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Fluid flows are omnipresent in nature and engineering disciplines. The reliable computation of fluids has been a long-lasting challenge due to nonlinear interactions over multiple spatio-temporal scales. The compressible Navier-Stokes…

Simulating physical systems using Partial Differential Equations (PDEs) has become an indispensible part of modern industrial process optimization. Traditionally, numerical solvers have been used to solve the associated PDEs, however…

Modeling complex systems using standard neural ordinary differential equations (NODEs) often faces some essential challenges, including high computational costs and susceptibility to local optima. To address these challenges, we propose a…

Neural operators have emerged as a powerful data-driven paradigm for solving partial differential equations (PDEs), while their accuracy and scalability are still limited, particularly on irregular domains where fluid flows exhibit rich…

Climate simulations are essential in guiding our understanding of climate change and responding to its effects. However, it is computationally expensive to resolve complex climate processes at high spatial resolution. As one way to speed up…

Spatio-temporal process models are often used for modeling dynamic physical and biological phenomena that evolve across space and time. These phenomena may exhibit environmental heterogeneity and complex interactions that are difficult to…

Physically plausible fluid simulations play an important role in modern computer graphics and engineering. However, in order to achieve real-time performance, computational speed needs to be traded-off with physical accuracy. Surrogate…

Data-driven, deep-learning modeling frameworks have been recently developed for forecasting time series data. Such machine learning models may be useful in multiple domains including the atmospheric and oceanic ones, and in general, the…

Time-periodic quantum systems exhibit a rich variety of far-from-equilibrium phenomena and serve as ideal platforms for quantum engineering and control. However, simulating their dynamics with conventional numerical methods remains…

Navier-Stokes equations are significant partial differential equations that describe the motion of fluids such as liquids and air. Due to the importance of Navier-Stokes equations, the development on efficient numerical schemes is important…

Global urbanization has underscored the significance of urban microclimates for human comfort, health, and building/urban energy efficiency. They profoundly influence building design and urban planning as major environmental impacts.…

Inverse problems in fluid dynamics are ubiquitous in science and engineering, with applications ranging from electronic cooling system design to ocean modeling. We propose a general and robust approach for solving inverse problems in the…

Fourier Neural Operators (FNOs) have demonstrated exceptional accuracy in mapping functional spaces by leveraging Fourier transforms to establish a connection with underlying physical principles. However, their opaque inner workings often…

This study investigates the application of machine learning, specifically Fourier Neural Operator (FNO) and Convolutional Neural Network (CNN), to learn time-advancement operators for parametric partial differential equations (PDEs). Our…

Finding the distribution of the velocities and pressures of a fluid by solving the Navier-Stokes equations is a principal task in the chemical, energy, and pharmaceutical industries, as well as in mechanical engineering and the design of…

Crashing ocean waves, cappuccino froths and microfluidic bubble crystals are examples of foamy flows. Foamy flows are critical in numerous natural and industrial processes and remain notoriously difficult to compute as they involve coupled,…

The existence and dynamical role of particular unstable Navier-Stokes solutions (exact coherent structures) is revealed in laboratory studies of weak turbulence in a thin, electromagnetically-driven fluid layer. We find that the dynamics…

Current groundwater models face a significant challenge in their implementation due to heavy computational burdens. To overcome this, our work proposes a cost-effective emulator that efficiently and accurately forecasts the impact of…

Learning probabilistic surrogates for partial differential equations remains challenging in data-scarce regimes: neural operators require large amounts of high-fidelity data, while generative approaches typically sacrifice resolution…

We report the first systematic evidence of hallucination in AI models of fluid dynamics, demonstrated in the canonical problem of hydrodynamically unstable transport known as viscous fingering. AI-based modeling of flow with instabilities…