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This article investigates the effect of explicitly adding auxiliary algebraic trajectory information to neural networks for dynamical systems. We draw inspiration from the field of differential-algebraic equations and differential equations…
We present a novel method for using Neural Networks (NNs) for finding solutions to a class of Partial Differential Equations (PDEs). Our method builds on recent advances in Neural Radiance Field research (NeRFs) and allows for a NN to…
An innovative physics-guided learning algorithm for predicting the mechanical response of materials and structures is proposed in this paper. The key concept of the proposed study is based on the fact that physics models are governed by…
This short, self-contained article seeks to introduce and survey continuous-time deep learning approaches that are based on neural ordinary differential equations (neural ODEs). It primarily targets readers familiar with ordinary and…
Partial differential equations (PDEs) are commonly derived based on empirical observations. However, recent advances of technology enable us to collect and store massive amount of data, which offers new opportunities for data-driven…
We propose a novel learning paradigm for Deep Neural Networks (DNN) by using Boolean logic algebra. We first present the basic differentiable operators of a Boolean system such as conjunction, disjunction and exclusive-OR and show how these…
This work proposes an autoencoder neural network as a non-linear generalization of projection-based methods for solving Partial Differential Equations (PDEs). The proposed deep learning architecture presented is capable of generating the…
With new advances in machine learning and in particular powerful learning libraries, we illustrate some of the new possibilities they enable in terms of nonlinear system identification. For a large class of hybrid systems, we explain how…
(Partial) differential equations (PDEs) are fundamental tools for describing natural phenomena, making their solution crucial in science and engineering. While traditional methods, such as the finite element method, provide reliable…
We introduce a quantum algorithm for simulating the dynamics of electrical circuits consisting of resistors, inductors and capacitors (aka RLC circuits) along with power sources. Given oracle access to the connectivity of the circuit and…
When the system is linear, why should learning be nonlinear? Linear dynamical systems, the analytical backbone of control theory, signal processing and circuit analysis, have exact closed-form solutions via the state transition matrix. Yet…
The growing prevalence of inverter-based resources (IBRs) for renewable energy integration and electrification greatly challenges power system dynamic analysis. To account for both synchronous generators (SGs) and IBRs, this work presents…
Ordinary and partial differential equations (ODEs/PDEs) play a paramount role in analyzing and simulating complex dynamic processes across all corners of science and engineering. In recent years machine learning tools are aspiring to…
Neural Ordinary Differential Equations (NeuralODEs) present an attractive way to extract dynamical laws from time series data, as they bridge neural networks with the differential equation-based modeling paradigm of the physical sciences.…
Physics-informed neural networks (PINNs) have emerged as a promising approach to solving partial differential equations (PDEs) using neural networks, particularly in data-scarce scenarios, due to their unsupervised training capability.…
Data-driven methodologies are nowadays ubiquitous. Their rapid development and spread have led to applications even beyond the traditional fields of science. As far as dynamical systems and differential equations are concerned, neural…
With the mass construction of Gen III nuclear reactors, it is a popular trend to use deep learning (DL) techniques for fast and effective diagnosis of possible accidents. To overcome the common problems of previous work in diagnosing…
To understand the fundamental trade-offs between training stability, temporal dynamics and architectural complexity of recurrent neural networks~(RNNs), we directly analyze RNN architectures using numerical methods of ordinary differential…
Deep neural networks (DNNs), especially physics-informed neural networks (PINNs), have recently become a new popular method for solving forward and inverse problems governed by partial differential equations (PDEs). However, these methods…
Complex systems in science and engineering sometimes exhibit behavior that changes across different regimes. Traditional global models struggle to capture the full range of this complex behavior, limiting their ability to accurately…