Physical Laws Research Articles

Physics-informed machine learning approach for reduced-order modeling of integrally bladed rotors: Theory and application

Integrally bladed rotors are commonly used in aircraft and rocket turbomachinery and known to exhibit complex dynamics when subject to operational loading conditions. Though nominally cyclic-symmetric structures, in practice, cyclic symmetry is destroyed due to mistuning caused by random sector-to-sector imperfections in material properties and geometry. Simulating mistuned blisk dynamics using high-fidelity models can be computationally expensive, thus, a variety of physics-based reduced-order models have been previously developed. However, these models cannot easily incorporate experimental data nor leverage potential benefits of data-driven and machine-learning-based approaches. Here, we present a novel first-of-its-kind physics-informed machine learning modeling approach that incorporates physical laws directly into a novel network architecture while maintaining a sector-level viewpoint. The approach is combined with an assembly procedure resulting in a significantly smaller linear system based on blade-alone response data, and can directly incorporate physical response data like that measured with blade tip timing and/or traveling-wave excitation. Validation is shown using a large-scale finite-element model, with multiple traveling-wave forced-response predictions and response selection cases considered. Using only as little as a single degree of freedom per sector from the blade tip, this approach shows high accuracy relative to high-fidelity simulations.

Side-channel free quantum digital signature with source monitoring

Abstract Quantum digital signature (QDS) can guarantee the information-theoretical security of a signature with the fundamental laws of quantum physics. However, most current QDS protocols do not take source security into account, leading to an overestimation of the signature rate. In this paper, we propose to utilize Hong-Ou-Mandel interference to characterize the upper-bound of the source imperfections, and further to quantify information leakage from potential side-channels. Additionally, we combine decoy-state methods and finite-size analysis in analyzing the signature rate. Simulation results demonstrate the performance and feasibility of our approach. Our current work can improve the practical security of QDS systems, thereby promoting their further networked applications.

ADAPT: AI‐Driven Artefact Purging Technique for IMU Based Motion Capture

AbstractWhile IMU based motion capture offers a cost‐effective alternative to premium camera‐based systems, it often falls short in matching the latter's realism. Common distortions, such as self‐penetrating body parts, foot skating, and floating, limit the usability of these systems, particularly for high‐end users. To address this, we employed reinforcement learning to train an AI agent that mimics erroneous sample motion. Since our agent operates within a simulated environment, it inherently avoids generating these distortions since it must adhere to the laws of physics. Impressively, the agent manages to mimic the sample motions while preserving their distinctive characteristics. We assessed our method's efficacy across various types of input data, showcasing an ideal blend of artefact‐laden IMU‐based data with high‐grade optical motion capture data. Furthermore, we compared the configuration of observation and action spaces with other implementations, pinpointing the most suitable configuration for our purposes. All our models underwent rigorous evaluation using a spectrum of quantitative metrics complemented by a qualitative review. These evaluations were performed using a benchmark dataset of IMU‐based motion data from actors not included in the training data.

High-Efficiency Finite Element Model Updating of Bridge Structure Using a Novel Physics-Guided Neural Network

An accurate finite element model (FEM) plays a critical role in the structural damage identification. However, due to the existence of the uncertainties, such as material properties and modeling errors, it always exists some gaps between the analytical FEM and experimental structure. While an artificial neural network (ANN)-based model updating methods have been widely adopted to narrow the gap and obtain a baseline FEM, it still faces inaccurate results and fails to meet the physical law. In this regard, the study proposes a novel physics-based loss function inspired by modal sensitivity analysis and incorporates it into the residual neural network, thereby forming a novel physics-guided neural network (PGNN) method. The mapping relationship between the input of structural responses and output of model updating variables is constrained to retain its physical meaning by guiding the training process instead of pure data association, which aims to improve the accuracy of the ANN-based method and achieve accurate and high-efficiency model updating. An experimental example of a continuous rigid frame bridge is adopted to verify the feasibility of the proposed method. Additionally, other common model updating methods, including moth-flame optimization and regularization method, are used to make a comparison. The noise-robustness of the proposed method is investigated as well. Compared to the existing method, the results illustrate that the proposed PGNN method can achieve better model updating and good noise-robustness under high uncertainties, which means the introduction of the physics-based loss function significantly enhances the parameters updating ability of the neural network. The proposed method exhibits high efficiency and promising potential for large-scale bridge structure model updating.

A novel constrained skew-Gaussian filter and its application to maneuverable reentry vehicle tracking

The state of the system generally satisfies specific constraints imposed by material properties or physical laws, so the application of these constraints can improve the accuracy of state estimation. In this paper, a novel recursive filter referred as constrained high-degree cubature skew-Gaussian filter (CHCSGF) is proposed, which achieves soft-constrained state estimation by compressing the probability density of unconstrained states with constraint information. First, the probability density of the state under inequality soft constraints is modeled as a skew-Gaussian (SG) distribution, rather than truncated or single Gaussian distributions. Then, a recursive constrained SG filter is developed to handle inequality soft constraints in linear systems. Addressing nonlinear challenges, a 5th-degree spherical-radial cubature approximation method is presented to numerically calculate SG-weighted integrals for the nonlinear transformation of SG distribution. Finally, the CHCSGF algorithm is proposed using this method to tackle nonlinear filtering problems. The CHCSGF is applied to reentry trajectory tracking to improve estimation accuracy by dealing with heat flow, dynamic pressure and overload constraints during reentry flight. Simulation results demonstrate that the CHCSGF achieves higher estimation accuracy than unconstrained methods under nonlinear inequality soft constraints, and is robust to the constraints with a prior error. Compared to particle filter and moving horizon estimation, the computational complexity of CHCSGF is significantly reduced.

A sound-vibration physical-information fusion constraint-guided deep learning method for rolling bearing fault diagnosis

Although current deep learning models for bearing fault diagnosis have achieved excellent accuracy, the lack of constraint-guided learning of the physical mechanisms of real bearing failures and a physically scientific training paradigm leads to low interpretability and unreliability of intelligent fault diagnosis models. In this study, a sound-vibration physical-information fusion constraint-guided (PFCG) deep learning (DL) method is proposed, aiming at weighted fusion of sound and vibration multi-physical information into a deep learning model, to guide the DL model to learn more realistic physical laws of bearing failure. Firstly, a 15-degree-of-freedom nonlinear dynamics model of multi-stage degraded bearing failure mechanism with sound-vibration response is developed, which considers the evolutionary mechanism of bearing failure from healthy state to different stages, and utilizes a particle filtering algorithm for dynamic calibration of hidden parameters. Moreover, a lightweight DL fault diagnosis model is designed to realize the deep interaction between the physical model and the DL model through the weighted fusion of the cross-entropy loss function, physical consistency loss and uncertainty loss. Moreover, the superior diagnostic performance of the proposed sound and vibration PFCG-DL model is verified by comparing the performance fluctuations and parameter attributes of different DL benchmark models before and after being guided by physical information fusion constraints (PFCG). Eventually, the proposed PFCG-Transformer model achieves a diagnostic accuracy of 99.45% while keeping the number of parameters at only 0.62M, which significantly improves the accuracy and reduces the computational complexity by 81.5% compared to the CAME-Transformer model's 3.24 M number of parameters and 95.00% diagnostic accuracy. In addition, the test time of PFCG-Transformer is reduced to 1.02 s, which is 60.2% less than CAME-Transformer, demonstrating higher computational efficiency and real-time performance. Importantly, in terms of interpretability, the engineering interpretability and credibility of the models are further improved by visualizing the feature learning results of the vibration modal and multimodal fusion models and the sensitivity analyses of the sound-vibration response models with internal and external physical hyperparameters. Therefore, this study proposes a physical information-guided deep learning method with strong interpretability and superior performance, which provides an important reference for further research and application in the field of bearing fault diagnosis.

Deep fuzzy physics-informed neural networks for forward and inverse PDE problems

As a grid-independent approach for solving partial differential equations (PDEs), Physics-Informed Neural Networks (PINNs) have garnered significant attention due to their unique capability to simultaneously learn from both data and the governing physical equations. Existing PINNs methods always assume that the data is stable and reliable, but data obtained from commercial simulation software often inevitably have ambiguous and inaccurate problems. Obviously, this will have a negative impact on the use of PINNs to solve forward and inverse PDE problems. To overcome the above problems, this paper proposes a Deep Fuzzy Physics-Informed Neural Networks (FPINNs) that explores the uncertainty in data. Specifically, to capture the uncertainty behind the data, FPINNs learns fuzzy representation through the fuzzy membership function layer and fuzzy rule layer. Afterward, we use deep neural networks to learn neural representation. Subsequently, the fuzzy representation is integrated with the neural representation. Finally, the residual of the physical equation and the data error are considered as the two components of the loss function, guiding the network to optimize towards adherence to the physical laws for accurate prediction of the physical field. Extensive experiment results show that FPINNs outperforms these comparative methods in solving forward and inverse PDE problems on four widely used datasets. The demo code will be released at https://github.com/siyuancncd/FPINNs.

Rotor dynamic response prediction using physics-informed multi-LSTM networks

The deep learning method provides an effective alternative to numerical simulations for establishing the nonlinear input-output relationship and calculating dynamic responses of rotor systems. To overcome the low generalization capability of pure data-driven long short-term memory (LSTM) networks when predicting dynamic responses to out-of-distribution inputs, a dynamic response prediction method using physics-informed multi-LSTM networks is proposed. This approach incorporates required physical constraints into the deep LSTM network, allowing the model training process to optimize the network parameters within the feasible solution space that adheres to physical laws. Consequently, this enhances the physical interpretability of the deep learning model. Specifically, two physics-informed multi-LSTM network architectures are introduced, and physical laws of equation of motion, state dependency and hysteretic constitutive relationship are considered to construct the physics loss. The feasibility of the proposed method is verified by a Bouc-Wen hysteresis model and a simulated gas generator rotor. The response prediction performance of the two networks is validated on a constructed fault rotor dataset with significant sample differences, along with cross-speed and cross-node prediction validation for the rotor system. The results demonstrate that the trained networks exhibit strong robustness and generalization capabilities, making them suitable as surrogate models for rotor systems.

Physics-informed deep convolutional network for combined sea ice concentration and velocity prediction

Accurate prediction of short-term fluctuations in Arctic sea ice is important for safe use of Arctic shipping routes. While deep-learning models can improve the accuracy of sea-ice predictions, the accuracy and predictability of short-term sea-ice conditions are limited in most purely data-driven deep-learning models that consider a single aspect of sea ice, without considering the physical variation law between several sea ice factors. We propose dual-task prediction models for sea ice concentration (SIC) and sea ice velocity (SIV), and incorporate a loss function that simultaneously addresses dynamic constraints of SIC and SIV into each model, based on dynamics terms in the sea ice control equation. Comparative experiments are performed to determine which model structure best performs at predicting SIC and SIV. We report a dual-task branching structure to be more suitable for predicting SIC and SIV, and a post-decoder branch network structure to best predict SIC and SIV. Adding a sea ice dynamics equation to the loss function improves the model fit with dynamics law, improving the predictability and prediction accuracy of SIC and SIV.

Physics-informed neural networks for V-notch stress intensity factor calculation

This paper proposes a physics-informed neural networks (PINNs) based approach for elastic structures with a V-notch, by which the displacement field, stress field as well as the V-notch stress intensity factor (NSIF) can be obtained through artificial neural networks. A PINN model is established for V-notch structures, integrating physical information into a deep neural network to ensure adherence to physical laws while fitting observational data. Subsequently, an adaptive local sampling strategy for V-notch structures is adopted, generating locally dense Gaussian points sampling around regions of stress concentration. Based on this, a sequential PINNs approach for V-notch structures is then established to calculate the NSIF for V-notch structures with arbitrary notch angles. Finally, the effectiveness of the proposed method is validated through three numerical examples. The results demonstrate the method can accurately predict the NSIFs for V-notch structures across a spectrum of opening angles. Compared to the traditional data-driven method, the proposed method is able to more effectively compute the NSIF of V-notch structures due to the integration of physical information and observational data.

Learning a CNN with the finite volume method for modelling fluid seepage flow under closed boundary

Physics-informed neural networks (PINNs) are an efficient technique for incorporating physics law in models based on neural networks (NNs). In this paper, we propose a local refinement physics-informed convolutional neural network (LR-PICNN) to solve the seepage equation in closed boundary reservoirs. LR-PICNN employs a local refinement method to enhance focus on the region containing the well. First, the finite volume (FV) method is used to discretize the seepage equation on the global reservoir domain and on the local domain around the well to construct the loss functions respectively. Second, the boundary between the global and local domains are used as boundary conditions to couple the two systems. Finally, two loss functions are added to train the CNN to solve the seepage equation in autoregressive way and coupled without any labeled data. Experimental results show that LR-PICNN can more accurately solve seepage flow equation. Due to the coupling of solving equations and that LR-PICNN focuses on the behaviors of the well, compared to physics-informed Deep Convolutional neural network (PIDCNN) under the same well grid size, LR-PICNN has a faster solving speed that is at least 8 times faster, higher solution accuracy for BHP that is at least twice as high, and more stable solution, which could be used in numerical well testing.

Монетарна ентропія в умовах економічної глобалізації

Introduction. Changes occurring in the nature of money in the context of globalization have long been of interest to economists. Instead, the events of recent years have shown that such changes can also be caused by profound transformations that are natural ones and subject to general physical laws. Problem Statement. Establishing the dependence of the further development of money as an economic category on the action of the second law of thermodynamics. The purpose is the analysis of scientific ideas at the junction of economics and physics (ecophysics) and their spread to the monetary sphere ,in particular considering the manifestation of monetary entropy in the process of the international monetary system. Methods. General scientific and special methods are used: analysis, synthesis, description, comparison, theoretical generalization and abstract-logical analyses. Results. This publication introduces the concept of monetary entropy as a state of chaoticization of the essence of money (entropy of money) and the monetary system as a whole. The development of monetary entropy is considered as the result of cyclical development according to the Hegelian model “thesis-antithesis-synthesis”, which allows to avoid complete chaosization of the monetary sphere due to its transition to a new level of the spiral of development. The current state of the development of money as an economic category and the international monetary system as a whole, caused by the impact of the globalization process on them, proves that they are at the stage of another transition from entropy to negentropy, which can lead to the emergence of Global Money. Conclusions. Turning to the issue of predicting the future of money, it should be noted that there is an opinion that soon money will simply become a relic of the past and disappear altogether, leaving the probable technological singularity as one of its consequences, the very liquidation (more precisely, the senselessness of existence ) of money as an economic category. One of the possibilities of the technological singularity is the emergence of a post-scarcity society in which there will be a surplus of resources and the needs of every member of society will be fully satisfied (a variant of capitalist communism, when even an unconditional basic income will appear to be an unacceptable minimum for satisfying needs, because the principle from each according to his abilities to each according to his needs will be implemented. However, the change will not happen overnight, so there will most likely be a transition period during which humanity will still use money and the concept of money will evolve rather than disappear completely.

Leveraging Numerical Simulation Technology to Advance Drug Preparation: A Comprehensive Review of Application Scenarios and Cases.

Numerical simulation plays an important role in pharmaceutical preparation recently. Mechanistic models, as a type of numerical model, are widely used in the study of pharmaceutical preparations. Mechanistic models are based on a priori knowledge, i.e., laws of physics, chemistry, and biology. However, due to interdisciplinary reasons, pharmacy researchers have greater difficulties in using computer models. In this paper, we highlight the application scenarios and examples of mechanistic modelling in pharmacy research and provide a reference for drug researchers to get started. By establishing a suitable model and inputting preparation parameters, researchers can analyze the drug preparation process. Therefore, mechanistic models are effective tools to optimize the preparation parameters and predict potential quality problems of the product. With product quality parameters as the ultimate goal, the experiment design is optimized by mechanistic models. This process emphasizes the concept of quality by design. The use of numerical simulation saves experimental cost and time, and speeds up the experimental process. In pharmacy experiments, part of the physical information and the change processes are difficult to obtain, such as the mechanical phenomena during tablet compression and the airflow details in the nasal cavity. Therefore, it is necessary to predict the information and guide the formulation with the help of mechanistic models.

Differentiable modeling and optimization of non-aqueous Li-based battery electrolyte solutions using geometric deep learning

Electrolytes play a critical role in designing next-generation battery systems, by allowing efficient ion transfer, preventing charge transfer, and stabilizing electrode-electrolyte interfaces. In this work, we develop a differentiable geometric deep learning (GDL) model for chemical mixtures, DiffMix, which is applied in guiding robotic experimentation and optimization towards fast-charging battery electrolytes. In particular, we extend mixture thermodynamic and transport laws by creating GDL-learnable physical coefficients. We evaluate our model with mixture thermodynamics and ion transport properties, where we show improved prediction accuracy and model robustness of DiffMix than its purely data-driven variants. Furthermore, with a robotic experimentation setup, Clio, we improve ionic conductivity of electrolytes by over 18.8% within 10 experimental steps, via differentiable optimization built on DiffMix gradients. By combining GDL, mixture physics laws, and robotic experimentation, DiffMix expands the predictive modeling methods for chemical mixtures and enables efficient optimization in large chemical spaces.

Enhancing VPPA welding quality prediction: A hybrid model integrating prior physical knowledge and CNN analysis

In response to the inconsistency between the features obtained by deep learning models and the quality features reflected by the physical laws of the welding process, this study proposes a solution by integrating a physical prior information model with a CNN model. Initially, the physical laws of the welding process are utilized to annotate the arc, weld pool, and weld seam features relevant to quality, which are then acquired through image processing algorithms, thereby converting the physical laws into a prior information model. Subsequently, this prior information model guides the CNN model for quality recognition, and the CNN model's attention to features is explained through visualization methods to elucidate the relationship between features and quality recognition. Experimental results demonstrate that under the guidance of the prior information model, the CNN model not only automatically focuses on features relevant to quality but also achieves a differential feature attention strategy, thereby improving the recognition accuracy of different outcomes. This research provides a new perspective for deep learning in the field of welding quality recognition.

A physics‐constrained hybrid residual neural network for the prediction of moisture content in a closed‐cycle drying system

AbstractClosed‐cycle drying technology has the advantages of safety, energy saving, and environmental protection, and has a wide application prospect. Due to the multi‐physics and multi‐scale nature of heat/mass transfer in the closed‐cycle drying process, as well as the characteristics of drying medium circulation and energy integration, it is difficult to obtain the product moisture content prediction model in closed‐cycle process based on rigorous closed‐cycle drying process mechanism model. However, accurate monitoring of product moisture content in the closed‐cycle drying process is the key to improving drying quality and process optimization. Aiming at the challenges in predicting moisture content, this paper proposes a physics‐constrained hybrid residual neural network (PC‐HRNN) for soft sensor modelling within a designed closed‐cycle drying system. The characteristic of this proposed method lies in its effective fusion of physics, knowledge, and data. First, a hybrid residual neural network (HRNN) is constructed based on the integration of a physics model and a data‐driven model. The HRNN takes the knowledge from the physics model as its auxiliary features and learns the prediction residuals of the physics model through a neural network model. Then, a new loss function that takes into account physical laws is introduced into HPNN to standardize model training and improve the generalization performance of the model. The experimental results show that the PC‐HRNN model improves prediction accuracy and model robustness, reduces the demand for data, and demonstrates stronger extrapolation capabilities under limited data.

Cosmopsychism and the Laws of Physics: A Hylomorphic Perspective

I outline a hylomorphic account of physical reality in which the cosmos as a whole has mental properties which explain its nomological order. According to this theory, the cosmos is directed in its temporal development toward certain ends or goals which it intends, and these ends are immanent to the cosmos rather than being imposed upon it. My object in doing so is to argue that, contrary to Sean Carroll (2021), a view of physical reality as having intrinsically mental aspects need not induce any modifications of the known laws of physics nor violate 'causal closure' under physical laws. Rather, this soft form of naturalism, which includes final causes within nature, provides a foundation for the laws of physics that is lacking in Carroll's hard form of naturalism, which excludes mind from fundamental reality. I propose a trilemma for Carroll in which he should either: abandon naturalism, by admitting that the laws of physics are imposed by a divine mind; abandon realism, by conceding that 'laws' are constructed by human minds; or embrace cosmopsychism, by acknowledging that the cosmos as a whole instantiates a mind. I argue that cosmic hylomorphism, which links consciousness with intentional cognition, is preferable to non-hylomorphic versions of cosmopsychism, which tend to prioritize consciousness over intentionality.

APPLICATION OF KEPLER'S LAWS IN PHYSICS

Kepler’s laws of planetary motion provide fundamental insights into the mechanics of celestial bodies. These laws are crucial in understanding orbital mechanics, which play a significant role in modern astrophysics, satellite engineering, and space exploration. This paper presents a comprehensive exploration of the application of Kepler's laws in physics, emphasizing their relevance to both historical and contemporary scientific advancements. The study evaluates the laws' contributions to Newtonian mechanics and modern applications in satellite technology and gravitational theory.

Physics, ecological acoustics and the auditory system

Sound occurs when vibrations travel through a medium. These vibrations, their propagation, and their interaction with the environment are dictated by laws of physics, and indirectly reflect underlying physical properties of things in the world. The sense of audition exists to measure sound and infer its causes in the world, so as to help organisms interact with the world around them. Audition is thus indirectly but intimately shaped by the physics of sound.

Balance equations for physics-informed machine learning

Using traditional machine learning (ML) methods may produce results that are inconsistent with the laws of physics. In contrast, physics-based models of complex physical, biological, or engineering systems incorporate the laws of physics as constraints on ML methods by introducing loss terms, ensuring that the results are consistent with these laws. However, accurately deriving the nonlinear and high order differential equations to enforce various complex physical laws is non-trivial. There is a lack of comprehensive guidance on the formulation of residual loss terms. To address this challenge, this paper proposes a new framework based on the balance equations, which aims to advance the development of PIML across multiple domains by providing a systematic approach to constructing residual loss terms that maintain the physical integrity of PDE solutions. The proposed balance equation method offers a unified treatment of all the fundamental equations of classical physics used in models of mechanical, electrical, and chemical systems and guides the derivation of differential equations for embedding physical laws in ML models. We show that all of these equations can be derived from a single equation known as the generic balance equation, in conjunction with specific constitutive relations that bind the balance equation to a particular domain. We also provide a few simple worked examples how to use our balance equation method in practice for PIML. Our approach suggests that a single framework can be followed to incorporate physics into ML models. This level of generalization may provide the basis for more efficient methods of developing physics-based ML for complex systems.