Related papers: Fourier Neural Operators for Arbitrary Resolution …

Four-dimensional variational data assimilation (4DVAR) is a cornerstone of numerical weather prediction, but its cost function is difficult to optimize and computationally intensive. We propose a neural field-based reformulation in which…

Reduced-order modeling is an efficient approach for solving parameterized discrete partial differential equations when the solution is needed at many parameter values. An offline step approximates the solution space and an online step…

We introduce a two-stage probabilistic framework for statistical downscaling using unpaired data. Statistical downscaling seeks a probabilistic map to transform low-resolution data from a biased coarse-grained numerical scheme to…

Owing to the remarkable development of deep learning technology, there have been a series of efforts to build deep learning-based climate models. Whereas most of them utilize recurrent neural networks and/or graph neural networks, we design…

Scientists conduct large-scale simulations to compute derived quantities-of-interest (QoI) from primary data. Often, QoI are linked to specific features, regions, or time intervals, such that data can be adaptively reduced without…

Thermal state reconstruction -- reversing convection to recover the thermal structure of the mantle at an earlier geologic time -- is an important tool to understand the evolution of mantle convection and its relation to seismic tomographic…

Numerical simulation of ordinary differential equations (ODEs) can be challenging when the system exhibits high accelerations and rapidly changing dynamics. Under these conditions the ODE solver often needs to take very small time steps in…

Deep learning offers promising capabilities for the statistical downscaling of climate and weather forecasts, with generative approaches showing particular success in capturing fine-scale precipitation patterns. However, most existing…

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…

High-fidelity simulations of laser welding capture complex thermo-fluid phenomena, including phase change, free-surface deformation, and keyhole dynamics, however their computational cost limits large-scale process exploration and real-time…

In meteorology, engineering and computer sciences, data assimilation is routinely employed as the optimal way to combine noisy observations with prior model information for obtaining better estimates of a state, and thus better forecasts,…

Fast and accurate underwater acoustic charting is crucial for downstream tasks such as environment-aware sensor placement optimization and autonomous vehicle path planning. Conventional methods rely on computationally expensive while…

Score-based stochastic denoising models have recently been demonstrated as powerful machine learning tools for conditional and unconditional image generation. The existing methods are based on a forward stochastic process wherein the…

Using simulations or experiments performed at some set of temperatures to learn about the physics or chemistry at some other arbitrary temperature is a problem of immense practical and theoretical relevance. Here we develop a framework…

In recent years, the concept of introducing physics to machine learning has become widely popular. Most physics-inclusive ML-techniques however are still limited to a single geometry or a set of parametrizable geometries. Thus, there…

Accurate quantification of uncertainty in neural network predictions remains a central challenge for scientific applications involving high-dimensional, correlated data. While existing methods capture either aleatoric or epistemic…

In this work, we propose a data-driven approach to optimize the parameters of a simulation such that control policies can be directly transferred from simulation to a real-world quadrotor. Our neural network-based policies take only onboard…

Robust generalization under climate change remains a major challenge for machine learning applications in climate science. Most existing approaches struggle to extrapolate beyond the climate they were trained on, leading to a strong…

We are interested in a reduced order method for the efficient simulation of blood flow in arteries. The blood dynamics is modeled by means of the incompressible Navier-Stokes equations. Our algorithm is based on an approximated…

FourNetFlows, the abbreviation of Fourier Neural Network for Airfoil Flows, is an efficient model that provides quick and accurate predictions of steady airfoil flows. We choose the Fourier Neural Operator (FNO) as the backbone architecture…