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In this paper, we propose a method to solve nonlinear optimal control problems (OCPs) with constrained control input in real-time using neural networks (NNs). We introduce what we have termed co-state Neural Network (CoNN) that learns the…

In this article, our goal is to solve two-parameter singular perturbation problems (SPPs) in one- and two-dimensions using an adapted Physics-Informed Neural Networks (PINNs) approach. Such problems are of major importance in engineering…

Physics-informed neural networks (PINNs) have been demonstrated to be efficient in solving partial differential equations (PDEs) from a variety of experimental perspectives. Some recent studies have also proposed PINN algorithms for PDEs on…

Standard Physics-Informed Neural Networks (PINNs) often face challenges when modeling parameterized dynamical systems with sharp regime transitions, such as bifurcations. In these scenarios, the continuous mapping from parameters to…

Learning to predict solutions to real-valued combinatorial graph problems promises efficient approximations. As demonstrated based on the NP-hard edge clique cover number, recurrent neural networks (RNNs) are particularly suited for this…

Recent research works for solving partial differential equations (PDEs) with deep neural networks (DNNs) have demonstrated that spatiotemporal function approximators defined by auto-differentiation are effective for approximating nonlinear…

We proposed the boundary-integral type neural networks (BINN) for the boundary value problems in computational mechanics. The boundary integral equations are employed to transfer all the unknowns to the boundary, then the unknowns are…

Solving high-frequency oscillatory partial differential equations (PDEs) is a critical challenge in scientific computing, with applications in fluid mechanics, quantum mechanics, and electromagnetic wave propagation. Traditional…

We propose a conservative energy method based on neural networks with subdomains for solving variational problems (CENN), where the admissible function satisfying the essential boundary condition without boundary penalty is constructed by…

This study introduces an accelerated training method for Vanilla Physics-Informed-Neural-Networks (PINN) addressing three factors that imbalance the loss function: initial weight state of a neural network, domain to boundary points ratio,…

Approximation capabilities of shallow neural networks (SNNs) form an integral part in understanding the properties of deep neural networks (DNNs). In the study of these approximation capabilities some very popular classes of target…

Recent methods for boundary or edge detection built on Deep Convolutional Neural Networks (CNNs) typically suffer from the issue of predicted edges being thick and need post-processing to obtain crisp boundaries. Highly imbalanced…

Physics-informed neural networks have attracted significant attention in scientific machine learning for their capability to solve forward and inverse problems governed by partial differential equations. However, the accuracy of PINN…

We introduce Structure Informed Neural Networks (SINNs), a novel method for solving boundary observation problems involving PDEs. The SINN methodology is a data-driven framework for creating approximate solutions to internal variables on…

This work addresses the scattering problem of an incident wave at a junction connecting two semi-infinite waveguides, which we intend to solve using Physics-Informed Neural Networks (PINNs). As with other deep learning-based approaches,…

A new method to solve computationally challenging (random) parametric obstacle problems is developed and analyzed, where the parameters can influence the related partial differential equation (PDE) and determine the position and surface…

We extend the method of layer potentials to manifolds with boundary and cylindrical ends. To obtain this extension along the classical lines, we have to deal with several technical difficulties due to the non-compactness of the boundary,…

Optimizing deep neural networks (DNNs) often suffers from the ill-conditioned problem. We observe that the scaling-based weight space symmetry property in rectified nonlinear network will cause this negative effect. Therefore, we propose to…

With the remarkable empirical success of neural networks across diverse scientific disciplines, rigorous error and convergence analysis are also being developed and enriched. However, there has been little theoretical work focusing on…

Convolutional Neural Networks (CNNs) have recently led to incredible breakthroughs on a variety of pattern recognition problems. Banks of finite impulse response filters are learned on a hierarchy of layers, each contributing more abstract…