Related papers: LyaNet: A Lyapunov Framework for Training Neural O…

This paper presents L-Learning, a novel data-driven control framework for robotics that integrates Lyapunov stability theory with Lagrangian mechanics to enhance trajectory tracking performance. While traditional control methods often…

This paper presents a theoretical overview of a Neural Contraction Metric (NCM): a neural network model of an optimal contraction metric and corresponding differential Lyapunov function, the existence of which is a necessary and sufficient…

In this work, we propose a novel layerwise adaptive construction method for neural network architectures. Our approach is based on a goal--oriented dual-weighted residual technique for the optimal control of neural differential equations.…

Brains need to predict how the body reacts to motor commands. It is an open question how networks of spiking neurons can learn to reproduce the non-linear body dynamics caused by motor commands, using local, online and stable learning…

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…

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…

Reinforcement learning (RL) excels in applications such as video games, but ensuring safety as well as the ability to achieve the specified goals remains challenging when using RL for real-world problems, such as human-aligned tasks where…

We present a technique for learning control Lyapunov-like functions, which are used in turn to synthesize controllers for nonlinear dynamical systems that can stabilize the system, or satisfy specifications such as remaining inside a safe…

This paper considers a wide class of smooth continuous dynamic nonlinear systems (control objects) with a measurable vector of state. The problem is to find a special function (Lyapunov function), which in the framework of the second…

Neural Ordinary Differential Equation (Neural ODE) has been proposed as a continuous approximation to the ResNet architecture. Some commonly used regularization mechanisms in discrete neural networks (e.g. dropout, Gaussian noise) are…

Ordinary differential equations (ODEs), via their induced flow maps, provide a powerful framework to parameterize invertible transformations for the purpose of representing complex probability distributions. While such models have achieved…

Ordinary differential equations (ODEs) provide a powerful framework for modeling dynamic systems arising in a wide range of scientific domains. However, most existing ODE methods focus on a single system, and do not adequately address the…

We present a unified convergence theory for gradient-based training of neural network methods for partial differential equations (PDEs), covering both physics-informed neural networks (PINNs) and the Deep Ritz method. For linear PDEs, we…

We propose a composite Lyapunov framework for nonlinear autonomous systems that ensures strict decay through a pair of differential inequalities. The approach yields integral estimates, quantitative convergence rates, vanishing of…

Neural Ordinary Differential Equations (Neural ODEs) are the continuous analog of Residual Neural Networks (ResNets). We investigate whether the discrete dynamics defined by a ResNet are close to the continuous one of a Neural ODE. We first…

Deep operator networks (DeepONets) are receiving increased attention thanks to their demonstrated capability to approximate nonlinear operators between infinite-dimensional Banach spaces. However, despite their remarkable early promise,…

We propose a method to enhance the stability of a neural ordinary differential equation (neural ODE) by reducing the maximum error growth subsequent to a perturbation of the initial value. Since the stability depends on the logarithmic norm…

This paper considers the problem of characterizing the stability region of a large-scale networked system comprised of dissipative nonlinear subsystems, in a distributed and computationally tractable way. One standard approach to estimate…

Robots capable of learning from demonstration (LfD) must exhibit stability while executing learned motion skills. To be effective in the real world, they should also remember multiple skills over time -- a capability lacking in current…

We propose a new method to ensure neural ordinary differential equations (ODEs) satisfy output specifications by using invariance set propagation. Our approach uses a class of control barrier functions to transform output specifications…