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Approximating solutions to partial differential equations (PDEs) is fundamental for the modeling of dynamical systems in science and engineering. Physics-informed neural networks (PINNs) are a recent machine learning-based approach, for…

The physics informed neural network (PINN) is evolving as a viable method to solve partial differential equations. In the recent past PINNs have been successfully tested and validated to find solutions to both linear and non-linear partial…

Physics-Informed Neural Networks have emerged as a promising methodology for solving PDEs, gaining significant attention in computer science and various physics-related fields. Despite being demonstrated the ability to incorporate the…

This work introduces Physics-informed State-space neural network Models (PSMs), a novel solution to achieving real-time optimization, flexibility, and fault tolerance in autonomous systems, particularly in transport-dominated systems such…

Deep learning has become a pivotal technology in fields such as computer vision, scientific computing, and dynamical systems, significantly advancing these disciplines. However, neural Networks persistently face challenges related to…

Physics-Informed Neural Networks (PINNs) offer a promising approach to solving differential equations and, more generally, to applying deep learning to problems in the physical sciences. We adopt a recently developed transfer learning…

We develop an unsupervised physics-informed neural network to solve saddle-point equations (SPEs) governing direct above-threshold ionization (ATI) within the strong-field approximation. This setting provides a well-understood testbed in…

In this paper, we evaluate the effectiveness of deep operator networks (DeepONets) in solving both forward and inverse problems of partial differential equations (PDEs) on unknown manifolds. By unknown manifolds, we identify the manifold by…

We present a data-enabled physics-informed neural network (DEPINN) with comprehensive numerical study for solving industrial scale neutron diffusion eigenvalue problems (NDEPs). In order to achieve an engineering acceptable accuracy for…

Parameterized partial differential equations (PDEs) underpin the mathematical modeling of complex systems in diverse domains, including engineering, healthcare, and physics. A central challenge in using PDEs for real-world applications is…

Mixed-dimensional partial differential equations (PDEs) are characterized by coupled operators defined on domains of varying dimensions and pose significant computational challenges due to their inherent ill-conditioning. Moreover, the…

Partial differential equations (PDEs) are central to scientific modeling. Modern workflows increasingly rely on learning-based components to support model reuse, inference, and integration across large computational processes. Despite the…

This work presents a physics-driven machine learning framework for the simulation of acoustic scattering problems. The proposed framework relies on a physics-informed neural network (PINN) architecture that leverages prior knowledge based…

This work introduces a new approach for accelerating the numerical analysis of time-domain partial differential equations (PDEs) governing complex physical systems. The methodology is based on a combination of a classical reduced-order…

Computational simulations of wildfire spread typically employ empirical rate-of-spread calculations under various conditions (such as terrain, fuel type, weather). Small perturbations in conditions can often lead to significant changes in…

Physics-informed deep operator networks (DeepONets) have emerged as a promising approach toward numerically approximating the solution of partial differential equations (PDEs). In this work, we aim to develop further understanding of what…

In various engineering and applied science applications, repetitive numerical simulations of partial differential equations (PDEs) for varying input parameters are often required (e.g., aircraft shape optimization over many design…

The widespread use of neural networks across different scientific domains often involves constraining them to satisfy certain symmetries, conservation laws, or other domain knowledge. Such constraints are often imposed as soft penalties…

Physics informed neural networks (PINNs) are nowadays used as efficient machine learning methods for solving differential equations. However, vanilla-PINNs fail to learn complex problems as ones involving stiff ordinary differential…

We deal with the solution of the forward problem for high-dimensional parabolic PDEs with random feature (projection) neural networks (RFNNs). We first prove that there exists a single-hidden layer neural network with randomized…