Related papers: Unconditional stability of a recurrent neural circ…

Recurrent neural networks (RNNs) are difficult to train on sequence processing tasks, not only because input noise may be amplified through feedback, but also because any inaccuracy in the weights has similar consequences as input noise. We…

Learning how complex dynamical systems evolve over time is a key challenge in system identification. For safety critical systems, it is often crucial that the learned model is guaranteed to converge to some equilibrium point. To this end,…

Whilst the Universal Approximation Theorem guarantees the existence of approximations to Sobolev functions -- the natural function spaces for PDEs -- by Neural Networks (NNs) of sufficient size, low-regularity solutions may lead to poor…

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…

Several variants of recurrent neural networks (RNNs) with orthogonal or unitary recurrent matrices have recently been developed to mitigate the vanishing/exploding gradient problem and to model long-term dependencies of sequences. However,…

This work provides a framework for nonlinear model-free control of systems with unknown input-output dynamics, but outputs that can be controlled by the inputs. This framework leads to real-time control of the system such that a feasible…

We introduce OS-net (Orbitally Stable neural NETworks), a new family of neural network architectures specifically designed for periodic dynamical data. OS-net is a special case of Neural Ordinary Differential Equations (NODEs) and takes…

Stability guarantees are crucial when ensuring that a fully autonomous robot does not take undesirable or potentially harmful actions. We recently proposed the Neural Contractive Dynamical Systems (NCDS), which is a neural network…

Consider an unknown nonlinear dynamical system that is known to be dissipative. The objective of this paper is to learn a neural dynamical model that approximates this system, while preserving the dissipativity property in the model. In…

Central Pattern Generators (CPGs) are biological neural circuits capable of producing coordinated rhythmic outputs in the absence of rhythmic input. As a result, they are responsible for most rhythmic motion in living organisms. This…

Recurrent Neural Networks (RNNs) achieve state-of-the-art results in many sequence-to-sequence modeling tasks. However, RNNs are difficult to train and tend to suffer from overfitting. Motivated by the Data Processing Inequality (DPI), we…

Cortical networks can maintain memories for decades despite the short lifetime of synaptic strength. Can a neural network store long-lasting memories in unstable synapses? Here, we study the effects of random noise on the stability of…

Neural networks can be fragile to input noise and adversarial attacks. In this work, we consider Convolutional Neural Ordinary Differential Equations (NODEs), a family of continuous-depth neural networks represented by dynamical systems,…

Motivated by the residual type neural networks (ResNet), this paper studies optimal control problems constrained by a non-smooth integral equation. Such non-smooth equations, for instance, arise in the continuous representation of…

Deep Neural Networks (DNNs) training can be difficult due to vanishing and exploding gradients during weight optimization through backpropagation. To address this problem, we propose a general class of Hamiltonian DNNs (H-DNNs) that stem…

We explore the possibility to use physics-informed neural networks to drastically accelerate the solution of ordinary differential-algebraic equations that govern the power system dynamics. When it comes to transient stability assessment,…

Neural Ordinary Differential Equations (ODEs) represent a significant advancement at the intersection of machine learning and dynamical systems, offering a continuous-time analog to discrete neural networks. Despite their promise, deploying…

We analyze Neural Ordinary Differential Equations (NODEs) from a control theoretical perspective to address some of the main properties and paradigms of Deep Learning (DL), in particular, data classification and universal approximation.…

In our previous work, we proposed a novel neuron model based on symmetric differential equations and demonstrated its potential as an efficient signal propagator. Building upon that foundation, the present study delves deeper into the…

This paper presents a new neural network (NN) paradigm for scalable and generalizable stability analysis of power systems. The paradigm consists of two parts: the neural stability descriptor and the sample-augmented iterative training…