Related papers: On the Limitations of Physics-informed Deep Learni…

Flash floods in urban areas occur with increasing frequency. Detecting these floods would greatlyhelp alleviate human and economic losses. However, current flood prediction methods are eithertoo slow or too simplified to capture the flood…

Deep learning has revolutionized the field of computer vision by introducing large scale neural networks with millions of parameters. Training these networks requires massive datasets and leads to intransparent models that can fail to…

Nowadays, Computational Fluid Dynamics (CFD) is a fundamental tool for industrial design. However, the computational cost of doing such simulations is expensive and can be detrimental for real-world use cases where many simulations are…

Physics-based numerical models have been the bedrock of atmospheric sciences for decades, offering robust solutions but often at the cost of significant computational resources. Deep learning (DL) models have emerged as powerful tools in…

Computational fluid dynamics (CFD) is a powerful tool for modeling turbulent flow and is commonly used for urban microclimate simulations. However, traditional CFD methods are computationally intensive, requiring substantial hardware…

Physics-informed neural networks (PINNs) as a means of discretizing partial differential equations (PDEs) are garnering much attention in the Computational Science and Engineering (CS&E) world. At least two challenges exist for PINNs at…

Physics-informed neural network (PINN) is a data-driven solver for partial and ordinary differential equations(ODEs/PDEs). It provides a unified framework to address both forward and inverse problems. However, the complexity of the…

In the realm of computational fluid dynamics, traditional numerical methods, which heavily rely on discretization, typically necessitate the formulation of partial differential equations (PDEs) in conservative form to accurately capture…

Foundation models for partial differential equations (PDEs) have emerged as powerful surrogates pre-trained on diverse physical systems, but adapting them to new downstream tasks remains challenging due to limited task-specific data and…

Physics Informed Neural Networks is a numerical method which uses neural networks to approximate solutions of partial differential equations. It has received a lot of attention and is currently used in numerous physical and engineering…

The simulation of traffic flow on networks requires knowledge on the behavior across traffic intersections. For macroscopic models based on hyperbolic conservation laws there exist nowadays many ad-hoc models describing this behavior. Based…

Physics-informed neural networks (PINNs) represent a new paradigm for solving partial differential equations (PDEs) by integrating physical laws into the learning process of neural networks. However, ensuring that such frameworks fully…

In this paper, we combine deep learning concepts and some proper orthogonal decomposition (POD) model reduction methods for predicting flow in heterogeneous porous media. Nonlinear flow dynamics is studied, where the dynamics is regarded as…

Driven by advancements in sensing and computing, deep reinforcement learning (DRL)-based methods have demonstrated significant potential in effectively tackling distribution system restoration (DSR) challenges under uncertain operational…

With the increases in computational power and advances in machine learning, data-driven learning-based methods have gained significant attention in solving PDEs. Physics-informed neural networks (PINNs) have recently emerged and succeeded…

Deep learning (DL) models for spatio-temporal traffic flow forecasting employ convolutional or graph-convolutional filters along with recurrent neural networks to capture spatial and temporal dependencies in traffic data. These models, such…

The increasing demand for autonomous systems in complex and dynamic environments has driven significant research into intelligent path planning methodologies. For decades, graph-based search algorithms, linear programming techniques, and…

Conservation laws are considered to be fundamental laws of nature. It has broad applications in many fields, including physics, chemistry, biology, geology, and engineering. Solving the differential equations associated with conservation…

Deep kernel learning is a promising combination of deep neural networks and nonparametric function learning. However, as a data driven approach, the performance of deep kernel learning can still be restricted by scarce or insufficient data,…

Accurate risk quantification and reachability analysis are crucial for safe control and learning, but sampling from rare events, risky states, or long-term trajectories can be prohibitively costly. Motivated by this, we study how to…