Related papers: Augmented Neural Ordinary Differential Equations f…

I show how to compute the nonlinear power spectrum across the entire $w(z)$ dynamical dark energy model space. Using synthetic $\Lambda$CDM data, I train a neural ordinary differential equation (ODE) to infer the evolution of the nonlinear…

We propose a new approach to learning the subgrid-scale model when simulating partial differential equations (PDEs) solved by the method of lines and their representation in chaotic ordinary differential equations, based on neural ordinary…

High percentage penetrations of renewable energy generations introduce significant uncertainty into power systems. It requires grid operators to solve alternative current optimal power flow (AC-OPF) problems more frequently for economical…

We investigate the efficient learning of magnetic phases using artificial neural networks trained on synthetic data, combining computational simplicity with physics-informed strategies. Focusing on the diluted Ising model, which lacks an…

State estimation is key to both analyzing physical mechanisms and enabling real-time control of fluid flows. A common estimation approach is to relate sensor measurements to a reduced state governed by a reduced-order model (ROM). (When…

In many commercial and academic settings, numerical solvers fail to achieve their theoretical performance levels due to issues in the system definition, parameterization, and even implementation. We propose a pair of methods for detecting…

Ordinary differential equation (ODE) is widely used in modeling biological and physical processes in science. In this article, we propose a new reproducing kernel-based approach for estimation and inference of ODE given noisy observations.…

As power systems transition toward renewable-rich and inverter-dominated operations, accurate time-domain dynamic analysis becomes increasingly critical. Such analysis supports key operational tasks, including transient stability…

Deformable image registration (DIR) is crucial in medical image analysis, enabling the exploration of biological dynamics such as organ motions and longitudinal changes in imaging. Leveraging Neural Ordinary Differential Equations (ODE) for…

Physics beyond the Standard Model that is resonant in one or more dimensions has been a longstanding focus of countless searches at colliders and beyond. Recently, many new strategies for resonant anomaly detection have been developed,…

Recent works on optical flow estimation use neural networks to predict the flow field that maps positions of one image to positions of the other. These networks consist of a feature extractor, a correlation volume, and finally several…

Automated medical image segmentation plays a key role in quantitative research and diagnostics. Convolutional neural networks based on the U-Net architecture are the state-of-the-art. A key disadvantage is the hard-coding of the receptive…

In this paper, we address the issue of modeling and estimating changes in the state of the spatio-temporal dynamical systems based on a sequence of observations like video frames. Traditional numerical simulation systems depend largely on…

The symbolic discovery of Ordinary Differential Equations (ODEs) from trajectory data plays a pivotal role in AI-driven scientific discovery. Existing symbolic methods predominantly rely on fixed, pre-collected training datasets, which…

Detecting anomalies in multivariate time-series data is essential in many real-world applications. Recently, various deep learning-based approaches have shown considerable improvements in time-series anomaly detection. However, existing…

This contribution deals with identification of fractional-order dynamical systems. System identification, which refers to estimation of process parameters, is a necessity in control theory. Real processes are usually of fractional order as…

Owing to the remarkable development of deep learning technology, there have been a series of efforts to build deep learning-based climate models. Whereas most of them utilize recurrent neural networks and/or graph neural networks, we design…

Discrete-time modeling of acoustic, mechanical and electrical systems is a prominent topic in the musical signal processing literature. Such models are mostly derived by discretizing a mathematical model, given in terms of ordinary or…

The data-driven recovery of the unknown governing equations of dynamical systems has recently received an increasing interest. However, the identification of governing equations remains challenging when dealing with noisy and partial…

In complex physical systems, conventional differential equations often fall short in capturing non-local and memory effects, as they are limited to local dynamics and integer-order interactions. This study introduces a stepwise data-driven…