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Deep learning has achieved remarkable success across a wide range of tasks, but its models often suffer from instability and vulnerability: small changes to the input may drastically affect predictions, while optimization can be hindered by…

Distinguishing active from passive dynamics is a fundamental challenge in understanding the motion of living cells and other active matter systems. Here, we introduce a framework that combines physical modeling, analytical theory, and…

Existing analyses of neural network training often operate under the unrealistic assumption of an extremely small learning rate. This lies in stark contrast to practical wisdom and empirical studies, such as the work of J. Cohen et al.…

It is by now established that, remarkably, the addition of noise to a nonlinear system may sometimes facilitate, rather than hamper the detection of weak signals. This phenomenon, usually referred to as stochastic resonance, was originally…

Chaotic oscillators have gained significant attention in the research community because of their ability to reproduce and investigate the complex dynamics of real-world phenomena. Recent advances in the design of chaotic oscillator…

The existence of instabilities, for example in the form of adversarial examples, has given rise to a highly active area of research concerning itself with understanding and enhancing the stability of neural networks. We focus on a popular…

Spectrum sensing is of critical importance in any cognitive radio system. When the primary user's signal has uncertain parameters, the likelihood ratio test, which is the theoretically optimal detector, generally has no closed-form…

In this paper we address the issue of output instability of deep neural networks: small perturbations in the visual input can significantly distort the feature embeddings and output of a neural network. Such instability affects many deep…

We consider the problem of learning stabilizable systems governed by nonlinear state equation $h_{t+1}=\phi(h_t,u_t;\theta)+w_t$. Here $\theta$ is the unknown system dynamics, $h_t $ is the state, $u_t$ is the input and $w_t$ is the…

In machine learning, it is very important for a robot to be able to estimate dynamics from sequences of input data. This problem can be solved using a recurrent neural network. In this paper, we will discuss the preprocessing of 10 states…

Noise is usually regarded as adversarial to extract the effective dynamics from time series, such that the conventional data-driven approaches usually aim at learning the dynamics by mitigating the noisy effect. However, noise can have a…

Many complex networks are known to exhibit sudden transitions between alternative steady states with contrasting properties. Such a sudden transition demonstrates a network's resilience, which is the ability of a system to persist in the…

Forecasting system behaviour near and across bifurcations is crucial for identifying potential shifts in dynamical systems. While machine learning has recently been used to learn critical transitions and bifurcation structures from data,…

This work presents a hybrid modeling approach to data-driven learning and representation of unknown physical processes and closure parameterizations. These hybrid models are suitable for situations where the mechanistic description of…

System identification is a fundamental problem in reinforcement learning, control theory and signal processing, and the non-asymptotic analysis of the corresponding sample complexity is challenging and elusive, even for linear time-varying…

Algorithmic stability is a classical framework for analyzing the generalization error of learning algorithms. It predicts that an algorithm has small generalization error if it is insensitive to small perturbations in the training set such…

Oscillatory dynamics are ubiquitous in biological networks. Possible sources of oscillations are well understood in low-dimensional systems, but have not been fully explored in high-dimensional networks. Here we study large networks…

In applications of dynamical systems, situations can arise where it is desired to predict the onset of synchronization as it can lead to characteristic and significant changes in the system performance and behaviors, for better or worse. In…

We employ a convolutional neural network to explore the distinct phases in random spin systems with the aim to understand the specific features that the neural network chooses to identify the phases. With the energy spectrum normalized to…

Neural networks have proven to be remarkably successful for a wide range of complicated tasks, from image recognition and object detection to speech recognition and machine translation. One of their successes is the skill in prediction of…