相关论文: On Lyapunov Exponents for RNNs: Understanding Info…

In this paper, we elaborate over the well-known interpretability issue in echo state networks. The idea is to investigate the dynamics of reservoir neurons with time-series analysis techniques taken from research on complex systems.…

We present Linear Diffusion Networks (LDNs), a novel architecture that reinterprets sequential data processing as a unified diffusion process. Our model integrates adaptive diffusion modules with localized nonlinear updates and a…

An iterated multistep forecasting scheme based on recurrent neural networks (RNN) is proposed for the time series generated by causal chains with infinite memory. This forecasting strategy contains, as a particular case, the iterative…

Classical methods of solving spatiotemporal dynamical systems include statistical approaches such as autoregressive integrated moving average, which assume linear and stationary relationships between systems' previous outputs. Development…

In this article we study if a Deep Learning technique can be used to obtain an approximated value of the Lyapunov exponents of a dynamical system. Moreover, we want to know if Machine Learning techniques are able, once trained, to provide…

A new order parameter approximation to Random Boolean Networks (RBN) is introduced, based on the concept of Boolean derivative. A statistical argument involving an annealed approximation is used, allowing to measure the order parameter in…

This paper addresses the problem of Neural Network (NN) based adaptive stability certification in a dynamical system. The state-of-the-art methods, such as Neural Lyapunov Functions (NLFs), use NN-based formulations to assess the stability…

Recurrent neural networks (RNNs) are commonly applied to clinical time-series data with the goal of learning patient risk stratification models. Their effectiveness is due, in part, to their use of parameter sharing over time (i.e., cells…

Recurrent Neural Networks (RNNs), and specifically a variant with Long Short-Term Memory (LSTM), are enjoying renewed interest as a result of successful applications in a wide range of machine learning problems that involve sequential data.…

Recurrent Networks are one of the most powerful and promising artificial neural network algorithms to processing the sequential data such as natural languages, sound, time series data. Unlike traditional feed-forward network, Recurrent…

Training recurrent neural networks (RNNs) remains a challenge due to the instability of gradients across long time horizons, which can lead to exploding and vanishing gradients. Recent research has linked these problems to the values of…

Expansion property of a graph refers to its strong connectivity as well as sparseness. It has been reported that deep neural networks can be pruned to a high degree of sparsity while maintaining their performance. Such pruning is essential…

We consider the method of Reduction of Dissipativity Domain to prove global Lyapunov stability of Discrete Time Recurrent Neural Networks. The standard and advanced criteria for Absolute Stability of these essentially nonlinear systems…

Experimental evidence indicates that intrinsic temporal dynamics operating across multiple time scales are closely associated with the emergence of periodic spatial activity of increasing complexity. However, how information encoded in…

The prediction of rail crack length propagation plays a crucial role in the maintenance and safety assessment of materials and structures. Traditional methods rely on physical models and empirical equations such as Paris law, which often…

Training neural networks to satisfy universal constraints over continuous domains poses unique challenges. Common examples include Lyapunov Neural Networks (Lyapunov NNs) and Physics-Informed Neural Networks (PINNs), where analytical…

Recurrent Neural Networks (RNNs) frequently exhibit complicated dynamics, and their sensitivity to the initialization process often renders them notoriously hard to train. Recent works have shed light on such phenomena analyzing when…

Drawing on ergodic theory, we introduce a novel training method for machine learning based forecasting methods for chaotic dynamical systems. The training enforces dynamical invariants--such as the Lyapunov exponent spectrum and fractal…

Recently, there has been growing interest in using physics-informed neural networks (PINNs) to solve differential equations. However, the preservation of structure, such as energy and stability, in a suitable manner has yet to be…

Representation learning in dynamic graphs is a challenging problem because the topology of graph and node features vary at different time. This requires the model to be able to effectively capture both graph topology information and…