scholarly journals Physics-informed learning of governing equations from scarce data

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Zhao Chen ◽  
Yang Liu ◽  
Hao Sun
Keyword(s):  
Automatic Differentiation ◽  
Initial Boundary ◽  
Representation Learning ◽  
Sparse Regression ◽  
Partial Differential ◽  
Computational Framework ◽  
Practical Applications ◽  
Novel Approach ◽  
Form Model ◽  
System Variables

AbstractHarnessing data to discover the underlying governing laws or equations that describe the behavior of complex physical systems can significantly advance our modeling, simulation and understanding of such systems in various science and engineering disciplines. This work introduces a novel approach called physics-informed neural network with sparse regression to discover governing partial differential equations from scarce and noisy data for nonlinear spatiotemporal systems. In particular, this discovery approach seamlessly integrates the strengths of deep neural networks for rich representation learning, physics embedding, automatic differentiation and sparse regression to approximate the solution of system variables, compute essential derivatives, as well as identify the key derivative terms and parameters that form the structure and explicit expression of the equations. The efficacy and robustness of this method are demonstrated, both numerically and experimentally, on discovering a variety of partial differential equation systems with different levels of data scarcity and noise accounting for different initial/boundary conditions. The resulting computational framework shows the potential for closed-form model discovery in practical applications where large and accurate datasets are intractable to capture.

W-MMP2Vec: Topic-driven network embedding model for link prediction in content-based heterogeneous information network

2021 ◽  
Vol 25 (3) ◽  
pp. 711-738
Author(s):  
Phu Pham ◽  
Phuc Do
Keyword(s):  
Link Prediction ◽  
Representation Learning ◽  
Information Network ◽  
Network Embedding ◽  
Heterogeneous Information Network ◽  
Heterogeneous Information ◽  
Learning Framework ◽  
Novel Approach ◽  
Proposed Model ◽  
Meta Path

Link prediction on heterogeneous information network (HIN) is considered as a challenge problem due to the complexity and diversity in types of nodes and links. Currently, there are remained challenges of meta-path-based link prediction in HIN. Previous works of link prediction in HIN via network embedding approach are mainly focused on exploiting features of node rather than existing relations in forms of meta-paths between nodes. In fact, predicting the existence of new links between non-linked nodes is absolutely inconvincible. Moreover, recent HIN-based embedding models also lack of thorough evaluations on the topic similarity between text-based nodes along given meta-paths. To tackle these challenges, in this paper, we proposed a novel approach of topic-driven multiple meta-path-based HIN representation learning framework, namely W-MMP2Vec. Our model leverages the quality of node representations by combining multiple meta-paths as well as calculating the topic similarity weight for each meta-path during the processes of network embedding learning in content-based HINs. To validate our approach, we apply W-TMP2Vec model in solving several link prediction tasks in both content-based and non-content-based HINs (DBLP, IMDB and BlogCatalog). The experimental outputs demonstrate the effectiveness of proposed model which outperforms recent state-of-the-art HIN representation learning models.

scholarly journals A Novel Cobalt Metallopolymer with Redox-Matched Conjugated Organic Backbone via Electropolymerization of a Readily Available N4 Cobalt Complex

Polymers ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1667
Author(s):  
Mikhail Karushev
Keyword(s):  
Redox Reactions ◽  
Repeat Unit ◽  
Cobalt Complex ◽  
Radical Cations ◽  
Electrochemical Quartz Crystal Microbalance ◽  
Practical Applications ◽  
Sensing Applications ◽  
Novel Approach ◽  
Redox Switching

Fast and reversible cobalt-centered redox reactions in metallopolymers are the key to using these materials in energy storage, electrocatalytic, and sensing applications. Metal-centered electrochemical activity can be enhanced via redox matching of the conjugated organic backbone and cobalt centers. In this study, we present a novel approach to redox matching via modification of the cobalt coordination site: a conductive electrochemically active polymer was electro-synthesized from [Co(Amben)] complex (Amben = N,N′-bis(o-aminobenzylidene)ethylenediamine) for the first time. The poly-[Co(Amben)] films were investigated by cyclic voltammetry, electrochemical quartz crystal microbalance (EQCM), in situ UV‑vis-NIR spectroelectrochemistry, and in situ conductance measurements between −0.9 and 1.3 V vs. Ag/Ag+. The polymer displayed multistep redox processes involving reversible transfer of the total of 1.25 electrons per repeat unit. The findings indicate consecutive formation of three redox states during reversible electrochemical oxidation of the polymer film, which were identified as benzidine radical cations, Co(III) ions, and benzidine di-cations. The Co(II)/Co(III) redox switching is retained in the thick polymer films because it occurs at potentials of high polymer conductivity due to the optimum redox matching of the Co(II)/Co(III) redox pair with the organic conjugated backbone. It makes poly-[Co(Amben)] suitable for various practical applications based on cobalt-mediated redox reactions.

scholarly journals On the integrability problem for systems of partial differential equations in one unknown function, I

2019 ◽  
Vol 11 (4) ◽  
pp. 35-71 ◽  
Author(s):  
Antonio Kumpera
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Unknown Function ◽  
Contact Structures ◽  
Partial Differential ◽  
Practical Applications ◽  
First Order ◽  
Integrability Problem ◽  
Integration Problem ◽  
In The Beginning

We discuss the integration problem for systems of partial differential equations in one unknown function and special attention is given to the first order systems. The Grassmannian contact structures are the basic setting for our discussion and the major part of our considerations inquires on the nature of the Cauchy characteristics in view of obtaining the necessary criteria that assure the existence of solutions. In all the practical applications of partial differential equations, what is mostly needed and what in fact is hardest to obtains are the solutions of the system or, occasionally, some specific solutions. This work is based on four most enlightening Mémoires written by Élie Cartan in the beginning of the last century.

Feature Subspace Estimation for Resolving Dimensionality Mismatch in Practical Color-Based Face Recognition Systems

2016 ◽  
Vol 30 (04) ◽  
pp. 1656004 ◽  
Author(s):  
Jae Young Choi
Keyword(s):  
Face Recognition ◽  
Color Image ◽  
Recognition Performance ◽  
Real Life ◽  
Practical Applications ◽  
Novel Approach ◽  
Feature Subspace ◽  
New Feature ◽  
Different Color ◽  
Input Level

Recently, considerable research efforts have been devoted to effective utilization of facial color information for improved recognition performance. Of all color-based face recognition (FR) methods, the most widely used approach is a color FR method using input-level fusion. In this method, augmented input vectors of the color images are first generated by concatenating different color components (including both luminance and chrominance information) by column order at the input level and feature subspace is then trained with a set of augmented input vectors. However, in practical applications, a testing image could be captured as a grayscale image, rather than as a color image, mainly caused by different, heterogeneous image acquisition environment. A grayscale testing image causes so-called dimensionality mismatch between the trained feature subspace and testing input vector. Disparity in dimensionality negatively impacts the reliable FR performance and even imposes a significant restriction on carrying out FR operations in practical color FR systems. To resolve the dimensionality mismatch, we propose a novel approach to estimate new feature subspace, suitable for recognizing a grayscale testing image. In particular, new feature subspace is estimated from a given feature subspace created using color training images. The effectiveness of proposed solution has been successfully tested on four public face databases (DBs) such as CMU, FERET, XM2VTSDB, and ORL DBs. Extensive and comparative experiments showed that the proposed solution works well for resolving dimensionality mismatch of importance in real-life color FR systems.

Optimal control of thermal processes with phase transitions

2021 ◽  
Author(s):  
Yury Evtushenko ◽  
Vladimir Zubov ◽  
Anna Albu
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Crystallization Process ◽  
Automatic Differentiation ◽  
Phase Interface ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Two Phase ◽  
Metal Solidification

The optimal control of the metal solidification process in casting is considered. Quality of the obtained detail greatly depends on how the crystallization process proceeds. It is known that to obtain a model of a good quality it is desirable that the phase interface would be as close as possible to a plane and that the speed of its motion would be close to prescribed. The proposed mathematical model of the crystallization process is based on a three dimensional two phase initial-boundary value problem of the Stefan type. The velocity of the mold in the furnace is used as the control. The control satisfying the technological requirements is determined by solving the posed optimal control problem. The optimal control problem was solved numerically using gradient optimization methods. The effective method is proposed for calculation of the cost functional gradient. It is based on the fast automatic differentiation technique and produces the exact gradient for the chosen approximation of the optimal control problem.

A numerical algorithm based on scale-3 Haar wavelets for fractional advection dispersion equation

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Sapna Pandit ◽  
R.C. Mittal
Keyword(s):  
Haar Wavelet ◽  
Haar Wavelets ◽  
System Control ◽  
Partial Differential ◽  
Content Type ◽  
Advection Dispersion ◽  
Novel Approach ◽  
Gauss Elimination ◽  
Time Variables ◽  
First Time

Purpose This paper aims to propose a novel approach based on uniform scale-3 Haar wavelets for unsteady state space fractional advection-dispersion partial differential equation which arises in complex network, fluid dynamics in porous media, biology, chemistry and biochemistry, electrode – electrolyte polarization, finance, system control, etc. Design/methodology/approach Scale-3 Haar wavelets are used to approximate the space and time variables. Scale-3 Haar wavelets converts the problems into linear system. After that Gauss elimination is used to find the wavelet coefficients. Findings A novel algorithm based on Haar wavelet for two-dimensional fractional partial differential equations is established. Error estimation has been derived by use of property of compactly supported orthonormality. The correctness and effectiveness of the theoretical arguments by numerical tests are confirmed. Originality/value Scale-3 Haar wavelets are used first time for these types of problems. Second, error analysis in new work in this direction.

Sign in / Sign up

Export Citation Format

Share Document