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Numerical simulations of groundwater flow are used to analyze and predict the response of an aquifer system to its change in state by approximating the solution of the fundamental groundwater physical equations. The most used and classical…

Early detection of energy losses, theft, and operational inefficiencies remains a critical challenge in oil and gas production systems due to complex interdependencies among wells and facilities, evolving operating conditions, and limited…

In the context of high penetration of renewables, the need to build dynamic models of power system components based on accessible measurement data has become urgent. To address this challenge, firstly, a neural ordinary differential…

Accurate short-term electricity load forecasting is a cornerstone of U.S. grid reliability; however, prevailing deep learning models remain opaque, limiting operator trust during extreme weather. A unified, interpretable, physics-informed…

Encoder-decoder-based recurrent neural network (RNN) has made significant progress in sequence-to-sequence learning tasks such as machine translation and conversational models. Recent works have shown the advantage of this type of network…

It has been observed that residual networks can be viewed as the explicit Euler discretization of an Ordinary Differential Equation (ODE). This observation motivated the introduction of so-called Neural ODEs, which allow more general…

A general purpose, modular program package for the integration of large number of independent ordinary differential equation systems capable of using professional graphics cards is presented. The available numerical schemes are the explicit…

When deploying time series forecasting models based on machine learning to real world settings, one often encounter situations where the data distribution drifts. Such drifts expose the forecasting models to out-of-distribution (OOD) data,…

Text-attributed graphs, where nodes are enriched with textual attributes, have become a powerful tool for modeling real-world networks such as citation, social, and transaction networks. However, existing methods for learning from these…

Graph neural ordinary differential equations (Graph ODEs) extend graph learning from discrete message-passing layers to continuous-time representation flows. While it supports adaptive long-range propagation, we show that Graph ODEs with…

Neural ordinary differential equations (neural ODE) are powerful continuous-time machine learning models for depicting the behavior of complex dynamical systems, but their verification remains challenging due to limited reachability…

Neural Ordinary Differential Equations (ODEs) represent a significant advancement at the intersection of machine learning and dynamical systems, offering a continuous-time analog to discrete neural networks. Despite their promise, deploying…

Achieving carbon neutrality, a key focus of UN SDG #13, drives the exploration of wave energy, a renewable resource with the potential to generate 30,000 TWh of clean electricity annually, surpassing global demand. However, wave energy…

Ordinary differential equations (ODEs) provide a powerful framework for modeling dynamic systems arising in a wide range of scientific domains. However, most existing ODE methods focus on a single system, and do not adequately address the…

District Heating Systems are essential infrastructure for delivering heat to consumers across a geographic region sustainably, yet efficient management relies on optimizing diverse energy sources, such as wood, gas, electricity, and solar,…

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…

Accurately learning solution operators for time-dependent partial differential equations (PDEs) from sparse and irregular data remains a challenging task. Recurrent DeepONet extensions inherit the discrete-time limitations of…

We explore in detail a method to solve ordinary differential equations using feedforward neural networks. We prove a specific loss function, which does not require knowledge of the exact solution, to be a suitable standard metric to…

Neural networks with physics based inductive biases such as Lagrangian neural networks (LNN), and Hamiltonian neural networks (HNN) learn the dynamics of physical systems by encoding strong inductive biases. Alternatively, Neural ODEs with…

Short-term demand forecasting models commonly combine convolutional and recurrent layers to extract complex spatiotemporal patterns in data. Long-term histories are also used to consider periodicity and seasonality patterns as time series…