Related papers: FxTS-Net: Fixed-Time Stable Learning Framework for…

Neural Ordinary Differential Equations (Neural ODEs) represent continuous-time dynamics with neural networks, offering advancements for modeling and control tasks. However, training Neural ODEs requires solving differential equations at…

Deep neural networks (DNNs) are well-known to be vulnerable to adversarial attacks, where malicious human-imperceptible perturbations are included in the input to the deep network to fool it into making a wrong classification. Recent…

We present a novel adaptive online learning (AOL) framework to predict human movement trajectories in dynamic video scenes. Our framework learns and adapts to changes in the scene environment and generates best network weights for different…

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…

Deep neural networks (DNNs) are a type of artificial intelligence models that are inspired by the structure and function of the human brain, designed to process and learn from large amounts of data, making them particularly well-suited for…

The paper investigates sufficient conditions on a differential inclusion which guarantee that the origin is a finite time stable equilibrium, namely a weak local one, a weak global one or a strong local one. The analysis relies on the…

Neural networks have become a widely adopted tool for tackling a variety of problems in machine learning and artificial intelligence. In this contribution we use the mathematical framework of local stability analysis to gain a deeper…

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…

In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms. As an expository contribution we demonstrate how to re-formulate a wide variety of challenges from deep neural networks, (stochastic)…

Time series forecasting poses significant challenges in non-stationary environments where underlying patterns evolve over time. In this work, we propose a novel framework that enhances deep neural network (DNN) performance by leveraging…

Deep learning has an increasing impact to assist research, allowing, for example, the discovery of novel materials. Until now, however, these artificial intelligence techniques have fallen short of discovering the full differential equation…

Delay-coupled systems often require low-latency decisions from sparse telemetry, where dense fixed-step neural inference is wasteful and can degrade near stability margins. We introduce Network-Optimised Spiking (NOS), a trainable two-state…

Prior-data fitted networks (PFNs) were recently proposed as a new paradigm for machine learning. Instead of training the network to an observed training set, a fixed model is pre-trained offline on small, simulated training sets from a…

This paper develops a new approach to the estimation of the degree of boundedness or stability of multidimensional nonlinear systems with time-dependent nonperiodic coefficients-an essential task in various engineering and natural science…

Fluctuation theorems (FTs) quantify the thermodynamic reversibility of a system, and for deterministic systems they are defined in terms of the dissipation function. However, in a nonequilibrium steady state of deterministic dynamics, the…

Finite element modeling is a well-established tool for structural analysis, yet modeling complex structures often requires extensive pre-processing, significant analysis effort, and considerable time. This study addresses this challenge by…

The well-known generalization problem hinders the application of artificial neural networks in continuous-time prediction tasks with varying latent dynamics. In sharp contrast, biological systems can neatly adapt to evolving environments…

In chaotic dynamical systems such as the weather, prediction errors grow faster in some situations than in others. Real-time knowledge about the error growth could enable strategies to adjust the modelling and forecasting infrastructure…

Federated Learning (FL) is an emerging domain in the broader context of artificial intelligence research. Methodologies pertaining to FL assume distributed model training, consisting of a collection of clients and a server, with the main…

There have been extensive studies on solving differential equations using physics-informed neural networks. While this method has proven advantageous in many cases, a major criticism lies in its lack of analytical error bounds. Therefore,…