Related papers: Physics-Constrained Taylor Neural Networks for Lea…

The present study develops a physics-constrained neural network (PCNN) to predict sequential patterns and motions of multiphase flows (MPFs), which includes strong interactions among various fluid phases. To predict the order parameters,…

Determination of the nature of the dynamical state of a system as a function of its parameters is an important problem in the study of dynamical systems. This problem becomes harder in experimental systems where the obtained data is…

Recurrent neural networks are capable of learning the dynamics of an unknown nonlinear system purely from input-output measurements. However, the resulting models do not provide any stability guarantees on the input-output mapping. In this…

There has been a wave of interest in applying machine learning to study dynamical systems. We present a Hamiltonian neural network that solves the differential equations that govern dynamical systems. This is an equation-driven machine…

This paper proposes methods for identification of large-scale networked systems with guarantees that the resulting model will be contracting -- a strong form of nonlinear stability -- and/or monotone, i.e. order relations between states are…

Neural network models become increasingly popular as dynamic modeling tools in the control community. They have many appealing features including nonlinear structures, being able to approximate any functions. While most researchers hold…

Currently, knowledge discovery in databases is an essential step to identify valid, novel and useful patterns for decision making. There are many real-world scenarios, such as bankruptcy prediction, option pricing or medical diagnosis,…

Hamiltonian neural networks (HNNs) are state-of-the-art models that regress the vector field of a dynamical system under the learning bias of Hamilton's equations. A recent observation is that embedding a bias regarding the additive…

We study the applicability of a Deep Neural Network (DNN) approach to simulate one-dimensional non-relativistic fluid dynamics. Numerical fluid dynamical calculations are used to generate training data-sets corresponding to a broad range of…

The memory physics induced unknown offset of the channel is a critical and difficult issue to be tackled for many non-volatile memories (NVMs). In this paper, we first propose novel neural network (NN) detectors by using the multilayer…

Sensory predictions by the brain in all modalities take place as a result of bottom-up and top-down connections both in the neocortex and between the neocortex and the thalamus. The bottom-up connections in the cortex are responsible for…

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…

Combining machine learning with physics is a trending approach for discovering unknown dynamics, and one of the most intensively studied frameworks is the physics-informed neural network (PINN). However, PINN often fails to optimize the…

This paper proposes a sparse Bayesian treatment of deep neural networks (DNNs) for system identification. Although DNNs show impressive approximation ability in various fields, several challenges still exist for system identification…

One of the most influential results in neural network theory is the universal approximation theorem [1, 2, 3] which states that continuous functions can be approximated to within arbitrary accuracy by single-hidden-layer feedforward neural…

We propose tensorial neural networks (TNNs), a generalization of existing neural networks by extending tensor operations on low order operands to those on high order ones. The problem of parameter learning is challenging, as it corresponds…

Identifying a linear system model from data has wide applications in control theory. The existing work on finite sample analysis for linear system identification typically uses data from a single system trajectory under i.i.d random inputs,…

There has been increasing interest in methodologies that incorporate physics priors into neural network architectures to enhance their modeling capabilities. A family of these methodologies that has gained traction are Hamiltonian neural…

We introduce Neural Dynamical Systems (NDS), a method of learning dynamical models in various gray-box settings which incorporates prior knowledge in the form of systems of ordinary differential equations. NDS uses neural networks to…

The hydrogen trapping behaviour of metallic alloys is generally characterised using Thermal Desorption Spectroscopy (TDS). However, as an indirect method, extracting key parameters (trap binding energies and densities) remains a significant…