Complex Physical Systems Research Articles

Advancing heat transfer modeling through machine learning: A focus on forced convection with nanoparticles

This study underscores the critical role of heat transfer modeling in the design and optimization of heat exchangers, recognizing the challenges posed by traditional numerical methods. To address the need for more efficient alternatives, machine learning emerges as a promising solution, leveraging its capacity to unravel intricate relationships in heat transfer processes. The research focuses on forced convection heat transfer involving nanoparticles (specifically TiO2, Al2O3, and Cu) dispersed in water, employing the Lagrangian–Eulerian approach under turbulent flow conditions with a constant surface heat flux. Machine-learning techniques, namely extreme gradient boosting, support vector regression, and tree regression are employed to predict heat transfer outcomes based on collected data. The achieved results exhibit promising accuracy levels, with eXtreme gradient boosting, support vector regression, and tree regression algorithm models demonstrating impressive accuracies of 91%, 91%, and 94%, respectively. The mean absolute errors for these machine-learning models were recorded as 1.07, 7.24, and 3.74. This research serves as a demonstration of the potential of machine-learning methodologies in modeling complex physical systems, as evidenced by their efficiency in capturing the behavior of nanofluids under various conditions. The obtained accuracy and low mean absolute error values indicate the robustness of these machine-learning models in predicting heat transfer results. The implications of these findings are substantial for the field of heat exchanger design and optimization. The study suggests that machine-learning techniques offer a more efficient and cost-effective approach compared to traditional numerical simulations. By leveraging the capabilities of these models, there is potential for enhanced accuracy and efficiency in the design and optimization processes of heat exchangers, contributing to advancements in thermal engineering.

Deep learning-based surrogate models for parametrized PDEs: Handling geometric variability through graph neural networks

Mesh-based simulations play a key role when modeling complex physical systems that, in many disciplines across science and engineering, require the solution to parametrized time-dependent nonlinear partial differential equations (PDEs). In this context, full order models (FOMs), such as those relying on the finite element method, can reach high levels of accuracy, however often yielding intensive simulations to run. For this reason, surrogate models are developed to replace computationally expensive solvers with more efficient ones, which can strike favorable trade-offs between accuracy and efficiency. This work explores the potential usage of graph neural networks (GNNs) for the simulation of time-dependent PDEs in the presence of geometrical variability. In particular, we propose a systematic strategy to build surrogate models based on a data-driven time-stepping scheme where a GNN architecture is used to efficiently evolve the system. With respect to the majority of surrogate models, the proposed approach stands out for its ability of tackling problems with parameter-dependent spatial domains, while simultaneously generalizing to different geometries and mesh resolutions. We assess the effectiveness of the proposed approach through a series of numerical experiments, involving both two- and three-dimensional problems, showing that GNNs can provide a valid alternative to traditional surrogate models in terms of computational efficiency and generalization to new scenarios.

Cracking the Neural Code of How the Brain Represents Time May Make the Dualistic Stance Obsolete

Abstract This is an invited commentary on the position paper of Gruber, Block and Montemayor (2022). First, I oppose the premise in Gruber et al.’s proposal according to which there exists a ‘real’ and an ‘illusory’ time. Second, our knowledge about the universe is hypothesized, tested, and verified by the most complex physical systems known to date (brains) hence postulating the coexistence of an ‘absolute’ and a ‘real’, or an ‘illusory’ and a ‘nonillusory’ time might be unnecessary. Instead, and parsimoniously, (organic or atomic) measuring devices for duration, simultaneity, order, and so forth, have variable precision. The most exquisite clock is atomic, a good enough one for survival on Earth is at the scale of neural networks. A difference between measuring devices and brains is that the latter compute on stored temporal information. Last, I suggest additional gadgets for the Information Gathering and Utilizing Systems (IGUs) proposal. In sum, I oppose some of the theoretical premises while lending support to the idea that representing temporal statistics is a useful heuristics for some aspects of temporal cognition. From the cognitive neuroscience standpoint, IGUs are compatible with information-theoretic approaches, and with current Bayesian and predictive models implemented in neural systems, in which brains code information and compute on symbolic representations.

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.

The application of a novel variable-order fractional calculus on rheological model for viscoelastic materials

Viscoelastic materials have become popular for novel multifunctional materials in emerging modern technologies, which have complex elastic-viscous-plastic behaviors. The variable-order fractional derivative has been gradually applied to characterize such variable memory effects of complex physical systems, while existing definitions are somewhat controversial. The new Scarpi’s variable-order fractional calculus has rigorous mathematical logic compared with the existed definitions. However, its practicality and feasibility in engineering are ambiguous due to the fewer applications up to now. In this paper, we aimed at introducing the Scarpi’s variable-order fractional derivative into the rheological applications of viscoelastic materials. Based on the Scarpi’s variable-order fractional derivative, the fractional Zener model and fractional viscoelastic-visoplastic models are established, and the parameters sensitivity on stress-strain relation is discussed. Then, the proposed models are then applied to depict different rheological behaviors of polymers at various temperatures and strain rates, and the results show that they have excellent agreement for experimental data compared to the reference model. It is observed that the order increases linearly with strain of the viscoelastic model and decreases exponentially with strain of the viscoplastic model. Furthermore, the physical significance of the corresponding fractional order parameters is investigated. It is found that they have the variation relation with temperatures and strain rates. It reveals that the variable fractional order can be regarded as an index to characterize the evolution of mechanical behaviors of polymers.

Langevin picture of subdiffusion in nonuniformly expanding medium.

Anomalous diffusion phenomena have been observed in many complex physical and biological systems. One significant advance recently is the physical extension of particle's motion in a static medium to a uniformly and even nonuniformly expanding medium. The dynamic mechanism of the anomalous diffusion in the nonuniformly expanding medium has only been investigated by the approach of continuous-time random walk. To study more physical observables and to supplement the physical models of the anomalous diffusion in the expanding mediums, we characterize the nonuniformly expanding medium with a spatiotemporal dependent scale factor a(x,t) and build the Langevin picture describing the particle's motion in the nonuniformly expanding medium. Besides the existing comoving and physical coordinates, by introducing a new coordinate and assuming that a(x,t) is separable at a long-time limit, we build the relation between the nonuniformly expanding medium and the uniformly expanding one and further obtain the moments of the comoving and physical coordinates. Different forms of the scale factor a(x,t) are considered to uncover the combined effects of the particle's intrinsic diffusion and the nonuniform expansion of medium. The theoretical analyses and simulations provide the foundation for studying more anomalous diffusion phenomena in the expanding mediums.

Purification-based quantum error mitigation of pair-correlated electron simulations

An important measure of the development of quantum computing platforms has been the simulation of increasingly complex physical systems. Before fault-tolerant quantum computing, robust error-mitigation strategies were necessary to continue this growth. Here, we validate recently introduced error-mitigation strategies that exploit the expectation that the ideal output of a quantum algorithm would be a pure state. We consider the task of simulating electron systems in the seniority-zero subspace where all electrons are paired with their opposite spin. This affords a computational stepping stone to a fully correlated model. We compare the performance of error mitigations on the basis of doubling quantum resources in time or in space on up to 20 qubits of a superconducting qubit quantum processor. We observe a reduction of error by one to two orders of magnitude below less sophisticated techniques such as postselection. We study how the gain from error mitigation scales with the system size and observe a polynomial suppression of error with increased resources. Extrapolation of our results indicates that substantial hardware improvements will be required for classically intractable variational chemistry simulations.

Tensor completion algorithm-aided structural color design.

In recent years, structural color has developed rapidly due to its distinct advantages, such as low loss, high spatial resolution and environmental friendliness. Various inverse design methods have been extensively investigated to efficiently design optical structures. However, the optimization method for the inverse design of structural color remains a formidable challenge. Traditional optimization approaches, such as genetic algorithms require time-consuming repetitions of structural simulations. Deep learning-assisted design necessitates prior simulations and large amounts of data, making it less efficient for systems with a small number of features. This study proposes a tensor completion algorithm capable of swiftly and accurately predicting missing datasets based on partially obtained datasets to assist in structural color design. Transforming the complex physical problem of structural color design into a spatial structure relationship problem linking geometric parameters and spectral data. The method utilizes tensor multilinear data analysis to effectively capture the complex relationships associated with geometric parameters and spectral data in higher-order data. Numerical and experimental results demonstrate that the algorithm exhibits high reliability in terms of speed and accuracy for diverse structures, datasets of varying sizes, and different materials, significantly enhancing design efficiency. The proposed algorithm offers a viable solution for inverse design problems involving complex physical systems, thereby introducing a novel approach to the design of photonic devices. Additionally, numerical experiments illustrate that the structural color of cruciform resonators with diamond can overcome the high loss issues observed in traditional dielectric materials within the blue wavelength region and enhance the corrosion resistance of the structure. We achieve a wide color gamut and a high-narrow reflection spectrum nearing 1 by this structure, and the theoretical analysis further verifies that diamond holds great promise in the realm of optics.

Enhancing accuracy of physically informed neural networks for nonlinear Schrödinger equations through multi-view transfer learning

In recent years, significant research efforts have been dedicated to developing solutions for nonlinear partial differential equations (PDEs) with applications in physics. Among these equations, the NonLinear Schrödinger (NLS) equation plays a pivotal role in modern nonlinear science, governing the behavior of optical solitons and serving as a crucial model. However, the practical application of these elegant PDE models is hindered by the challenge of high dimensionality and computational cost. To address these challenges, we introduce a novel approach to enhance the training accuracy of physically informed neural networks (PINNs) for the NLS equation. Leveraging the concept of multi-view transfer learning, we utilize a pre-trained NLS model that considers different initial–boundary conditions as multiple views, enabling exploration of their contributions to the overall understanding and solution of the NLS equation. Additionally, we investigate the influence of different loss functions on PINN training results and find that employing the Huber Loss function yields superior fitting outcomes compared to traditional PINNs that use mean squared error (MSE) loss. We demonstrate significant improvements in precision and accuracy over traditional PINNs. Extensive experiments validate the effectiveness of our proposed optimization techniques. This work paves a novel way for solving complex physical systems using data-driven approaches.

Geophysical Constraints to Reconstructing the Geometry of a Shallow Groundwater Body in Caronia (Sicily)

The characterization of a groundwater body involves the construction of a conceptual model that constitutes the base knowledge for monitoring programs, hydrogeological risk assessment, and correct management of water resources. In particular, a detailed geological and geophysical approach was applied to define the alluvial Caronia Groundwater Body (CGWB) and to reconstruct a hydrogeological flow model. The analysis of the CGWB, located in north-eastern Sicily, was initially approached through a reanalysis of previous stratigraphic (boreholes) and geophysical (vertical electrical soundings and seismic refraction profiles) data, subsequently integrated by new seismic acquisitions, such as Multichannel Analysis of Surface Waves (MASW) and horizontal-to-vertical seismic ratio (HVSR). The analysis and reinterpretation of geoelectrical data allowed the construction of a preliminary 3D resistivity model. This initial modeling was subsequently integrated by a geophysical data campaign in order to define the depth of the bottom of the shallow CGWB and the thickness of alluvial deposits. Finally, a preliminary mathematical model flow was generated in order to reconstruct the dynamics of underground water. The results show that integration of multidisciplinary data represent an indispensable tool for the characterization of complex physical systems.

Photonic molecule based on coupled ring quantum cascade lasers

Photonic molecules—particular systems composed of coupled optical resonators—emulate the behavior of complex physical systems exhibiting discrete energy levels. In this work, we present a photonic molecule composed of two strongly coupled, mid-infrared ring quantum cascade lasers. We explore both experimentally and numerically the key features of the photonic molecule such as the energy level splitting of bonding and antibonding supermodes. Due to the large size of the resonators, the energy splitting results in bands containing tens of modes. Each of these modes is furthermore doubly degenerate with respect to the direction of propagation, namely, clockwise and counterclockwise. We explore several methods to carefully break these symmetries of the system in a controlled manner by introducing spatial and temporal asymmetries in the pumping scheme of the ring lasers. By employing these techniques, we achieve a high degree of precision in the dynamic control of the photonic molecule. Owing to their inherent suitability for on-chip integration, this class of devices may enable applications as varied as mid-infrared sensors or a rich playground for studying non-Hermitian photonics and quantum optics with quantum cascade lasers.

PhySR: Physics-informed deep super-resolution for spatiotemporal data

High-fidelity simulation of complex physical systems is exorbitantly expensive and inaccessible across spatiotemporal scales. Recently, there has been an increasing interest in leveraging deep learning to augment scientific data based on the coarse-grained simulations, which is of cheap computational expense and retains satisfactory solution accuracy. However, the major existing work focuses on data-driven approaches which rely on rich training datasets and lack sufficient physical constraints. To this end, we propose a novel and efficient spatiotemporal super-resolution framework via physics-informed learning (i.e., PhySR), inspired by the independence between temporal and spatial derivatives in partial differential equations (PDEs). The general principle is to leverage the temporal interpolation for flow estimation, and then introduce convolutional-recurrent neural networks for learning temporal refinement. Furthermore, we employ the stacked residual blocks with wide activation and sub-pixel layers with pixelshuffle for spatial reconstruction, where feature extraction is conducted in a low-resolution latent space. Moreover, we consider hard imposition of boundary conditions in the network to improve reconstruction accuracy. Results demonstrate the superior effectiveness and efficiency of the proposed method, which outperforms existing baseline algorithms, based on extensive numerical experiments.

On the Solitary Waves and Nonlinear Oscillations to the Fractional Schrödinger–KdV Equation in the Framework of the Caputo Operator

The fractional Schrödinger–Korteweg-de Vries (S-KdV) equation is an important mathematical model that incorporates the nonlinear dynamics of the KdV equation with the quantum mechanical effects described by the Schrödinger equation. Motivated by the several applications of the mentioned evolution equation, in this investigation, the Laplace residual power series method (LRPSM) is employed to analyze the fractional S-KdV equation in the framework of the Caputo operator. By incorporating both the Caputo operator and fractional derivatives into the mentioned evolution equation, we can account for memory effects and non-local behavior. The LRPSM is a powerful analytical technique for the solution of fractional differential equations and therefore it is adapted in our current study. In this study, we prove that the combination of the residual power series expansion with the Laplace transform yields precise and efficient solutions. Moreover, we investigate the behavior and properties of the (un)symmetric solutions to the fractional S-KdV equation using extensive numerical simulations and by considering various fractional orders and initial fractional values. The results contribute to the greater comprehension of the interplay between quantum mechanics and nonlinear dynamics in fractional systems and shed light on wave phenomena and symmetry soliton solutions in such equations. In addition, the proposed method successfully solves fractional differential equations with the Caputo operator, providing a valuable computational instrument for the analysis of complex physical systems. Moreover, the obtained results can describe many of the mysteries associated with the mechanism of nonlinear wave propagation in plasma physics.

A Digital Twin Based Residual Stress Prediction Method for Turbine Blades

The investment casting process is the conventional method for manufacturing turbine blades, and the residual stress generated through this process is widely regarded as a critical factor that markedly impacts the quality and serviceability of turbine blades. However, real-time measurement of residual stress is extremely complex and expensive, especially for single-crystal turbine blades. Current experimental measurement techniques such as X-ray or neutron diffraction can only measure residual stresses at specific points or within a very small area. Studies on residual stress of turbine blades are mainly performed by finite element (FE) simulation, but the accuracy is difficult to guarantee due to the inability to establish accurate mathematical models for complex physical systems. To address this issue, this paper proposes utilizing a digital twin (DT) model to predict residual stresses in turbine blades. By combining real-time sensor and FE simulation data, the DT model is able to update and correct the mathematical models, resulting in more accurate predictions compared to traditional FE simulations.

Symmetry analysis, closed-form invariant solutions and dynamical wave structures of the Benney-Luke equation using optimal system of Lie subalgebras

Nonlinear evolution equations (NLE-Es) arise in a variety of domains, including fluid dynamics, biological sciences, the study of solid states, optical fibres, coastal engineering, ocean physics, and nonlinear complex physical systems. This work examines the Lie symmetry study of the Benney-Luke (B-L) equation relying on two nonzero real parameters. The Lie infinitesimal generators, the one-dimensional optimal system, and the geometric vector fields are all obtained using the Lie symmetry technique. To start, we find close-form invariant solutions by employing symmetry reduction of Lie subalgebras. In some reduction cases, we transform the B-L equation into a variety of non-linear ordinary differential equations (NL-ODEs), which have the benefit of providing a significant number of closed-form solitary wave solutions. The traveling wave solutions contain special functional parameter solutions, trigonometric function solutions, rational function solutions, and hyperbolic trigonometric function solutions. The dynamical profile of closed-form wave solutions exhibits periodic solitons, dark peakon solitons, bright solitons, and bright solitons (bell shape) which we reveal in our study for the first time. By using Noether’s method, we also determine the conservation laws. Finally, three-dimensional diagrams are used to reveal the dynamical investigation of some known solutions.

Bayesian Model Calibration Using High-Fidelity Simulations of a Mach 8 Scramjet Isolator and Combustor

ABSTRACT The development of complex physical systems, such as scramjets, requires comprehensive assessments of the relevant performance envelopes. Because high-fidelity simulations and experiments are generally too expensive to perform over a wide range of operating conditions, reduced models can be especially useful for exploring the design space. However, these models often involve empirical parameters which must be calibrated using high-fidelity data sets. The present work develops a calibration procedure for a one-dimensional model of the wall pressure in a scramjet flowpath. Using wall pressure measurements from three-dimensional simulations, the six model parameters are tuned using a Bayesian methodology. The results show that the tuned model is largely able to capture the mean wall pressure in both the isolator and combustor. The calibration procedure is able to converge for both uniform and Gaussian priors, provided that the Gaussian priors are sufficiently wide. Physically-consistent correlations between parameters are obtained, which could inform further reductions in the model’s dimensionality. Application of the model to additional flow conditions shows good agreement to simulations not used in the calibration procedure.

On the application of neural networks for service life prediction of steel fibre-reinforced concrete

While physics-based modelling entails the capability to describe the mechanisms and physics of a system across multiple scales, these models often are decoupled from external measurements available for specific systems of interest. On the other hand, data analysis methods allow the decoding of information on particular systems, yet such mathematical analyses struggle with context of the domain physics under study. Although it is common to have both methods positioned as antagonizing, the real challenge is to combine them, capitalizing on their strength and information. Proper integration between physics-based models and data-driven inference will enable understanding, optimising, and predicting complex physical systems around us. This study exemplifies the application of machine learning to predict corrosion in fibre-reinforced concrete. Focus is placed on current limitations concerning the application of machine learning to predict the underlying mechanisms for fibre corrosion and opportunities to integrate physics-based modelling and data-driven interference truly. Results indicate that it is possible to train neural networks with high accuracy through training examples (>99% classification accuracy), while a loss in the ability to generalize patterns and thus predict the degree of fibre corrosion is observed for samples beyond the training set (<60% classification accuracy). The absence of the ability to generalize is mainly caused by the loss of physics, such as material history dependency, physical invariance, and conservation laws, which are not naturally resolved in the current machine learning models.

Numerical Analysis of Nonlinear Fractional System of Jaulent–Miodek Equation

This paper presents the optimal auxiliary function method (OAFM) implementation to solve a nonlinear fractional system of the Jaulent–Miodek Equation with the Caputo operator. The OAFM is a vital method for solving different kinds of nonlinear equations. In this paper, the OAFM is applied to the fractional nonlinear system of the Jaulent–Miodek Equation, which describes the behavior of a physical system via a set of coupled nonlinear equations. The Caputo operator represents the fractional derivative in the equations, improving the system’s accuracy and applicability to the real world. This study demonstrates the effectiveness and efficiency of the OAFM in solving the fractional nonlinear system of the Jaulent–Miedek equation with the Caputo operator. This study’s findings provide important insights into the behavior of complex physical systems and may have practical applications in fields such as engineering, physics, and mathematics.

Robust Metric Hybrid Planning in Stochastic Nonlinear Domains Using Mathematical Optimization

The deployment of automated planning in safety critical systems has resulted in the need for the development of robust automated planners that can (i) accurately model complex systems under uncertainty, and (ii) provide formal guarantees on the model they act on. In this paper, we introduce a robust automated planner that can represent such stochastic systems with metric specifications and constrained continuous-time nonlinear dynamics over mixed (i.e., real and discrete valued) concurrent action spaces. The planner uses inverse transform sampling to model uncertainty, and has the capability of performing bi-objective optimization to first enforce the constraints of the problem as best as possible, and second optimize the metric of interest. Theoretically, we show that the planner terminates in finite time and provides formal guarantees on its solution. Experimentally, we demonstrate the capability of the planner to robustly control four complex physical systems under uncertainty.

Neural extended Kalman filters for learning and predicting dynamics of structural systems

Accurate structural response prediction forms a main driver for structural health monitoring and control applications. This often requires the proposed model to adequately capture the underlying dynamics of complex structural systems. In this work, we utilize a learnable extended Kalman filter (EKF), named the neural extended Kalman filter (neural EKF) throughout this article, for learning the latent evolution dynamics of complex physical systems. The neural EKF is a generalized version of the conventional EKF, where the modeling of process dynamics and sensory observations can be parameterized by neural networks, therefore learned by end-to-end training. The method is implemented under the variational inference framework with the EKF conducting inference from sensing measurements. Typically, conventional variational inference models are parameterized by neural networks independent of the latent dynamics models. This characteristic makes the inference and reconstruction accuracy weakly based on the dynamics models and renders the associated training inadequate. In this work, we show that the structure imposed by the Neural EKF is beneficial to the learning process. We demonstrate the efficacy of the framework on both simulated and real-world structural monitoring datasets, with the results indicating significant predictive capabilities of the proposed scheme.