Related papers: Graph Neural Ordinary Differential Equations for P…
Random ordinary differential equations (RODEs), i.e. ODEs with random parameters, are often used to model complex dynamics. Most existing methods to identify unknown governing RODEs from observed data often rely on strong prior knowledge.…
This paper proposes the use of spectral element methods \citep{canuto_spectral_1988} for fast and accurate training of Neural Ordinary Differential Equations (ODE-Nets; \citealp{Chen2018NeuralOD}) for system identification. This is achieved…
Cascading failures in power grids pose severe risks to infrastructure reliability, yet real-time prediction of their progression remains an open challenge. Physics-based simulators require minutes to hours per scenario, while existing graph…
Learning dynamics governed by differential equations is crucial for predicting and controlling the systems in science and engineering. Neural Ordinary Differential Equation (NODE), a deep learning model integrated with differential…
We introduce steerable neural ordinary differential equations on homogeneous spaces $M=G/H$. These models constitute a novel geometric extension of manifold neural ordinary differential equations (NODEs) that transport associated feature…
The physical world is governed by the laws of physics, often represented in form of nonlinear partial differential equations (PDEs). Unfortunately, solution of PDEs is non-trivial and often involves significant computational time. With…
One of the main challenges in using deep learning-based methods for simulating physical systems and solving partial differential equations (PDEs) is formulating physics-based data in the desired structure for neural networks. Graph neural…
The large-scale integration of renewable energy and power electronic devices has increased the complexity of power system stability, making transient stability assessment more challenging. Conventional methods are limited in both accuracy…
Despite extensive research efforts focused on OOD detection on images, OOD detection on nodes in graph learning remains underexplored. The dependence among graph nodes hinders the trivial adaptation of existing approaches on images that…
Estimating the structure of directed acyclic graphs (DAGs) of features (variables) plays a vital role in revealing the latent data generation process and providing causal insights in various applications. Although there have been many…
Accurately modelling the dynamics of complex systems and discovering their governing differential equations are critical tasks for accelerating scientific discovery. Using noisy, synthetic data from two damped oscillatory systems, we…
Neural ordinary differential equations (NODE) have garnered significant attention for their design of continuous-depth neural networks and the ability to learn data/feature dynamics. However, for high-dimensional systems, estimating…
Many physical processes such as weather phenomena or fluid mechanics are governed by partial differential equations (PDEs). Modelling such dynamical systems using Neural Networks is an active research field. However, current methods are…
Voltage prediction in distribution grids is a critical yet difficult task for maintaining power system stability. Machine learning approaches, particularly Graph Neural Networks (GNNs), offer significant speedups but suffer from poor…
Parameter Estimation (PE) and State Estimation (SE) are the most wide-spread tasks in the system engineering. They need to be done automatically, fast and frequently, as measurements arrive. Deep Learning (DL) holds the promise of tackling…
Real data collected from different applications that have additional topological structures and connection information are amenable to be represented as a weighted graph. Considering the node labeling problem, Graph Neural Networks (GNNs)…
Revealing the continuous dynamics on the networks is essential for understanding, predicting, and even controlling complex systems, but it is hard to learn and model the continuous network dynamics because of complex and unknown governing…
Accurate and efficient simulations of physical phenomena governed by partial differential equations (PDEs) are important for scientific and engineering progress. While traditional numerical solvers are powerful, they are often…
Neural ordinary differential equations (NODEs) have been proven useful for learning non-linear dynamics of arbitrary trajectories. However, current NODE methods capture variations across trajectories only via the initial state value or by…
With the increased complexity of power systems due to the integration of smart grid technologies and renewable energy resources, more frequent changes have been introduced to system status, and the traditional serial mode of state…