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The prohibitive cost and low fidelity of experimental data in industry scale thermofluid systems limit the usefulness of pure data-driven machine learning methods. Physics-informed neural networks (PINN) strive to overcome this by embedding…
Information on natural phenomena and engineering systems is typically contained in data. Data can be corrupted by systematic errors in models and experiments. In this paper, we propose a tool to uncover the spatiotemporal solution of the…
Three dimensional convolutional neural networks (3DCNNs) have been applied in many tasks, e.g., video and 3D point cloud recognition. However, due to the higher dimension of convolutional kernels, the space complexity of 3DCNNs is generally…
In this paper, we propose a constrained linear data-feature mapping model as an interpretable mathematical model for image classification using convolutional neural network (CNN) such as the ResNet. From this viewpoint, we establish the…
Many DNN-enabled vision applications constantly operate under severe energy constraints such as unmanned aerial vehicles, Augmented Reality headsets, and smartphones. Designing DNNs that can meet a stringent energy budget is becoming…
We introduce a simplified model of the electron-beam/plasma system to model the electrical breakdown caused by the inductive electric field created by a rapidly rising electron beam current. The rigid-beam model is a reduction to the…
Physics-informed neural networks have been widely applied to partial differential equations with great success because the physics-informed loss essentially requires no observations or discretization. However, it is difficult to optimize…
In this paper we apply neural networks with local converging inputs (NNLCI), originally introduced in [arXiv:2109.09316], to solve the two dimensional Maxwell's equation around perfect electric conductors (PECs). The input to the networks…
Real-world visual data exhibit intrinsic hierarchical structures that can be represented effectively in hyperbolic spaces. Hyperbolic neural networks (HNNs) are a promising approach for learning feature representations in such spaces.…
Physics informed neural networks (PINNs) have emerged as a powerful tool to provide robust and accurate approximations of solutions to partial differential equations (PDEs). However, PINNs face serious difficulties and challenges when…
The simulation of power system dynamics poses a computationally expensive task. Considering the growing uncertainty of generation and demand patterns, thousands of scenarios need to be continuously assessed to ensure the safety of power…
Despite the great promise of the physics-informed neural networks (PINNs) in solving forward and inverse problems, several technical challenges are present as roadblocks for more complex and realistic applications. First, most existing…
Under a particular choice of the Ernst potential, we solve analytically the Einstein-Maxwell equations to derive a new exact solution depending on five parameters: the mass, the angular-momentum (per unit mass), the electromagnetic-field…
Graph neural networks (GNNs) naturally align with sparse operators and unstructured discretizations, making them a promising paradigm for physics-informed machine learning in computational mechanics. Motivated by discrete physics losses and…
We introduce a practical method to enforce partial differential equation (PDE) constraints for functions defined by neural networks (NNs), with a high degree of accuracy and up to a desired tolerance. We develop a differentiable…
Geophysical inversion attempts to estimate the distribution of physical properties in the Earth's interior from observations collected at or above the surface. Inverse problems are commonly posed as least-squares optimization problems in…
Physics-Informed Neural Networks (PINNs) have enabled significant improvements in modelling physical processes described by partial differential equations (PDEs). PINNs are based on simple architectures, and learn the behavior of complex…
Lagrangian Neural Networks (LNNs) are a powerful tool for addressing physical systems, particularly those governed by conservation laws. LNNs can parametrize the Lagrangian of a system to predict trajectories with nearly conserved energy.…
We combine concepts from multilevel solvers for partial differential equations (PDEs) with neural network based deep learning and propose a new methodology for the efficient numerical solution of high-dimensional parametric PDEs. An…
We propose a novel method for fast and accurate training of physics-informed neural networks (PINNs) to find solutions to boundary value problems (BVPs) and initial boundary value problems (IBVPs). By combining the methods of training deep…