A combined Physics-informed neural network and particle filter approach to solve a state estimation problem during the heating of a nanofluid

Development of integrated approaches for hydrological data assimilation through combination of ensemble Kalman filter and particle filter methods

Combined neural network and particle filter state estimation with application to a run-of-mine ore mill

A metalearning approach for Physics-Informed Neural Networks (PINNs): Application to parameterized PDEs

Physics-informed neural networks (PINNs) as a means of discretizing partial differential equations (PDEs) are garnering much attention in the Computational Science and Engineering (CS&E) world. At least two challenges exist for PINNs at present: an understanding of accuracy and convergence characteristics with respect to tunable parameters and identification of optimization strategies that make PINNs as efficient as other computational science tools. The cost of PINNs training remains a major challenge of Physics-informed Machine Learning (PiML) - and, in fact, machine learning (ML) in general. This paper is meant to move towards addressing the latter through the study of PINNs on new tasks, for which parameterized PDEs provides a good testbed application as tasks can be easily defined in this context. Following the ML world, we introduce metalearning of PINNs with application to parameterized PDEs. By introducing metalearning and transfer learning concepts, we can greatly accelerate the PINNs optimization process. We present a survey of model-agnostic metalearning, and then discuss our model-aware metalearning applied to PINNs as well as implementation considerations and algorithmic complexity. We then test our approach on various canonical forward parameterized PDEs that have been presented in the emerging PINNs literature.

At present, tremendous evidences indicate reduced credit risk measurement models are comparatively accurate. However, this kind of model is complex. Thereby, it is often difficult to estimate parameters of it. To solve this problem, this paper uses adaptive estimation algorithm based on the combination of particle filter and simultaneous perturbation stochastic approximation to estimate parameters of the reduced credit risk measurement model. Moreover, this paper compares particle filter approach with Markov-chain Monte Carlo (MCMC). The estimation accuracy of the two approaches is basically identical. However, the calculation speed of particle filter is quicker than MCMC. Finally, authors do empirical analysis with American personal housing mortgage loan data.

Physics-informed neural networks involving unsteady friction for transient pipe flow.

In this study, we utilize the emerging physics-informed neural networks (PINNs) approach for the first time to predict the flowfield of a compressor cascade. Different from conventional training methods, a new adaptive learning strategy that mitigates gradient imbalance through incorporating adaptive weights in conjunction with a dynamically adjusting learning rate is used during the training process to improve the convergence of PINNs. The performance of PINNs is assessed here by solving both the forward and inverse problems. In the forward problem, by encapsulating the physical relations among relevant variables, PINNs demonstrate their effectiveness in accurately forecasting the compressor’s flowfield. PINNs also show obvious advantages over the traditional computational fluid dynamics (CFD) approaches, particularly in scenarios lacking complete boundary conditions, as is often the case in inverse engineering problems. PINNs successfully reconstruct the flowfield of the compressor cascade solely based on partial velocity vectors and near-wall pressure information. Furthermore, PINNs show robust performance in the environment of various levels of aleatory uncertainties stemming from labeled data. This research provides evidence that PINNs can offer turbomachinery designers an additional and promising option alongside the current dominant CFD methods.

Solving large-scale variational inequalities with dynamically adjusting initial condition in physics-informed neural networks

Flow reconstruction based on limited measurement data, which can be considered as a state estimation problem, constitutes a fundamental task within the realm of fluid mechanics. In recent years, the physics-informed neural networks (PINNs) have been proposed to achieve flow field reconstruction by integrating the measurements with governing equations during network training. However, the performance is compromised by the presence of high-level data noise, and the uncertainty of the reconstructed flow fields remains unattainable. In this paper, we first perform a systematic study to investigate the impact of data noise on the reconstruction result of PINNs. Subsequently, we present strategies of early stopping and loss regularization, which can suppress the overfitting issue to some extent. Ensemble learning is also employed to quantify the uncertainty of the results from vanilla PINNs. In addition, we propose to use a Bayesian framework of PINNs (BPINNs) for flow field reconstruction, which incorporates the Bayesian neural network with PINNs. It is demonstrated that BPINNs are capable of reconstructing the velocity and pressure fields from sparse and noisy velocity measurements, while providing comprehensive uncertainty quantification of the flow fields simultaneously. Compared to the vanilla PINNs, BPINNs are more accurate and robust when there is a high level of data noise. We conduct experiments on two-dimensional cavity flow and the flow past a cylinder to validate the effectiveness of the proposed methods throughout the paper.

Physics-informed neural networks for understanding shear migration of particles in viscous flow

The FitzHugh–Nagumo (FHN) equation in one dimension is solved in this paper using an improved physics-informed neural network (PINN) approach. Examining test problems with known analytical solutions and the explicit finite difference method (EFDM) allowed for the demonstration of the PINN’s effectiveness. Our study presents an improved PINN formulation tailored to the FitzHugh–Nagumo reaction–diffusion system. The proposed framework is efficiently designed, validated, and systematically optimized, demonstrating that a careful balance among model complexity, collocation density, and training strategy enables high accuracy within limited computational time. Despite the very strong agreement that both methods provide, we have demonstrated that the PINN results exhibit a closer agreement with the analytical solutions for Test Problem 1, whereas the EFDM yielded more accurate results for Test Problem 2. This study is crucial for evaluating the PINN’s performance in solving the FHN equation and its application to nonlinear processes like pulse propagation in optical fibers, drug delivery, neural behavior, geophysical fluid dynamics, and long-wave propagation in oceans, highlighting the potential of PINNs for complex systems. Numerical models for this class of nonlinear partial differential equations (PDEs) may be developed by existing and future model creators of a wide range of various nonlinear physical processes in the physical and engineering sectors using the concepts of the solution methods employed in this study.

In order to perform autonomous manipulation in underwater missions, a robust object localization technique is crucial. This paper proposes a monocular vision based pose estimation algorithm that is intended to be a part of a supervisory manipulation system for underwater intervention missions such as DIFIS. The proposed technique incorporates a deterministic scheme into a particle filter framework in solving simultaneously the marker correspondence and pose estimation problem. Preliminary simulation results have shown that the deterministic particle filter outperforms the standard particle filter in pose estimation even in the presence of minimal noise and occlusion. However, the accuracy and speed offered by the algorithm are still insufficient for close range intervention tasks. Improvements and further testing are required before the algorithm could be used on an I-AUV.

This paper discusses a sparse data driven approach for training Physics Informed Neural Networks (PINNs) to solve the Navier-Stokes equation. A benchmark problem of 2D unsteady laminar flow past a cylinder is chosen for comparing the accuracy of existing PINN training approaches to the proposed methodology. The proposed training scheme is an improvement on the existing Backward Compatible PINN (BC-PINN) methodology. We have demonstrated that the performance of BC-PINN methodology in solving Navier Stokes equation is at a similar level to that of Standard PINN methodology using mini-batches. The proposed methodology resulted in a significant increase in accuracy in comparison with vanilla BC-PINN. Furthermore, transfer learning of parameters of a pre-trained model for different Reynolds numbers has resulted in a reduction of training time.

1-D coupled surface flow and transport equations revisited via the physics-informed neural network approach

Water temperature plays an important role in our environment and is applicable to nearly all limnology research, as the temperature of a body of water affects biological activity and growth of organisms such as algae and bacteria. Certain organisms have a preferred temperature range within which they can survive, while others become dormant or die when the water reaches extreme temperatures. The temperature of water also governs the maximum dissolved oxygen concentration of water. Dissolved oxygen in water is important for aquatic life because of its vital role in cellular respiration. Predicting water temperature is also an important factor in determining whether a body of water is acceptable for human use. Warm bodies of water may contain pathogens that can be dangerous to humans.
 
 Our research presents a computational method of determining lake water temperature through a novel technique known as physics-informed neural networks (PINNs). PINNs can be used to model and forecast the temperature of water over a specific time period by training a neural network using the data points derived from the discrete form of a partial differential equation and taking into account the boundary conditions. Several factors such as wind, precipitation, and solar energy effects on water temperature were investigated. By using a computer simulation in place of an analytical mathematical model, a tremendous increase in run time speed can be achieved. The results can be used to determine the patterns in water temperature throughout a year, demonstrating the advantages of a PINN over an analytical model.