相关论文: Universal Differential Equations for Scientific Ma…
Deep learning has an increasing impact to assist research, allowing, for example, the discovery of novel materials. Until now, however, these artificial intelligence techniques have fallen short of discovering the full differential equation…
Multiscale dynamical systems, modeled by high-dimensional stiff ordinary differential equations (ODEs) with wide-ranging characteristic timescales, arise across diverse fields of science and engineering, but their numerical solvers often…
This paper presents a physics-informed neural network approach for dynamic modeling of saturable synchronous machines, including cases with spatial harmonics. We introduce an architecture that incorporates gradient networks directly into…
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…
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…
Neural Ordinary Differential Equations replace the right-hand side of a conventional ODE with a neural net, which by virtue of the universal approximation theorem, can be trained to the representation of any function. When we do not know…
The inverse problem of supervised reconstruction of depth-variable (time-dependent) parameters in a neural ordinary differential equation (NODE) is considered, that means finding the weights of a residual network with time continuous…
The trending integrations of Battery Energy Storage System (BESS, stationary battery) and Electric Vehicles (EV, mobile battery) to distribution grids call for advanced Demand Side Management (DSM) technique that addresses the scalability…
We introduce a novel grid-independent model for learning partial differential equations (PDEs) from noisy and partial observations on irregular spatiotemporal grids. We propose a space-time continuous latent neural PDE model with an…
Differential equations (DE) constrained optimization plays a critical role in numerous scientific and engineering fields, including energy systems, aerospace engineering, ecology, and finance, where optimal configurations or control…
The growing integration of electric vehicle (EV) fleets into transportation services and energy systems requires accurate modeling of battery discharge and state-of-charge (SoC) evolution to ensure reliable vehicle operation and grid…
Deep neural networks have revolutionized machine learning, yet their training dynamics remain theoretically unclear-we develop a continuous-time, matrix-valued stochastic differential equation (SDE) framework that rigorously connects the…
Neural ordinary differential equations (Neural ODEs) are an effective framework for learning dynamical systems from irregularly sampled time series data. These models provide a continuous-time latent representation of the underlying…
Neural Ordinary Differential Equations (NODEs) use a neural network to model the instantaneous rate of change in the state of a system. However, despite their apparent suitability for dynamics-governed time-series, NODEs present a few…
The data-driven discovery of partial differential equations (PDEs) consistent with spatiotemporal data is experiencing a rebirth in machine learning research. Training deep neural networks to learn such data-driven partial differential…
Model identification of battery dynamics is a central problem in energy research; many energy management systems and design processes rely on accurate battery models for efficiency optimization. The standard methodology for battery…
Accurate prediction of the Remaining Useful Life (RUL) is essential for enabling timely maintenance of lithium-ion batteries, impacting the operational efficiency of electric applications that rely on them. This paper proposes a RUL…
Neural Ordinary Differential Equations (NODEs) are a new class of models that transform data continuously through infinite-depth architectures. The continuous nature of NODEs has made them particularly suitable for learning the dynamics of…
The understanding and modeling of complex physical phenomena through dynamical systems has historically driven scientific progress, as it provides the tools for predicting the behavior of different systems under diverse conditions through…
The combination of ordinary differential equations and neural networks, i.e., neural ordinary differential equations (Neural ODE), has been widely studied from various angles. However, deciphering the numerical integration in Neural ODE is…