Related papers: Fast Modeling and Understanding Fluid Dynamics Sys…

Humans gain an implicit understanding of physical laws through observing and interacting with the world. Endowing an autonomous agent with an understanding of physical laws through experience and observation is seldom practical: we should…

The representation of nonlinear sub-grid processes, especially clouds, has been a major source of uncertainty in climate models for decades. Cloud-resolving models better represent many of these processes and can now be run globally but…

Fluid dynamics spans phenomena from the Cheerios effect to cosmic evolution and has been called the 'queen mother' of science. Traditional modelling relies on numerical methods, including finite differences, volumes, and elements, that…

This script offers an implementation-oriented introduction to deep learning methods for solving and estimating high-dimensional dynamic stochastic models in economics and finance. Its starting point is the curse of dimensionality:…

We propose a novel denoising diffusion generative model for predicting nonlinear fluid fields named FluidDiff. By performing a diffusion process, the model is able to learn a complex representation of the high-dimensional dynamic system,…

Data driven models of dynamical systems help planners and controllers to provide more precise and accurate motions. Most model learning algorithms will try to minimize a loss function between the observed data and the model's predictions.…

Modeling and simulation of complex fluid flows with dynamics that span multiple spatio-temporal scales is a fundamental challenge in many scientific and engineering domains. Full-scale resolving simulations for systems such as highly…

We propose a method for learning dynamical systems from high-dimensional empirical data that combines variational autoencoders and (spatio-)temporal attention within a framework designed to enforce certain scientifically-motivated…

The steep computational cost of diffusion models at inference hinders their use as fast physics emulators. In the context of image and video generation, this computational drawback has been addressed by generating in the latent space of an…

Deep learning has been widely used within learning algorithms for robotics. One disadvantage of deep networks is that these networks are black-box representations. Therefore, the learned approximations ignore the existing knowledge of…

Dynamical systems are found in innumerable forms across the physical and biological sciences, yet all these systems fall naturally into universal equivalence classes: conservative or dissipative, stable or unstable, compressible or…

Learning the dynamics of robots from data can help achieve more accurate tracking controllers, or aid their navigation algorithms. However, when the actual dynamics of the robots change due to external conditions, on-line adaptation of…

Fine-scale simulation of complex systems governed by multiscale partial differential equations (PDEs) is computationally expensive and various multiscale methods have been developed for addressing such problems. In addition, it is…

Fluid data completion is a research problem with high potential benefit for both experimental and computational fluid dynamics. An effective fluid data completion method reduces the required number of sensors in a fluid dynamics experiment,…

In computational fluid dynamics, there is an inevitable trade off between accuracy and computational cost. In this work, a novel multi-fidelity deep generative model is introduced for the surrogate modeling of high-fidelity turbulent flow…

Simulation techniques based on accurate and efficient representations of potential energy surfaces are urgently needed for the understanding of complex aqueous systems such as solid-liquid interfaces. Here, we present a machine learning…

Recent advances in data-generating techniques led to an explosive growth of geo-spatiotemporal data. In domains such as hydrology, ecology, and transportation, interpreting the complex underlying patterns of spatiotemporal interactions with…

Understanding the mechanisms underlying deep neural networks remains a fundamental challenge in machine learning and computer vision. One promising, yet only preliminarily explored approach, is feature inversion, which attempts to…

Recurrent neural networks have a strong inductive bias towards learning temporally compressed representations, as the entire history of a sequence is represented by a single vector. By contrast, Transformers have little inductive bias…

The numerical simulation and optimization of technical systems described by partial differential equations is expensive, especially in multi-query scenarios in which the underlying equations have to be solved for different parameters. A…