Self-induced stochastic resonance: A physics-informed machine learning approach

Stochastic coherence (SC) and self-induced stochastic resonance (SISR) are two distinct mechanisms of noise-induced coherent motion. For interacting SC and SISR oscillators, we find that whether or not phase synchronization is achieved depends sensitively on the coupling strength and noise intensities. Specifically, in the case of weak coupling, individual oscillators are insensitive to each other, whereas in the case of strong coupling, one fixed oscillator with optimal coherence can be entrained to the other, adjustable oscillator (i.e., its noise intensity is tunable), achieving phase-locking synchronization, as long as the tunable noise intensity is not beyond a threshold; such synchronization is lost otherwise. For an array lattice of SISR oscillators, except for coupling-enhanced coherence similar to that found in the case of coupled SC oscillators, there is an optimal network topology degree (i.e., number of coupled nodes), such that coherence and synchronization are optimally achieved, implying that the system-size resonance found in an ensemble of noise-driven bistable systems can occur in coupled SISR oscillators.

Microstructure-sensitive materials design has become popular among materials engineering researchers in the last decade because it allows the control of material performance through the design of microstructures. In this study, the microstructure is defined by an orientation distribution function. A physics-informed machine learning approach is integrated into microstructure design to improve the accuracy, computational efficiency, and explainability of microstructure-sensitive design. When data generation is costly and numerical models need to follow certain physical laws, machine learning models that are domain-aware perform more efficiently than conventional machine learning models. Therefore, a new paradigm called the physics-informed neural network (PINN) is introduced in the literature. This study applies the PINN to microstructure-sensitive modeling and inverse design to explore the material behavior under deformation processing. In particular, we demonstrate the application of PINN to small-data problems driven by a crystal plasticity model that needs to satisfy the physics-based design constraints of the microstructural orientation space. For the first problem, we predict the microstructural texture evolution of copper during a tensile deformation process as a function of initial texturing and strain rate. The second problem aims to calibrate the crystal plasticity parameters of the Ti-7Al alloy by solving an inverse design problem to match the PINN-predicted final texture prediction and the experimental data.

We characterize and remedy a failure mode that may arise from multi-scale dynamics with scale imbalances during training of deep neural networks, such as physics informed neural networks (PINNs). PINNs are popular machine-learning templates that allow for seamless integration of physical equation models with data. Their training amounts to solving an optimization problem over a weighted sum of data-fidelity and equation-fidelity objectives. Conflicts between objectives can arise from scale imbalances, heteroscedasticity in the data, stiffness of the physical equation, or from catastrophic interference during sequential training. We explain the training pathology arising from this and propose a simple yet effective inverse Dirichlet weighting strategy to alleviate the issue. We compare with Sobolev training of neural networks, providing the baseline of analytically ε-optimal training. We demonstrate the effectiveness of inverse Dirichlet weighting in various applications, including a multi-scale model of active turbulence, where we show orders of magnitude improvement in accuracy and convergence over conventional PINN training. For inverse modeling using sequential training, we find that inverse Dirichlet weighting protects a PINN against catastrophic forgetting.

We explore the data-parallel acceleration of physics-informed machine learning (PIML) schemes, with a focus on physics-informed neural networks (PINNs) for multiple graphics processing units (GPUs) architectures. In order to develop scale-robust and high-throughput PIML models for sophisticated applications which may require a large number of training points (e.g., involving complex and high-dimensional domains, non-linear operators or multi-physics), we detail a novel protocol based on h-analysis and data-parallel acceleration through the Horovod training framework. The protocol is backed by new convergence bounds for the generalization error and the train-test gap. We show that the acceleration is straightforward to implement, does not compromise training, and proves to be highly efficient and controllable, paving the way towards generic scale-robust PIML. Extensive numerical experiments with increasing complexity illustrate its robustness and consistency, offering a wide range of possibilities for real-world simulations.

Nowadays, noise was considered to play a key role in the neural system, which improved the weak signal detection and enhanced the information transmission, as deeply research on stochastic resonance (SR). Traditionally, stochastic resonance was thought to be the result of the interaction between subthreshold signals with noise in nonlinear system. Particularly, the existence of noise was thought to be harmful to the response of system with suprathreshold signal input commonly. Observing the response of FitzHugh-Nagumo (FHN) neuron model to the suprathreshold input, it was improved gradually as the amplitude of input rising from subthreshold to suprathreshold. Signal-to-noise ratio and cross correlation coefficient were defined as performance evaluation functions separately, then the response of FHN neuron model to periodic and aperiodic suprathreshold signal input was studied. At the same time, the threshold characteristic was discussed, and some basic parameters for practical application were provided. The simulation result illustrates the information transmission can be enhanced by the noise even if input signal is suprathreshold in FHN neuron model.

This study presents a comprehensive nowcasting and forecasting approach for ionospheric peak parameters, including foF2, NmF2, and TEC, using a Physics Informed Neural Network (PINN). This approach integrates multiple datasets, utilizing extensive ground-based ionosonde station measurements and COSMIC satellite observations to model and predict these parameters in relation to ionospheric conditions and space weather dynamics.Our work also explores the response of ionospheric peak parameters to extreme solar eruptions and geomagnetic storms, providing critical insights into the behaviour of the ionosphere under these challenging conditions. The PINN incorporates fundamental physical laws as constraints, including the Chapman function, continuity equation, ion production rates as a function of F10.7, recombination reactions, geomagnetic and electric fields, and Abel inversion effects. Our model utilizes a comprehensive set of input features, including COSMIC satellite foF2, NmF2, TEC measurements, temporal and spatial parameters, and various solar and geomagnetic indices. Data normalization and a deep neural network architecture with multiple dense layers and batch normalization were employed to capture complex, non-linear relationships in the ionospheric data. These constraints enable highly accurate predictions  achieving a high average correlation of 0.92 between COSMIC satellite and ionosonde measurements.A detailed random forest parameter importance analysis identified key contributors to ionospheric variability, revealing that atmospheric dynamics (meridional and zonal winds) and solar activity (notably F10.7) play dominant roles. Spatial and temporal factors were also considered critical compared to other space weather parameters.These findings highlight the potential of physics-informed machine learning as a robust tool for advancing our understanding of ionospheric behaviour and improving predictive capabilities for space weather applications. Furthermore, this study underscores the value of integrating ground- and space-based observations with physical principles to achieve accurate and reliable forecasts of ionospheric peak parameters.

Predicting performance of in-situ microbial enhanced oil recovery process and screening of suitable microbe-nutrient combination from limited experimental data using physics informed machine learning approach

Physics-informed machine learning models for ship speed prediction

This study models the temperature evolution during additive friction stir deposition (AFSD) using machine learning. AFSD is a solid-state additive manufacturing technology that deposits metal using plastic flow without melting. However, the ability to predict its performance using the underlying physics is in the early stage. A physics-informed machine learning approach, AFSD-Nets, is presented here to predict temperature profiles based on the combined effects of heat generation and heat transfer. The proposed AFSD-Nets includes a set of customized neural network approximators, which are used to model the coupled temperature evolution for the tool and build during multi-layer material deposition. Experiments are designed and performed using 7075 aluminum feedstock deposited on a substrate of the same material for 30 layers. A comparison of predictions and measurements shows that the proposed AFSD-Nets approach can accurately describe and predict the temperature evolution during the AFSD process.

Based on the FitzHugh-Nagumo (FHN) neuron model subjected to sine-Wiener (SW) noise, impacts of SW noise on weak periodic signal detection are investigated by calculating response measure Q for characterizing synchronization between the input signal and the output temporal activities of the neuron. It is numerically demonstrated that the response measure Q can achieve the optimal value under appropriate and moderate intensity or correlation time of SW noise, suggesting the occurrence of SW-noise-induced stochastic resonance. Furthermore, the optimal value of Q is sensitive to correlation time. Consequently, the correlation time of SW noise has a great influence on the performance of signal detection in the FHN neuron.

Systems influenced by Gaussian white noise, Poisson white noise, and periodic excitation are common in many engineering and scientific applications, making accurate response prediction essential. Poisson noise introduces impulsive jumps, while high-frequency from the periodic excitation adds complexity, highlighting the need for a new approach to address these combined challenges. In this paper, we propose a novel deep learning framework, the radial-basis-function neural network (RBF-NN), specifically designed to resolve high-frequency oscillatory solutions in the transient probability density function (PDF) of systems under combined Gaussian white noise, Poisson white noise, and periodic excitation. This method utilizes a single-layer network with uniformly distributed neurons, where the distribution matches that of the variables, and employs RBFs as activation functions. The physical information of the equationis used as a constraint to solve the corresponding forward Kolmogorov equationthat governs the transient PDF. The presence of Poisson white noise results in the forward Kolmogorov equationbeing an integro-differential equation, making it challenging to solve. In this method, the Gauss-Legendre quadrature is used to efficiently compute the integrals. Additionally, the Monte Carlo (MC) method is employed to solve the normalization constraint, providing approximate solutions through random sampling. Several numerical examples demonstrate the efficacy of the RBF-NN, which significantly outperforms standard Physics-Informed Neural Networks (PINNs) and PINNs with periodic layer (P-PINNs) in both computational efficiency and accuracy, especially in high-frequency scenarios. RBF-NN expands the applicability of PINNs under Gaussian white noise, Poisson white noise, and high-frequency periodic excitation. Furthermore, the influence of neuron spacing and the shape parameter on the performance and accuracy of the RBF-NN method is investigated. The effects of Poisson noise intensity and frequency of periodic excitation on the three models are explored, with clear advantages of the RBF-NN method demonstrated in handling composite stochastic noise with high frequency.

This paper studies the famous Fitzhugh-Nagumo and Izhikevich neuron models in the fractional-order domain. Generalization of the integer models into the fractional-order domain providing a wider scope understanding of the neuron systems. The fractional Fitzhugh-Nagumo circuit model and the state space equations are introduced. Different fractional orders are studied as an example. Numerical solutions of the systems are given using non-standard finite difference scheme together with Grunwald-Letnikov discretization technique which is computationally efficient and accurate. The two models are compared and their behaviors are investigated at different fractional orders.

Summary Since the original algorithm by John Vidale in 1988 to numerically solve the isotropic eikonal equation, there has been tremendous progress on the topic addressing an array of computational challenges, including improvement of the solution accuracy, incorporation of surface topography, the addition of accurate physics by accounting for anisotropy/attenuation in the medium, and speeding up computations. Despite these advances, these algorithms have no mechanism to carry information gained by solving one problem to the next. Moreover, these approaches may breakdown for certain complex forms of the eikonal equation, requiring simplification of the equations to estimate approximate solutions. Therefore, we seek an alternate approach to address these challenges holistically. We propose an algorithm based on the emerging paradigm of physics-informed neural network to solve different forms of the eikonal equation. We show how transfer learning can be used to speed up computations by utilizing information gained from prior solutions. Such an approach makes the implementation of eikonal solvers much simpler and puts us on a much faster path to progress. The method paves the pathway to solving complex forms of the eikonal equation that have remained unsolved using conventional algorithms or solved using some approximation techniques at best.

As critical components of spacecraft systems, electronic equipment requires accurate remaining useful life (RUL) prediction to ensure reliable operations. Traditional physics-based and data-driven methods are limited by poor generalization and substantial data demands, respectively. While Physics-Informed Neural Networks (PINNs) integrate physical laws to enhance accuracy, they remain susceptible to performance degradation under shifting operational conditions due to catastrophic forgetting. This paper proposes a novel online PINN framework integrated with continual learning to dynamically adapt to new degradation patterns. Validated on NASA's IGBT dataset, our method reduces RUL prediction error to 27.2% of a traditional LSTM model and achieves an online update time of less than 800ms/cycle. These results demonstrate a significant improvement in robustness and accuracy, providing a superior solution for RUL estimation of aerospace power electronics under extreme environments.

Using harmonic noise, the frequency effect of noise on the FitzHugh—Nagumo neuron model is investigated. The results show that the neuron has a resonance characteristic and responds strongly to the noise with a certain frequency at fixed power. Driven by the noise with this frequency, the train is most regular and the coefficient of variation R has a minimum. The imperfect synchronization takes place, which, however, is optimal only for noise with an appropriate frequency. It is shown that there exists coherence resonance related to frequency.