Non-intrusive surrogate modeling for parametrized time-dependent partial differential equations using convolutional autoencoders

Quasi-static and dynamic response of functionally graded viscoelastic plates

On stability and convergence of semi-Lagrangian methods for the first-order time-dependent nonlinear partial differential equations in 1D

This paper presents a research methodology for identifying the Pratt & Whitney Canada PW127G turboprop engine from simulation data using optimized feedforward neural networks (FNN). A set of measurable variables - ground speed, throttle lever angle, pressure altitude ​, high-pressure spool speed , and propeller speed ​ - is used to predict normalized engine torque, providing a surrogate engine model suitable for integration into flight simulators. The methodology follows a two-stage strategy. First, a baseline L-BFGS–trained FNN is combined with two architecture-search methods, Extended Great Deluge (EGD) and Bayesian Optimization (BO). On the turboprop dataset, BO achieves a lower test RMSE than EGD and is therefore selected as the preferred architecture optimization strategy. Second, BO is fixed and used to optimize two FNN configurations: Baseline FNN with inputs (ground speed, throttle lever angle, pressure altitude , propeller speed ​) and Core-Enhanced FNN additionally including high-pressure spool speed . The optimized Core-Enhanced FNN significantly reduces the root mean square error from 1.066 to 0.4834 on testing data, corresponding to an average error reduction of about 55% compared with Baseline FNN, and also decreases mean relative error and error variance, confirming the importance of core-speed information for high-fidelity torque prediction. The results demonstrate that L-BFGS–trained FNNs, combined with BO-based architecture search and simulation-derived data, provide an effective and computationally efficient surrogate engine model for turboprop torque (and indirectly thrust) estimation in advanced flight simulation and training applications.

High dimensional covariance matrices have attracted much attention of statisticians and econometricians during the past decades. Vast literature is devoted to the research in high dimensional covariance matrices. However, most of them are for constant covariance matrices. In many applications, constant covariance matrices are not appropriate, e.g. in portfolio allocation, dynamic covariance matrices would make much more sense. Simply assuming each entry of a covariance matrix is a function of time to introduce a dynamic structure would not work. In this paper, we are going to introduce a class of high dimensional dynamic covariance matrices in which a kind of additive structure is embedded. We will show the proposed high dimensional dynamic covariance matrices have many advantages in applications. An estimation procedure is also proposed to estimate the proposed high dimensional dynamic covariance matrices. Asymptotic properties are built to justify the proposed estimation procedure. Intensive simulation studies show the proposed estimation procedure works very well when sample size is finite. Finally, we apply the proposed high dimensional dynamic covariance matrices, together with the proposed estimation procedure, to portfolio allocation. The results look very interesting.

With recent advances in autonomous navigation technology, the importance of ship maneuvering models that can predict maneuvering motions with high accuracy and interpretability has increased. This study proposes a hybrid maneuvering model for predicting ship motions using the Maneuvering Modeling Group (MMG) model and the Feedforward Neural Network (FNN). In the proposed model, the modular structure of the MMG model is enhanced through the addition of a complementary FNN module. This approach improves the prediction accuracy while maintaining the interpretability of the model. Furthermore, to prevent the FNN output from depending too heavily on its training data, an output constraint and a mechanism for detecting Out-of-Distribution (OOD) based on k-Nearest Neighbors (kNN) distance are introduced. Numerical verification using multiple maneuvering test datasets demonstrates that the proposed model consistently exhibits higher prediction accuracy than both the MMG-only and the FNN-only models. Specifically, it attains an average reduction of 30–40% in Root-Mean-Squared Error (RMSE) compared to the MMG-only model. In particular, under highly nonlinear maneuvering conditions, such as Turning test and Random maneuver, the model shows up to a 70% RMSE reduction. Additionally, the model exhibits low accuracy degradation over long-term predictions, ensuring stable motion predictions. Based on these results, the proposed hybrid model successfully integrates the characteristics of physical models and data-driven models, providing a practical maneuvering model that offers high accuracy, lower data dependency, and interpretability. This model offers a valuable foundation for applications in autonomous navigation support systems.

Wave episode based Gaussian process regression for extreme event statistics in ship dynamics: Between the Scylla of Karhunen–Loève convergence and the Charybdis of transient features

Capturing stochastic variabilities in pedestrian flows: A dynamic continuum modeling approach

Summary In the field of subsurface flow simulation, deep-learning-based surrogate modeling is shown as a promising approach to significantly reduce the computational cost associated with full-physics reservoir simulations. However, the successful construction of highly accurate deep-learning-based models often requires a large number of training simulations, which can be very time-consuming to generate by itself for large-scale systems. The incorporation of physics constraints during the training process was shown to be an effective approach to reduce the training cost and to improve model accuracy. However, it remains challenging to reimplement the physics constraints correctly for modeling training when it comes to reservoir models with complex physics or gridding methods. In this study, we propose a physics-constrained surrogate (PCS) model training approach for production optimization that integrates multifidelity training data, together with a new way of implementing the physics constraints that leverages an existing mature reservoir simulator. The proposed approach starts with model pretraining on a relatively large number of low-cost, low-fidelity training data, followed by model fine-tuning with a smaller number of high-fidelity training samples and the inclusion of physics constraints. The physics constraints are implemented by adding the residuals of discretized governing equations into the loss function. Training with multifidelity data and incorporating physics constraints allows for reduced reliance on high-fidelity data while enhancing physical consistency. Systematic comparison studies were performed for both 2D and 3D cases, and it was shown that the proposed approach can reduce the computational costs associated with training data generation by about 80%, while achieving a similar level of prediction accuracy of the surrogate model. In addition, under a small number of training simulations (i.e., 50 equivalent high-fidelity runs), our proposed PCS model with multifidelity data can reduce the prediction error by 90%, in comparison with the model trained with only high-fidelity data. Finally, the trained surrogate model was applied to a well-control optimization problem. In comparison with the use of full-order simulations, the total computational time can be reduced by 97.7%.

Associative memory has been a prominent candidate for the computation performed by the massively recurrent neocortical networks. Attractor networks implementing associative memory have offered mechanistic explanation for many cognitive phenomena. However, attractor memory models are typically trained using orthogonal or random patterns to avoid interference between memories, which makes them unfeasible for naturally occurring complex correlated stimuli like images. We approach this problem by combining a recurrent attractor network with a feedforward network that learns distributed representations using an unsupervised Hebbian-Bayesian learning rule. The resulting network model incorporates many known biological properties: unsupervised learning, Hebbian plasticity, sparse distributed activations, sparse connectivity, columnar and laminar cortical architecture, etc. We evaluate the synergistic effects of the feedforward and recurrent network components in complex pattern recognition tasks on the MNIST handwritten digits dataset. We demonstrate that the recurrent attractor component implements associative memory when trained on the feedforward-driven internal (hidden) representations. The associative memory is also shown to perform prototype extraction from the training data and make the representations robust to severely distorted input. We argue that several aspects of the proposed integration of feedforward and recurrent computations are particularly attractive from a machine learning perspective.

By using a non-linear 3-D elastic waves real-time expert system, the new theory of “ Non-linear Real-Time Expert Seismology ” is investigated, for the exploration of the on-shore and off-shore petroleum and gas reserves all over the world. Such a highly innovative and groundbreaking technology is working under Real Time Logic for searching the on-shore and off-shore hydrocarbon reserves developed on the continental crust and in deeper water ranging from 300 to 3000 m, or even deeper. Consequently, this real-time expert system, will be the best device for the exploration of the continental margin areas (shelf, slope and rise) and the very deep waters, as well. The proposed modern technology can be used at any depth of seas and oceans all over the world and for any depth in the subsurface of existing oil reserves. Beyond the above, the various mechanical properties of rock regulating the wave propagation phenomenon appear as spatially varying coefficients in a system of time-dependent hyperbolic partial differential equations. The propagation of the seismic waves through the earth subsurface is described by the wave equation, which is then reduced to a Helmholz differential equation. Furthermore, the Helmholtz differential equation is numerically evaluated by using the Singular Integral Operators Method (S.I.O.M.). Several properties are further analyzed and investigated for the wave equation. Finally, an application is proposed for the determination of the seismic field radiated from a pulsating sphere into an infinite homogeneous medium. Thus, by using the S.I.O.M., then the acoustic pressure radiated from the above pulsating sphere is determined. Key word s : Non-linear real-time expert seismology; Singular integral operators method (S.I.O.M.); Time-dependent hyperbolic partial differential equations; Oil and gas reserves; Petroleum reservoir engineering; Helmholtz differential equation; Real-time expert system; Wave equation

In this manuscript, we investigate the approximate controllability for time-dependent impulsive neutral stochastic partial differential equations with fractional Brownian motion and memory in Hilbert space. By using semigroup theory, stochastic analysis techniques and fixed point approach, we derive a new set of sufficient conditions for the approximate controllability of nonlinear stochastic system under the assumption that the corresponding linear system is approximately controllable. Finally, an example is provided to illustrate our results.

The global increase in greenhouse gas emissions from automobiles has brought about the manufacture and usage of large quantities of electric vehicles (EVs). However, to ensure proper integration of EVs into the grid, there is a need to forecast the charging demand of EVs accurately. This paper presents a short-term electric vehicle charging demand forecast using a feedforward artificial neural network optimized with a modified local leader phase spider monkey optimization (MLLP-SMO) algorithm, a proposed variant of spider monkey optimization. A proportionate fitness selection is employed to improve the update process of the local leader phase of the spider monkey optimization. The proposed algorithm trains a feedforward neural network to forecast electric vehicle charging demand. The effectiveness of the proposed forecasting model was tested and validated with electric vehicle public charging data from the United Kingdom Power Networks Low Carbon London Project. The model's performance was compared to a feedforward neural network trained with particle swarm optimization, genetic algorithm, classical spider monkey optimization, and two conventional forecasting models, multi-linear regression and Monte Carlo simulation. The performance of the proposed forecasting model was assessed using the mean absolute percentage error of forecast and forecasting accuracy. The model produced a forecast accuracy and mean absolute percentage error of 99.88% and 3.384%, respectively. The results show that MLLP-SMO as a trainer predicted better than the other forecasting models and met industry standard forecast accuracy.

Dynamic simulation of reversible solid-fluid reactions in nonisothermal porous spheres with Stefan-Maxwell diffusion

The controlled Cholesky factorization (CCF) has been shown to be a robust preconditioner for the conjugate gradient (CG) method. In this scheme the amount of fill-in is defined in terms of a parameter $\eta$, the number of extra nonzero elements allowed per column. This parameter $\eta$ can be chosen in such a way that the preconditioning factor will require more or less storage than the coefficient matrix. The selection of nonzero elements kept for the preconditioner is made by value instead of by position, so the sparsity pattern of the original matrix is never considered by the proposed factorization. This preconditioned method is termed the CCCG($\eta$) method and is a generalization of a method developed by Jones and Plassmann [\textit{ACM Trans.\ Math.\ Software}, 21 (1995), pp.\ 5--17]. It is demonstrated how an optimum value of $\eta$ can be automatically determined when solving systems with multiple right-hand sides. Typically such systems occur when using time-stepping procedures. Numerical examples are presented for some time-dependent parabolic partial differential equations discretized using linear triangular finite elements on unstructured grids. Comparisons made between CCCG($\eta$), standard ICCG, and the Jones and Plassmann method show CCCG($\eta$) to be an efficient solver.

In present days, real time navigation depends on Kalman filter to fuse data from Global Positioning System (GPS) and Inertial Navigation System (INS). But there exist drawbacks like long design time, requirement of prior knowledge in fusing data from GPS and INS using Kalman Filter. In order to overcome the drawbacks of Kalman filter, GPS and INS integration are done using Artificial Neural Networks (ANN) like FFNNs. But still there exists certain drawbacks like less accuracy in FFNNs for GPS and INS data integration. Therefore, this paper introduces Higher Order Neural Networks (HONNs) approach for INS and GPS data integration to overcome the drawback. A higher order feed forward neural network architecture with optimum number of nodes is used. In the given architectures, the replacement of summation at each node by multiplication results in more powerful mapping, because of its capability of processing higher-order information from training data. Performance comparison of HONNs with FFNNs shows that the proposed architecture provides satisfactory results in terms of error rate and number of epochs. The HONNs like Multiplicative Neural Network (MNN) module and Sigma-Pi-ANN module and Traditional Feed Forward Neural Networks(FFNNs) like Radial Basis Function Neural Network (RBF) module and Back propagation Neural Network (BPN) module are trained to predict the INS position error and provide accurate position of the moving aircrafts. Sigma-Pi ANN is found to be the best in terms of accuracy, number of epochs and execution time among the two HONNs.