Related papers: Differentiable Multiple Shooting Layers

In the present work, a multi-scale framework for neural network enhanced methods is proposed for approximation of function and solution of partial differential equations (PDEs). By introducing the multi-scale concept, the total solution of…

Inverse medium scattering is an ill-posed, nonlinear wave-based imaging problem arising in medical imaging, remote sensing, and non-destructive testing. Machine learning (ML) methods offer increased inference speed and flexibility in…

Automated segmentation of multiple sclerosis (MS) lesions using multicontrast magnetic resonance (MR) images improves efficiency and reproducibility compared to manual delineation, with deep learning (DL) methods achieving state-of-the-art…

Neural ordinary differential equations (Neural ODEs) is a class of machine learning models that approximate the time derivative of hidden states using a neural network. They are powerful tools for modeling continuous-time dynamical systems,…

When training large machine learning models with many variables or parameters, a single machine is often inadequate since the model may be too large to fit in memory, while training can take a long time even with stochastic updates. A…

Differentiable logics (DL) have recently been proposed as a method of training neural networks to satisfy logical specifications. A DL consists of a syntax in which specifications are stated and an interpretation function that translates…

Astronomical time series from large-scale surveys like LSST are often irregularly sampled and incomplete, posing challenges for classification and anomaly detection. We introduce a new framework based on Neural Stochastic Delay Differential…

Time series data, including univariate and multivariate ones, are characterized by unique composition and complex multi-scale temporal variations. They often require special consideration of decomposition and multi-scale modeling to…

Multi-modal large language models (MLLMs) have enabled numerous advances in understanding and reasoning in domains like vision, but we have not yet seen this broad success for time-series. Although prior works on time-series MLLMs have…

Stochastic differential equations (SDEs) provide a flexible framework for modeling temporal dynamics in partially observed systems. A central task is to calibrate such models from data, which requires inferring latent trajectories and…

Training large machine learning (ML) models with many variables or parameters can take a long time if one employs sequential procedures even with stochastic updates. A natural solution is to turn to distributed computing on a cluster;…

Sparse coding aims to model data vectors as sparse linear combinations of basis elements, but a majority of related studies are restricted to continuous data without spatial or temporal structure. A new model-based sparse coding (MSC)…

Time series with non-uniform intervals occur in many applications, and are difficult to model using standard recurrent neural networks (RNNs). We generalize RNNs to have continuous-time hidden dynamics defined by ordinary differential…

When applying pre-trained large language models (LLMs) to address anomaly detection tasks, the multivariate time series (MTS) modality of anomaly detection does not align with the text modality of LLMs. Existing methods simply transform the…

Sensitivity analysis methods are important tools for research and design with simulations. Many important simulations exhibit chaotic dynamics, including scale-resolving turbulent fluid flow simulations. Unfortunately, conventional…

Recent advances in parallel computing and GPU acceleration have created new opportunities for computation-intensive learning problems such as Active SLAM -- where actions are selected to reduce uncertainty and improve joint mapping and…

Partial differential equations (PDEs) are often computationally challenging to solve, and in many settings many related PDEs must be be solved either at every timestep or for a variety of candidate boundary conditions, parameters, or…

Large language models (LLMs) are increasingly integrated into real-time machine learning applications, where safeguarding user privacy is paramount. Traditional differential privacy mechanisms often struggle to balance privacy and accuracy,…

Identification of time-varying linear systems, which introduce both time-shifts (delays) and frequency-shifts (Doppler-shifts), is a central task in many engineering applications. This paper studies the problem of identification of…

A core capability of intelligent systems is the ability to quickly learn new tasks by drawing on prior experience. Gradient (or optimization) based meta-learning has recently emerged as an effective approach for few-shot learning. In this…