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The use of machine learning in fluid dynamics is becoming more common to expedite the computation when solving forward and inverse problems of partial differential equations. Yet, a notable challenge with existing convolutional neural…

Physical systems whose dynamics are governed by partial differential equations (PDEs) find applications in numerous fields, from engineering design to weather forecasting. The process of obtaining the solution from such PDEs may be…

Quantum computational fluid dynamics (QCFD) offers a promising alternative to classical computational fluid dynamics (CFD) by leveraging quantum algorithms for higher efficiency. This paper introduces a comprehensive QCFD method, including…

Recently, physics informed neural networks (PINNs) have been explored extensively for solving various forward and inverse problems and facilitating querying applications in fluid mechanics applications. However, work on PINNs for unsteady…

Is a deep learning model capable of understanding systems governed by certain first principle laws by only observing the system's output? Can deep learning learn the underlying physics and honor the physics when making predictions? The…

The convergence of statistical learning and molecular physics is transforming our approach to modeling biomolecular systems. Physics-informed machine learning (PIML) offers a systematic framework that integrates data-driven inference with…

A critical factor in adopting machine learning for time-sensitive financial tasks is computational speed, including model training and inference. This paper demonstrates that a broad class of such problems, especially those previously…

Physics-Informed Neural Networks (PINNs) have shown great potential in the context of fluid dynamics simulations, particularly in reconstructing flow fields and identifying key parameters. In this study, we explore the application of PINNs…

Physics-informed neural networks (PINNs) have gained prominence for their capability to tackle supervised learning tasks that conform to physical laws, notably nonlinear partial differential equations (PDEs). This paper presents…

Partial differential equation (PDE) simulation holds extensive significance in scientific research. Currently, the integration of deep neural networks to learn solution operators of PDEs has introduced great potential. In this paper, we…

Machine learning methods have been successful in many areas, like image classification and natural language processing. However, it still needs to be determined how to apply ML to areas with mathematical constraints, like solving PDEs.…

Traditional data-driven deep learning models often struggle with high training costs, error accumulation, and poor generalizability in complex physical processes. Physics-informed deep learning (PiDL) addresses these challenges by…

Numerical discretisations of partial differential equations (PDEs) can be written as discrete convolutions, which, themselves, are a key tool in AI libraries and used in convolutional neural networks (CNNs). We therefore propose to…

Deep learning has shown great potential for modeling the physical dynamics of complex particle systems such as fluids. Existing approaches, however, require the supervision of consecutive particle properties, including positions and…

Reaction-diffusion (RD) systems provide fundamental models for understanding self-organized spatiotemporal patterns across natural and engineered settings, yet reliable parameter estimation remains challenging, particularly when…

Physics-Informed Neural Networks (PINN) has evolved into a powerful tool for solving partial differential equations, which has been applied to various fields such as energy, environment, en-gineering, etc. When utilizing PINN to solve…

Physics-informed neural networks (PINNs) have emerged as a promising approach to solving partial differential equations (PDEs) using neural networks, particularly in data-scarce scenarios, due to their unsupervised training capability.…

We leverage Physics-Informed Neural Networks (PINNs) to learn solution functions of parametric Navier-Stokes Equations (NSE). Our proposed approach results in a feasible optimization problem setup that bypasses PINNs' limitations in…

This paper introduces a novel approach to solve inverse problems by leveraging deep learning techniques. The objective is to infer unknown parameters that govern a physical system based on observed data. We focus on scenarios where the…

We study the combination of the alternating direction method of multipliers (ADMM) with physics-informed neural networks (PINNs) for a general class of nonsmooth partial differential equation (PDE)-constrained optimization problems, where…