems in physics. Interpretability helps us understand a model's ability to…
Identifying governing equations for a dynamical system is a topic of critical interest across an array of disciplines, from mathematics to engineering to biology. Machine learning -- specifically deep learning -- techniques have shown their…
While deep feature learning has revolutionized techniques for static-image understanding, the same does not quite hold for video processing. Architectures and optimization techniques used for video are largely based off those for static…
The feasibility of deep neural networks (DNNs) to address data stream problems still requires intensive study because of the static and offline nature of conventional deep learning approaches. A deep continual learning algorithm, namely…
This paper presents a method for time series forecasting with deep learning and its assessment on two datasets. The method starts with data preparation, followed by model training and evaluation. The final step is a visual inspection.…
We build on the dynamical systems approach to deep learning, where deep residual networks are idealized as continuous-time dynamical systems, from the approximation perspective. In particular, we establish general sufficient conditions for…
The quality of data representation in deep learning methods is directly related to the prior model imposed on the representations; however, generally used fixed priors are not capable of adjusting to the context in the data. To address this…
Time-series forecasting remains difficult in real-world settings because temporal patterns operate at multiple scales, from broad contextual trends to fast, fine-grained fluctuations that drive critical decisions. Existing neural models…
We consider the problem of forecasting complex, nonlinear space-time processes when observations provide only partial information of on the system's state. We propose a natural data-driven framework, where the system's dynamics are modelled…
We investigate recurrent neural networks with asymmetric interactions and demonstrate that the inclusion of self-couplings or sparse excitatory inter-module connections leads to the emergence of a densely connected manifold of dynamically…
We describe a novel method for modeling non-stationary multivariate time series, with time-varying conditional dependencies represented through dynamic networks. Our proposed approach combines traditional multi-scale modeling and network…
A common problem in time series analysis is to predict dynamics with only scalar or partial observations of the underlying dynamical system. For data on a smooth compact manifold, Takens theorem proves a time delayed embedding of the…
In this paper we explore the performance of deep hidden physics model (M. Raissi 2018) for autonomous systems. These systems are described by set of ordinary differential equations which do not explicitly depend on time. Such systems can be…
In comparison to classical shallow representation learning techniques, deep neural networks have achieved superior performance in nearly every application benchmark. But despite their clear empirical advantages, it is still not well…
Time series forecasting based on deep architectures has been gaining popularity in recent years due to their ability to model complex non-linear temporal dynamics. The recurrent neural network is one such model capable of handling…
Recently there has been substantial interest in spectral methods for learning dynamical systems. These methods are popular since they often offer a good tradeoff between computational and statistical efficiency. Unfortunately, they can be…
Graph deep learning methods have become popular tools to process collections of correlated time series. Unlike traditional multivariate forecasting methods, graph-based predictors leverage pairwise relationships by conditioning forecasts on…
Time series analysis is a fundamental task in various application domains, and deep learning approaches have demonstrated remarkable performance in this area. However, many real-world time series data exhibit significant periodic or…