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We introduce Sparse Symplectically Integrated Neural Networks (SSINNs), a novel model for learning Hamiltonian dynamical systems from data. SSINNs combine fourth-order symplectic integration with a learned parameterization of the…
Opinion formation and propagation are crucial phenomena in social networks and have been extensively studied across several disciplines. Traditionally, theoretical models of opinion dynamics have been proposed to describe the interactions…
A physics-informed neural network (PINN) models the dynamics of a system by integrating the governing physical laws into the architecture of a neural network. By enforcing physical laws as constraints, PINN overcomes challenges with data…
We introduce Structure Informed Neural Networks (SINNs), a novel method for solving boundary observation problems involving PDEs. The SINN methodology is a data-driven framework for creating approximate solutions to internal variables on…
Machine learning, with its remarkable ability for retrieving information and identifying patterns from data, has emerged as a powerful tool for discovering governing equations. It has been increasingly informed by physics, and more recently…
Due to the increasing system stability issues caused by the technological revolutions of power system equipment, the assessment of the dynamic security of the systems for changing operating conditions (OCs) is nowadays crucial. To address…
Multiscale stochastic dynamical systems have been widely adopted to a variety of scientific and engineering problems due to their capability of depicting complex phenomena in many real world applications. This work is devoted to…
In recent years, scientific machine learning, particularly physic-informed neural networks (PINNs), has introduced new innovative methods to understanding the differential equations that describe power system dynamics, providing a more…
Physics-Informed Neural Networks (PINNs) have recently shown great promise as a way of incorporating physics-based domain knowledge, including fundamental governing equations, into neural network models for many complex engineering systems.…
This paper contributes to a development of randomized methods for neural networks. The proposed learner model is generated incrementally by stochastic configuration (SC) algorithms, termed as Stochastic Configuration Networks (SCNs). In…
There has been an increasing interest in integrating physics knowledge and machine learning for modeling dynamical systems. However, very limited studies have been conducted on seismic wave modeling tasks. A critical challenge is that these…
We propose a stochastic projection-based gradient free physics-informed neural network. The proposed approach, referred to as the stochastic projection based physics informed neural network (SP-PINN), blends upscaled stochastic projection…
In order to drastically reduce the heavy computational burden associated with time-domain simulations, this paper introduces a Physics-Informed Neural Network (PINN) to directly learn the solutions of power system dynamics. In contrast to…
Physics informed neural networks (PINNs) represent a very popular class of neural solvers for partial differential equations. In practice, one often employs stochastic gradient descent type algorithms to train the neural network. Therefore,…
We develop Structured-Knowledge-Informed Neural Networks (SKINNs), a unified estimation framework that embeds theoretical, simulated, previously learned, or cross-domain insights as differentiable constraints within flexible neural function…
State estimation for nonlinear dynamical systems is a critical challenge in control and engineering applications, particularly when only partial and noisy measurements are available. This paper introduces a novel Adaptive Physics-Informed…
Spatio-temporal forecasting is of great importance in a wide range of dynamical systems applications from atmospheric science, to recent COVID-19 spread modeling. These applications rely on accurate predictions of spatio-temporal structured…
A physics-informed neural network (PINN) uses physics-augmented loss functions, e.g., incorporating the residual term from governing partial differential equations (PDEs), to ensure its output is consistent with fundamental physics laws.…
The concept of integrating physics-based and data-driven approaches has become popular for modeling sustainable energy systems. However, the existing literature mainly focuses on the data-driven surrogates generated to replace physics-based…
Transition phenomena between metastable states play an important role in complex systems due to noisy fluctuations. In this paper, the physics informed neural networks (PINNs) are presented to compute the most probable transition pathway.…