Related papers: Error bounds for Physics Informed Neural Networks …

Machine learning (ML) is promising in assisting technology computer-aided design (TCAD) simulations to alleviate difficulty in convergence and prolonged simulation time. While ML is widely used in TCAD, they either require access to the…

Physics-informed neural networks (PINNs) [31] use automatic differentiation to solve partial differential equations (PDEs) by penalizing the PDE in the loss function at a random set of points in the domain of interest. Here, we develop a…

Machine learning models have emerged as powerful tools in physics and engineering. Although flexible, a fundamental challenge remains on how to connect new machine learning models with known physics. In this work, we present an autoencoder…

Training deep neural networks for solving machine learning problems is one great challenge in the field, mainly due to its associated optimisation problem being highly non-convex. Recent developments have suggested that many training…

Physics-Informed Neural Networks (PINNs) combine deep learning with physical constraints for solving partial differential equations (PDEs), and are widely applied in fluid mechanics, heat transfer, and solid mechanics. However, PINN…

We present a deep learning framework for quantifying and propagating uncertainty in systems governed by non-linear differential equations using physics-informed neural networks. Specifically, we employ latent variable models to construct…

Approximate solutions of partial differential equations (PDEs) obtained by neural networks are highly affected by hyper parameter settings. For instance, the model training strongly depends on loss function design, including the choice of…

Partial Differential Equations (PDEs) are central to modeling complex systems across physical, biological, and engineering domains, yet traditional numerical methods often struggle with high-dimensional or complex problems. Physics-Informed…

In this paper we introduce and analyze the learning scenario of \emph{coupled nonlinear dimensionality reduction}, which combines two major steps of machine learning pipeline: projection onto a manifold and subsequent supervised learning.…

We explore conditions for when the gradient of a deep declarative node can be approximated by ignoring constraint terms and still result in a descent direction for the global loss function. This has important practical application when…

Physics-informed neural networks (PINNs) have emerged as a promising approach to solving partial differential equations (PDEs) using neural networks, particularly in data-scarce scenarios, due to their unsupervised training capability.…

Neural networks have shown significant potential in solving partial differential equations (PDEs). While deep networks are capable of approximating complex functions, direct one-shot training often faces limitations in both accuracy and…

Currently, deep neural networks are deployed on low-power portable devices by first training a full-precision model using powerful hardware, and then deriving a corresponding low-precision model for efficient inference on such systems.…

In this paper, we prove the output feedback stabilization for the linearized Korteweg-de Vries (KdV) equation posed on a finite domain in the case the full state of the system cannot be measured. We assume that there is a sensor at the left…

In this paper, we develop a physics-informed neural network (PINN) model for parabolic problems with a sharply perturbed initial condition. As an example of a parabolic problem, we consider the advection-dispersion equation (ADE) with a…

The Local Randomized Neural Networks with Discontinuous Galerkin (LRNN-DG) methods, introduced in [42], were originally designed for solving linear partial differential equations. In this paper, we extend the LRNN-DG methods to solve…

Surrogate modeling and uncertainty quantification tasks for PDE systems are most often considered as supervised learning problems where input and output data pairs are used for training. The construction of such emulators is by definition a…

Discrete choice models are fundamental tools in management science, economics, and marketing for understanding and predicting decision-making. Logit-based models are dominant in applied work, largely due to their convenient closed-form…

This paper explores the application of physics-informed neural networks (PINNs) to tackle forward problems in 3D contact mechanics, focusing on small deformation elasticity. We utilize a mixed-variable formulation, enhanced with output…

In recent studies, several asymptotic upper bounds on generalization errors on deep neural networks (DNNs) are theoretically derived. These bounds are functions of several norms of weights of the DNNs, such as the Frobenius and spectral…