Related papers: KITINet: Kinetics Theory Inspired Network Architec…

We introduce a Lattice-Boltzmann-driven kinetic physics-informed neural network (K-PINN) for predictive modeling of droplet dynamics on structured surfaces, in which the discrete Boltzmann-BGK equation is incorporated into the learning…

Modeling the traffic dynamics is essential for understanding and predicting the traffic spatiotemporal evolution. However, deriving the partial differential equation (PDE) models that capture these dynamics is challenging due to their…

We consider using deep neural networks to solve time-dependent partial differential equations (PDEs), where multi-scale processing is crucial for modeling complex, time-evolving dynamics. While the U-Net architecture with skip connections…

Physics-informed neural network architectures have emerged as a powerful tool for developing flexible PDE solvers which easily assimilate data, but face challenges related to the PDE discretization underpinning them. By instead adapting a…

In this paper, we propose two hybrid quantum-inspired neural networks with adaptive residual and dense connections respectively for pattern recognition. We explain the frameworks of the symmetrical circuit models in the quantum-inspired…

We propose characteristics-informed neural networks (CINN), a simple and efficient machine learning approach for solving forward and inverse problems involving hyperbolic PDEs. Like physics-informed neural networks (PINN), CINN is a…

Residual networks (ResNets) are a deep learning architecture that substantially improved the state of the art performance in certain supervised learning tasks. Since then, they have received continuously growing attention. ResNets have a…

Real-time continuous learning over streaming data remains a central challenge in deep learning and AI systems. Traditional gradient-based models such as backpropagation through time (BPTT) face computational and stability limitations when…

In this paper we develop a kernel density estimation (KDE) approach to modeling and forecasting recurrent trajectories on a compact manifold. For the purposes of this paper, a trajectory is a sequence of coordinates in a phase space defined…

Flow-based generative models can be viewed through a physics lens: sampling transports a particle from noise to data by integrating a time-varying velocity field, and each sample corresponds to a trajectory with its own dynamical effort.…

Spatiotemporal partial differential equations (PDEs) underpin a wide range of scientific and engineering applications. Neural PDE solvers offer a promising alternative to classical numerical methods. However, existing approaches typically…

We present a new physics informed neural network (PINN) algorithm for solving brittle fracture problems. While most of the PINN algorithms available in the literature minimize the residual of the governing partial differential equation, the…

Chemical kinetics and reaction engineering consists of the phenomenological framework for the disentanglement of reaction mechanisms, optimization of reaction performance and the rational design of chemical processes. Here, we utilize…

In dynamic positron emission tomography (PET) reconstruction, the importance of leveraging the temporal dependence of the data has been well appreciated. Current deep-learning solutions can be categorized in two groups in the way the…

Understanding the nature of the changes exhibited by evolving neuronal dynamics from high-dimensional activity data is essential for advancing neuroscience, particularly in the study of neuronal network development and the pathophysiology…

The residual loss in Physics-Informed Neural Networks (PINNs) alters the simple recursive relation of layers in a feed-forward neural network by applying a differential operator, resulting in a loss landscape that is inherently different…

We propose a new method for spatio-temporal forecasting on arbitrarily distributed points. Assuming that the observed system follows an unknown partial differential equation, we derive a continuous-time model for the dynamics of the data…

Biologically-informed neural networks (BINNs), an extension of physics-informed neural networks [1], are introduced and used to discover the underlying dynamics of biological systems from sparse experimental data. In the present work, BINNs…

Various architectures (such as GoogLeNets, ResNets, and DenseNets) have been proposed. However, the existing networks usually suffer from either redundancy of convolutional layers or insufficient utilization of parameters. To handle these…

We propose a partial differential-integral equation (PDE) framework for deep neural networks (DNNs) and their associated learning problem by taking the continuum limits of both network width and depth. The proposed model captures the…