相关论文: SeqLink: A Robust Neural-ODE Architecture for Mode…

Lasso problems arise in many areas, including signal processing, machine learning, and control, and are closely connected to sparse coding mechanisms observed in neuroscience. A continuous-time ordinary differential equation (ODE)…

Neural operators have emerged as promising surrogate models for solving partial differential equations (PDEs), but struggle to generalise beyond training distributions and are often constrained to a fixed temporal discretisation. This work…

Transformers excel at time series modelling through attention mechanisms that capture long-term temporal patterns. However, they assume uniform time intervals and therefore struggle with irregular time series. Neural Ordinary Differential…

Neural ordinary differential equations (ODEs) are an emerging class of deep learning models for dynamical systems. They are particularly useful for learning an ODE vector field from observed trajectories (i.e., inverse problems). We here…

We consider the problem of forecasting complex, nonlinear space-time processes when observations provide only partial information of on the system's state. We propose a natural data-driven framework, where the system's dynamics are modelled…

Partial differential equations (PDEs) play a crucial role in studying a vast number of problems in science and engineering. Numerically solving nonlinear and/or high-dimensional PDEs is often a challenging task. Inspired by the traditional…

Continuous deep learning models, referred to as Neural Ordinary Differential Equations (Neural ODEs), have received considerable attention over the last several years. Despite their burgeoning impact, there is a lack of formal analysis…

Detecting out-of-distribution (OOD) inputs is critical for safely deploying deep learning models in the real world. Existing approaches for detecting OOD examples work well when evaluated on benign in-distribution and OOD samples. However,…

Modern graph representation learning works mostly under the assumption of dealing with regularly sampled temporal graph snapshots, which is far from realistic, e.g., social networks and physical systems are characterized by continuous…

Poverty is a complex dynamic challenge that cannot be adequately captured using predefined differential equations. Nowadays, artificial machine learning (ML) methods have demonstrated significant potential in modelling real-world dynamical…

We study the problem of out-of-distribution dynamics (OODD) detection, which involves detecting when the dynamics of a temporal process change compared to the training-distribution dynamics. This is relevant to applications in control,…

Forecasting time series and time-dependent data is a common problem in many applications. One typical example is solving ordinary differential equation (ODE) systems $\dot{x}=F(x)$. Oftentimes the right hand side function $F(x)$ is not…

Time series modeling and analysis have become critical in various domains. Conventional methods such as RNNs and Transformers, while effective for discrete-time and regularly sampled data, face significant challenges in capturing the…

We develop a numerical method to reconstruct systems of ordinary differential equations (ODEs) from time series data without {\it a priori} knowledge of the underlying ODEs using sparse basis learning and sparse function reconstruction. We…

Real-world multivariate time series anomalies are rare and often unlabeled. Additionally, prevailing methods rely on increasingly complex architectures tuned to benchmarks, detecting only fragments of anomalous segments and overstating…

A key requirement in sequence to sequence processing is the modeling of long range dependencies. To this end, a vast majority of the state-of-the-art models use attention mechanism which is of O($n^2$) complexity that leads to slow…

Smooth dynamics interrupted by discontinuities are known as hybrid systems and arise commonly in nature. Latent ODEs allow for powerful representation of irregularly sampled time series but are not designed to capture trajectories arising…

A class of neural networks that gained particular interest in the last years are neural ordinary differential equations (neural ODEs). We study input-output relations of neural ODEs using dynamical systems theory and prove several results…

Modeling dynamical systems is crucial for a wide range of tasks, but it remains challenging due to complex nonlinear dynamics, limited observations, or lack of prior knowledge. Recently, data-driven approaches such as Neural Ordinary…

Ordinary differential equations (ODEs) are foundational in modeling intricate dynamics across a gamut of scientific disciplines. Yet, a possibility to represent a single phenomenon through multiple ODE models, driven by different…