Related papers: Tracking Finite-Time Lyapunov Exponents to Robusti…

Robust loss functions are crucial for training deep neural networks in the presence of label noise, yet existing approaches require extensive, dataset-specific hyperparameter tuning. In this work, we introduce Fractional Classification Loss…

In the framework of the Fermi-Pasta-Ulam (FPU) model, we show a simple method to give an accurate analytical estimation of the maximal Lyapunov exponent at high energy density. The method is based on the computation of the mean value of the…

Constraints are found on the spatial variation of finite-time Lyapunov exponents of two and three-dimensional systems of ordinary differential equations. In a chaotic system, finite-time Lyapunov exponents describe the average rate of…

Neural ordinary differential equations (NODEs) -- parametrizations of differential equations using neural networks -- have shown tremendous promise in learning models of unknown continuous-time dynamical systems from data. However, every…

The pursuit of robustness has recently been a popular topic in reinforcement learning (RL) research, yet the existing methods generally suffer from efficiency issues that obstruct their real-world implementation. In this paper, we introduce…

Observer-based methods are widely used to estimate the disturbances of different dynamic systems. However, a drawback of the conventional disturbance observers is that they all assume persistent excitation (PE) of the systems. As a result,…

In this work, we present a machine learning approach for reducing the error when numerically solving time-dependent partial differential equations (PDE). We use a fully convolutional LSTM network to exploit the spatiotemporal dynamics of…

Deep Neural Networks (DNNs) are increasingly used in control applications due to their powerful function approximation capabilities. However, many existing formulations focus primarily on tracking error convergence, often neglecting the…

In this study, we tackle the challenge of outlier-robust predictive modeling using highly expressive neural networks. Our approach integrates two key components: (1) a transformed trimmed loss (TTL), a computationally efficient variant of…

Neural differential equations are a promising new member in the neural network family. They show the potential of differential equations for time series data analysis. In this paper, the strength of the ordinary differential equation (ODE)…

Multimodal large language models (MLLMs) have achieved impressive performance, but high-resolution visual inputs result in long sequences of visual tokens and substantial inference latency. Reducing redundant visual tokens is critical to…

Neural Ordinary Differential Equations (NODEs) have proven to be a powerful modeling tool for approximating (interpolation) and forecasting (extrapolation) irregularly sampled time series data. However, their performance degrades…

Anomaly and missing data constitute a thorny problem in industrial applications. In recent years, deep learning enabled anomaly detection has emerged as a critical direction, however the improved detection accuracy is achieved with the…

We propose a novel second-order optimization framework for training the emerging deep continuous-time models, specifically the Neural Ordinary Differential Equations (Neural ODEs). Since their training already involves expensive gradient…

In the framework of a recently developed theory for Hamiltonian chaos, which makes use of the formulation of Newtonian dynamics in terms of Riemannian differential geometry, we obtained analytic values of the largest Lyapunov exponent for…

This paper studies robust output tracking and disturbance rejection for boundary controlled infinite-dimensional port--Hamiltonian systems including second order models such as the Euler--Bernoulli beam. The control design is achieved using…

Over the past decade, Finite Element Method (FEM) has served as a foundational numerical framework for approximating the terms of Time Series Expansion (TSE) as solutions to transient Partial Differential Equation (PDE). However, the…

Fine-tuning plays a crucial role in enabling pre-trained LLMs to evolve from general language comprehension to task-specific expertise. To preserve user data privacy, federated fine-tuning is often employed and has emerged as the de facto…

Training Neural Ordinary Differential Equations (ODEs) is often computationally expensive. Indeed, computing the forward pass of such models involves solving an ODE which can become arbitrarily complex during training. Recent works have…

Designing controllers that achieve task objectives while ensuring safety is a key challenge in control systems. This work introduces Opt-ODENet, a Neural ODE framework with a differentiable Quadratic Programming (QP) optimization layer to…