Related papers: On the Limitations of Physics-informed Deep Learni…
This paper investigates the limitations of neural operators in learning solutions for a Hughes model, a first-order hyperbolic conservation law system for crowd dynamics. The model couples a Fokker-Planck equation representing pedestrian…
We introduce physics informed neural networks -- neural networks that are trained to solve supervised learning tasks while respecting any given law of physics described by general nonlinear partial differential equations. In this two part…
Physics-Informed Neural Networks (PINNs) integrate physical principles into machine learning, finding wide applications in various science and engineering fields. However, solving nonlinear hyperbolic partial differential equations (PDEs)…
Particle Image Velocimetry (PIV) is a classical flow estimation problem which is widely considered and utilised, especially as a diagnostic tool in experimental fluid dynamics and the remote sensing of environmental flows. Recently, the…
Stiff differential equations are prevalent in various scientific domains, posing significant challenges due to the disparate time scales of their components. As computational power grows, physics-informed neural networks (PINNs) have led to…
Deep reinforcement learning (DRL) has recently been adopted in a wide range of physics and engineering domains for its ability to solve decision-making problems that were previously out of reach due to a combination of non-linearity and…
We present a framework for fine-tuning flow-matching generative models to enforce physical constraints and solve inverse problems in scientific systems. Starting from a model trained on low-fidelity or observational data, we apply a…
Turbulent-flow control aims to develop strategies that effectively manipulate fluid systems, such as the reduction of drag in transportation and enhancing energy efficiency, both critical steps towards reducing global CO$_2$ emissions. Deep…
Existing ineffective and inflexible traffic light control at urban intersections can often lead to congestion in traffic flows and cause numerous problems, such as long delay and waste of energy. How to find the optimal signal timing…
Deriving governing equations of complex physical systems based on first principles can be quite challenging when there are certain unknown terms and hidden physical mechanisms in the systems. In this work, we apply a deep learning…
In many scientific fields, the generation and evolution of data are governed by partial differential equations (PDEs) which are typically informed by established physical laws at the macroscopic level to describe general and predictable…
Diffusion models have recently emerged as powerful stochastic frameworks for high-dimensional inference and generation. However, existing applications to partial differential equations (PDEs) predominantly rely on physics-informed training…
The paper presents an efficient and robust data-driven deep learning (DL) computational framework developed for linear continuum elasticity problems. The methodology is based on the fundamentals of the Physics Informed Neural Networks…
In this work, we develop a method for learning interpretable, thermodynamically stable and Galilean invariant partial differential equations (PDEs) based on the Conservation-dissipation Formalism of irreversible thermodynamics. As governing…
We introduce physics informed neural networks -- neural networks that are trained to solve supervised learning tasks while respecting any given law of physics described by general nonlinear partial differential equations. In this second…
Modeling the precise dynamics of off-road vehicles is a complex yet essential task due to the challenging terrain they encounter and the need for optimal performance and safety. Recently, there has been a focus on integrating nominal…
Electric Vehicles (EVs) offer substantial flexibility for grid services, yet large-scale, uncoordinated charging can threaten voltage stability in distribution networks. Existing Reinforcement Learning (RL) approaches for smart charging…
As applications of deep learning (DL) continue to seep into critical scientific use-cases, the importance of performing uncertainty quantification (UQ) with DL has become more pressing than ever before. In scientific applications, it is…
Control theory provides engineers with a multitude of tools to design controllers that manipulate the closed-loop behavior and stability of dynamical systems. These methods rely heavily on insights about the mathematical model governing the…
Modeling nonlinear spatiotemporal dynamical systems has primarily relied on partial differential equations (PDEs). However, the explicit formulation of PDEs for many underexplored processes, such as climate systems, biochemical reaction and…