Physical Laws Research Articles

Structure-preserving discretization of fractional vector calculus using discrete exterior calculus

Fractional vector calculus is the building block of the fractional partial differential equations that model non-local or long-range phenomena, e.g., anomalous diffusion, fractional electromagnetism, and fractional advection-dispersion. In this work, we reformulate a type of fractional vector calculus that uses Caputo fractional partial derivatives and discretize this reformulation using discrete exterior calculus on a cubical complex in the structure-preserving way, meaning that the continuous-level properties curlαgradα=0 and divαcurlα=0 hold exactly on the discrete level. We discuss important properties of our fractional discrete exterior derivatives and verify their second-order convergence in the root mean square error numerically. Our proposed discretization has the potential to provide accurate and stable numerical solutions to fractional partial differential equations and exactly preserve fundamental physics laws on the discrete level regardless of the mesh size.

Time-averaged flow field reconstruction based on a multifidelity model using physics-informed neural network (PINN) and nonlinear information fusion

PurposeCurrent methods for flow field reconstruction mainly rely on data-driven algorithms which require an immense amount of experimental or field-measured data. Physics-informed neural network (PINN), which was proposed to encode physical laws into neural networks, is a less data-demanding approach for flow field reconstruction. However, when the fluid physics is complex, it is tricky to obtain accurate solutions under the PINN framework. This study aims to propose a physics-based data-driven approach for time-averaged flow field reconstruction which can overcome the hurdles of the above methods.Design/methodology/approachA multifidelity strategy leveraging PINN and a nonlinear information fusion (NIF) algorithm is proposed. Plentiful low-fidelity data are generated from the predictions of a PINN which is constructed purely using Reynold-averaged Navier–Stokes equations, while sparse high-fidelity data are obtained by field or experimental measurements. The NIF algorithm is performed to elicit a multifidelity model, which blends the nonlinear cross-correlation information between low- and high-fidelity data.FindingsTwo experimental cases are used to verify the capability and efficacy of the proposed strategy through comparison with other widely used strategies. It is revealed that the missing flow information within the whole computational domain can be favorably recovered by the proposed multifidelity strategy with use of sparse measurement/experimental data. The elicited multifidelity model inherits the underlying physics inherent in low-fidelity PINN predictions and rectifies the low-fidelity predictions over the whole computational domain. The proposed strategy is much superior to other contrastive strategies in terms of the accuracy of reconstruction.Originality/valueIn this study, a physics-informed data-driven strategy for time-averaged flow field reconstruction is proposed which extends the applicability of the PINN framework. In addition, embedding physical laws when training the multifidelity model leads to less data demand for model development compared to purely data-driven methods for flow field reconstruction.

Adversarial machine learning phases of matter

We study the robustness of machine learning approaches to adversarial perturbations, with a focus on supervised learning scenarios. We find that typical phase classifiers based on deep neural networks are extremely vulnerable to adversarial perturbations: adding a tiny amount of carefully crafted noises into the original legitimate examples will cause the classifiers to make incorrect predictions at a notably high confidence level. Through the lens of activation maps, we find that some important underlying physical principles and symmetries remain to be adequately captured for classifiers with even near-perfect performance. This explains why adversarial perturbations exist for fooling these classifiers. In addition, we find that, after adversarial training the classifiers will become more consistent with physical laws and consequently more robust to certain kinds of adversarial perturbations. Our results provide valuable guidance for both theoretical and experimental future studies on applying machine learning techniques to condensed matter physics.

Neural networks informed by physics for modeling mass flow rate in a production wellbore

Optimal control strategies may efficiently manage and operate assets in contemporary oil and gas fields, lowering costs and maximizing yield. However, during this process, we encounter a traditional modeling challenge: obtaining an appropriate system representation. Concerning this task, the current research introduces a new hybrid model for simulating multi-phase mass flow in an offshore oil and gas production field. We investigate a concept based on Physics-Informed Neural Networks (PINN) to characterize the mass flow dynamics in a production wellbore. PINN models have been demonstrated as a feasible alternative for training neural networks using a small number of training data samples and estimating the parameters of physics equations that guide the underlying dynamics. The concept might provide alternatives to modeling and balancing the task of learning from physics and data in oil-gas systems. This research analyzes the performance of neural networks inspired by physics in a synthetic database constructed from the physics laws of mass conservation and conservation of momentum. After solidifying the principles, the study assessed the power of model assimilation in a real-world oilfield situation.

Bringing uncertainty quantification to the extreme-edge with memristor-based Bayesian neural networks

Safety-critical sensory applications, like medical diagnosis, demand accurate decisions from limited, noisy data. Bayesian neural networks excel at such tasks, offering predictive uncertainty assessment. However, because of their probabilistic nature, they are computationally intensive. An innovative solution utilizes memristors’ inherent probabilistic nature to implement Bayesian neural networks. However, when using memristors, statistical effects follow the laws of device physics, whereas in Bayesian neural networks, those effects can take arbitrary shapes. This work overcome this difficulty by adopting a variational inference training augmented by a “technological loss”, incorporating memristor physics. This technique enabled programming a Bayesian neural network on 75 crossbar arrays of 1,024 memristors, incorporating CMOS periphery for in-memory computing. The experimental neural network classified heartbeats with high accuracy, and estimated the certainty of its predictions. The results reveal orders-of-magnitude improvement in inference energy efficiency compared to a microcontroller or an embedded graphics processing unit performing the same task.

Physics-informed deep learning for structural vibration identification and its application on a benchmark structure

Structural vibration identification is an important task in civil engineering that is based on processing measured data from structural monitoring. However, predicting the response at unsensed locations based on limited sensor data can be challenging. Deep learning (DL) methods have shown promise in vibration data feature extraction and generation, but they struggle to capture the underlying physics laws and dynamic equations that govern vibration identification. This paper presents a novel framework called physics-informed deep learning (PIDL) that combines deep generative networks with structural dynamics knowledge to address these challenges. The PIDL framework consists of a data-driven convolutional neural network for structural excitation identification and a physics-informed variational autoencoder for explicit time-domain (ETD) vibration analysis with the generated unit impulse response (UIR) signal of the measured structure. The proposed framework is evaluated on a benchmark structure for structural health monitoring, demonstrating its effectiveness in extracting physics-related dynamics features and accurately identifying excitation signals and latent physics parameters across different damage patterns. Additionally, the incorporation of an ETD method-aided convolution function in the loss function aligns the generated UIR signals with the dynamic properties of the measured structure. Compared with conventional DL-based vibration analysis methods, the PIDL framework offers improved accuracy and reliability by integrating structural dynamics knowledge. This study contributes to the advancement of structural vibration identification and showcases the potential of the PIDL framework in civil structure monitoring applications. This article is part of the theme issue 'Physics-informed machine learning and its structural integrity applications (Part 2)'.

Fuzzy modelling and inference for physics-aware road vehicle driver behaviour model calibration

Traffic simulation is a crucial tool for testing and evaluating hypotheses in both the design of autonomous driving systems and the optimization of urban transportation, where modelling and calibrating driver behaviour is key. In this article, we introduce a novel approach to calibrating driver models by combining fuzzy logic and inference to produce a plausible parametrization that, simultaneously, reproduces drivers’ behaviour peculiarities and road traffic characteristics. The calibration system uses solely vehicle trajectories that describe cars’ movements through the road network, with a resolution of time and space enough to allow for determining the lane of the road used, speed, and acceleration at every second of the survey period. This data is processed by a lightweight modelling and inference system capable of interpreting the input data through the lens of domain knowledge and physics laws in order to learn plausible driver model parameters using fuzzy computation. The outcome is a set of parameters for mathematical models which emulate the social and physical features of the behaviour of a driver-vehicle unit. Albeit this study limits itself to determining parameters for car-following and lane-change models, the systematic approach for calibration can be seen as a framework where also other driver model components can be calibrated (e.g. gap-acceptance). We evaluate our system on both synthetic and real data while comparing it with other approaches for calibration. We summarize our findings using a thorough analysis where we point out the most relevant aspects to consider when calibrating driver models.

Analysis of the Functions of Cosmology Dust in Galaxy Formation

The physical laws related to star formation in galaxies are the key to understanding the formation and evolution of galaxies. The dust in the interstellar medium has a significant effect on both the star formation and the observational properties of the galaxy. Understanding the properties, effects, and evolution of cosmology dust in galaxies is an essential part of a complete picture of galaxy formation and evolution. In this study, the background of interstellar dust research in galaxy formation will be summarized. Some basic concepts and physical properties of galaxies are introduced. The definition, classification and evolution of galaxies will be discussed. It then states the properties of cosmology dust in galaxies, including the basic concepts of physics, properties, generation, and evolution of dust. It will then focus on the role of interstellar dust in galaxies, including its basic concepts and background. These results shed light on guiding better understanding of the functions of cosmology dust in galaxy formation.

Universal differential equations for glacier ice flow modelling

Abstract. Geoscientific models are facing increasing challenges to exploit growing datasets coming from remote sensing. Universal differential equations (UDEs), aided by differentiable programming, provide a new scientific modelling paradigm enabling both complex functional inversions to potentially discover new physical laws and data assimilation from heterogeneous and sparse observations. We demonstrate an application of UDEs as a proof of concept to learn the creep component of ice flow, i.e. a nonlinear diffusivity differential equation, of a glacier evolution model. By combining a mechanistic model based on a two-dimensional shallow-ice approximation partial differential equation with an embedded neural network, i.e. a UDE, we can learn parts of an equation as nonlinear functions that then can be translated into mathematical expressions. We implemented this modelling framework as ODINN.jl, a package in the Julia programming language, providing high performance, source-to-source automatic differentiation (AD) and seamless integration with tools and global datasets from the Open Global Glacier Model in Python. We demonstrate this concept for 17 different glaciers around the world, for which we successfully recover a prescribed artificial law describing ice creep variability by solving ∼ 500 000 ordinary differential equations in parallel. Furthermore, we investigate which are the best tools in the scientific machine learning ecosystem in Julia to differentiate and optimize large nonlinear diffusivity UDEs. This study represents a proof of concept for a new modelling framework aiming at discovering empirical laws for large-scale glacier processes, such as the variability in ice creep and basal sliding for ice flow, and new hybrid surface mass balance models.

Robust data driven discovery of a seismic wave equation

Summary Despite the fact that our physical observations can often be described by derived physical laws, such as the wave equation, in many cases, we observe data that do not match the laws or have not been described physically yet. Therefore recently, a branch of machine learning has been devoted to the discovery of physical laws from data. We test this approach for discovering the wave equation from the observed spatial-temporal wavefields. The algorithm first pretrains a neural network (NN) in a supervised fashion to establish the mapping between the spatial-temporal locations (x, y, z, t) and the observation displacement wavefield function u(x, y, z, t). The trained NN serves to generate meta-data and provide the time and spatial derivatives of the wavefield (e.g., utt and uxx) by automatic differentiation. Then, a preliminary library of potential terms for the wave equation is optimized from an overcomplete library by using a genetic algorithm. We, then, use a physics-informed information criterion to evaluate the precision and parsimony of potential equations in the preliminary library and determine the best structure of the wave equation. Finally, we train the ”physics-informed” neural network to identify the corresponding coefficients of each functional term. Examples in discovering the 2D acoustic wave equation validate the feasibility and effectiveness of our implementation. We also verify the robustness of this method by testing it on noisy and sparsely acquired wavefield data.

The Mechanism of Droplet Thermocapillary Migration Coupled with Multi-Physical Fields

In this paper, the coupling effect of multiphysical fields of droplet migration is deeply studied by constructing a physical model of droplet migration with multiphysical fields. Digital holographic interferometry and particle image velocimetry are used to simultaneously measure the temperature and velocity fields of the mother liquor in the process of droplet migration for the first time. Due to the advancements of measuring, the zero-velocity region is also in the region where the thermal wake appears, four vortexes appear in the droplet migration and the off-axis behavior of double-droplet migration is found. The aim of this work is to analyze the coupling relationship of multiphysical fields, so as to reveal the physical laws of thermocapillary migration of single droplet and multiple droplets with the same phase and heterophase and to study the driving mechanism of the thermocapillary force and the flow of the mother liquor.

Bioconvection effects on the heat and mass transfer of unsteady MHD blood flow over a permeable artery

The mathematical analysis of blood’s non-Newtonian behavior in the presence of drug nanoparticles and microbes with magnetic and thermal radiation effects is the focus of the current article. The response surface methodology (RSM) is used to conduct a sensitivity study of the bioconvection impacts on the heat and mass transmission rate of the unsteady magnetohydrodynamic blood flow. The physical laws governing unsteady blood flow over stretching blood vessels are mathematically represented as a system of partial differential equations, which are numerically solved using the Fourth Order Runge–Kutta Method in conjunction with the Shooting Technique. Following an analysis of the numerical data, statistical conclusions are drawn on the heat and mass transfer rates. The impact of Brownian motion and thermophoresis factors is discovered to increase blood temperature. Additionally, at the largest Brownian motion factor and maximum thermophoresis effect, the largest heat transfer rate occurs. It is also observed that the lowest mass transfer rates are generated by higher radiation parameter and chemical reaction parameter values. The findings of the study show potential for important applications in therapeutic hypothermia, magnetic therapy, and targeted drug delivery.

Physics-Informed Neural Networks for solving transient unconfined groundwater flow

Neural networks excel in various machine learning applications; however, they lack the physical interpretability and constraints crucial for numerous scientific and engineering problems. This limitation hinders their ability to accurately capture and predict complex physical systems’ behavior, potentially yielding inaccurate or unreliable results. Physics-Informed Neural Networks (PINNs) are a class of machine learning models that integrate the power of neural networks with the physical laws governing natural phenomena. PINNs provide an effective tool for solving intricate physical problems, ranging from fluid dynamics to materials science, by incorporating physical constraints into the neural network architecture. PINNs can substantially enhance the accuracy and efficiency of model predictions, even in data-limited situations. This work offers insight into recent developments in the PINN field, including their mathematical formulation and training algorithms, and emphasizes their application in solving transient unconfined groundwater flow. In this context, the phreatic surface acts as a spatiotemporally varying boundary condition, and properly accounting for its position is vital for precise predictions of unconfined groundwater flow and related environmental and engineering applications. The study’s objective is to develop a reliable model for estimating the phreatic surface and the spatiotemporal distribution of piezometric heads in a vertical cross-section of an unconfined aquifer. Two cases are examined: the first involves a homogeneous and isotropic aquifer, while the second comprises a mildly heterogeneous and anisotropic one. The challenges and opportunities arising from this emerging research area are also explored, and essential directions for future research are underscored.

On the One‐Dimensional Transition State Theory and the Relation between Statistical and Deterministic Oscillation Frequencies of Anharmonic Energy Wells

AbstractThe transition state theory allows the development of approximated models useful to study the non‐equilibrium evolution of systems undergoing transformations between two states (e.g., chemical reactions). In a simplified 1D setting, the characteristic rate constants are typically written in terms of a temperature‐dependent characteristic oscillation frequency , describing the exploration of the phase space. As a particular case, this statistical oscillation frequency can be defined for an arbitrary convex potential energy well. This value is compared here with the deterministic oscillation frequency of the corresponding anharmonic oscillator. It is proved that there is a universal relationship between statistical and deterministic frequencies, which is the same for classical and relativistic mechanics. The independence of this relationship from the adopted physical laws gives it an interesting thermodynamic and pedagogical meaning. Several examples clarify the meaning of this relationship from both physical and mathematical viewpoints.

The joint conservation assumption of CPT and weak isospin and color charge

The conservation of CPT is considered applicable to all physical laws, but more and more research has discovered the possibility of CPT violation. This paper attempts to find a more complex and essential conservation than CPT conservation. This paper uses the method of theoretical structural analysis to discover the relationship between C, P, T symmetry, phase rotation symmetry, space rotation symmetry, and time translation symmetry, and prove the relationship between CPT symmetry, charge conservation, angular momentum conservation and energy conservation by studying the transformation modes of phase space, space, and time. Then the composition rules of uncertainty relationships and the fact that charge, weak isospin, and color charge are all related to the internal symmetry of matter are used to provide evidence for the inherent connection between charge, weak isospin rotation, and color charge demonstrating the similarity among these three. Finally, the joint conservation of CPT, weak isospin, and color charge are proposed.

Solving seepage equation using physics-informed residual network without labeled data

Physics-informed neural network (PINN) is an innovative universal function approximator which adds physical constraints to neural network to make the fitting results satisfy the physical laws better. In this paper, a physics-informed residual network (PIResNet) is proposed to solve the single-phase seepage equation without labeled data. The loss function is constructed by summarizing the residuals of the discretized seepage equation based on the finite volume method (FVM), and the boundary conditions are embedded in the PDE residuals in a “hard constraint” way. The PIResNet is simple in network structure, fast in convergence and easy to optimize. Furthermore, the convergence of the residual structure used in this paper is proved and the theoretical analysis of time complexity illustrates the computational efficiency of PIResNet. The correctness of the proposed method is proved and the experiments display that the solution time of PIResNet is reduced by more than six times compared to physics-informed convolutional neural networks (PICNN).

Solution of FPK equation for stochastic dynamics subjected to additive Gaussian noise via deep learning approach

The Fokker-Plank-Kolmogorov (FPK) equation is an idealized model representing many stochastic systems commonly encountered in the analysis of stochastic structures as well as many other applications. Its solution thus provides an invaluable insight into the performance of many engineering systems. Despite its great importance, the solution of the FPK equation is still extremely challenging. For systems of practical significance, the FPK equation is usually high dimensional, rendering most of the numerical methods ineffective. In this respect, the present work introduces the FPK-DP Net as a physics-informed network that encodes the physical insights, i.e. the governing constrained differential equations emanated out of physical laws, into a deep neural network. FPK-DP Net is a mesh-free learning method that can solve the density evolution of stochastic dynamics subjected to additive white Gaussian noise without any prior simulation data and can be used as an efficient surrogate model afterward. FPK-DP Net uses the dimension-reduced FPK equation. Therefore, it can be used to address high-dimensional practical problems as well. To demonstrate the potential applicability of the proposed framework, and to study its accuracy and efficacy, numerical implementations on five different benchmark problems are investigated.

COMPARATIVE ANALYSIS OF SELF-ORGANIZING PROCESSES IN BIOLOGY AND PROJECT MANAGEMENT

A bee swarm, termite colony, anthill, mycelia are just a few biological systems that exist in nature for millions of years, survive and evolve. All the biological systems listed above are united by one concept - the concept of self-organization. Evolutionary processes occurring in these biological systems have been studied for decades by various scientists. This article analyzes the similarity of self-organization processes in biological systems and project teams. The relevance of the topic lies in the importance of rethinking the processes of self-organization in project teams and in building a new structure for the further development of the concepts of self-learning and self-management. As you know, the key resource for the development of society and the economy is the human resource, which cannot always be systematically managed under the supervision of the manager. Self-organization is an important aspect of team life in our future, precisely because of the mobility of functions. This process is characterized by the ability to rationally organize work, both one's own and the work of subordinate teams. Thereby, an effectively designed system of self-management, which takes into account the specifics of the organization's work and the current economic situation, is considered one of the key factors contributing to the achievement of the goals set by the organization. A new look at the structures of the synergetic level, which were established by the laws of physics and nature, will allow us to develop and establish new paradigms in the processes of self-organization and self-management.

Physics-informed Neural Network for Quadrotor Dynamical Modeling

The explosive growth of civil applications of Unmanned Aerial Vehicles (UAVs) calls for control algorithms that enable safe and trustworthy operations, especially in complex environments to facilitate real-world deployment. Although Model-Based Control (MBC) has found great applicability in the last decades, it relies heavily on the accuracy of the underlying mathematical models. Thanks to their powerful approximation capability, data-driven approaches such as Artificial Neural Networks (ANNs) have raised a great interest in UAV dynamical modeling in recent years. Despite the promising results achieved in learning either full or partial dynamics such as aerodynamic effects, prior studies merely pay little to no attention to the black-box nature of ANNs, yielding poorly interpretable learning processes and implying a lack of generalization capability due to undesirably learned spurious relationships among features and labels. While nowadays practitioners and society are far from being concerned just with performance, such risk evidently reduces the overall trustworthiness of the control system with ANNs as control-oriented models. With the goal of both accurate and interpretable neural modeling of nonlinear dynamics, we propose a novel modeling approach that utilizes Physics-Informed Neural Networks (PINN), designed to seamlessly embed physical laws into Deep Neural Networks (DNN). To further enhance model interpretability, we adopt the Covariance Confidence Ellipse (CCE) as post-hoc visualization to help understand the model behavior. We also set up a visual and physical simulator based on AirSim with custom implementation on quadrotor ground effect, which is made publicly available to facilitate further experiments for the community. An extensive simulation campaign validates our approach on data sets including aerodynamics and periodic wind, highlighting advantages regarding the accuracy and physical consistency, pointing to further insight on the development of learning-based control-oriented models for quadrotors, and facilitating flight controller design with performance guarantees.

Physics laboratory work using cloud technologies

The article describes the structure and content of the physics textbook «Laboratory work using cloud technologies» for students of vocational higher education institutions. The importance of modernizing the educational process in physics in general and approaches to conducting laboratory work in particular using the methods of modern information and communication and cloud technologies are analyzed. The importance and advantages of digitization of the educational process in physics through the use of cloud services, virtual laboratory works, simulators, mobile applications, flash animations, etc. are substantiated. The theoretical and practical blocks of the manual are described in detail. The theoretical unit is represented by three sections and is filled with didactic and methodical materials that contain recommendations, advice and rules for organizing, preparing and conducting a physical experiment. The practical unit of the manual is represented by one section «Laboratory works», which presents instructions for seven laboratory works. A feature of such works is the use of virtual laboratories, simulators, and cloud environments for testing physical laws, researching physical phenomena, and determining physical quantities. The article provides an example of instructions for laboratory work «Determining the index of refraction of light at the boundary of separation of two media». The research presented in this experiment is carried out using the «Refraction of Light» physical simulator of the website Phet.colorado.edu - the website of the University of Colorado. The process of measuring the refractive index of light at the boundary between two media is described in detail and step by step. The order of performing some tasks is illustrated by the corresponding screen images of the «Refraction of Light» physics simulator. The materials for surveying and monitoring the educational achievements of students are given, among which three directions of questions and tasks are singled out for the didactic purpose: to check the assimilation of knowledge, to check the formation of skills and abilities, to check the formation of beliefs. This manual has been tested in groups of students of the humanitarian profile of institutions of vocational pre-higher education. At the All-Ukrainian competition «Pedagogical OSCAR – 2023», the manual won the 2nd place in the nomination «Innovative approaches to the organization of practical training of students of vocational pre-university education».