Related papers: Waveformer for modelling dynamical systems

In the growing domain of scientific machine learning, in-context operator learning has shown notable potential in building foundation models, as in this framework the model is trained to learn operators and solve differential equations…

In traditional quantitative trading practice, navigating the complicated and dynamic financial market presents a persistent challenge. Fully capturing various market variables, including long-term information, as well as essential signals…

In recent years, machine learning has been used to create data-driven solutions to problems for which an algorithmic solution is intractable, as well as fine-tuning existing algorithms. This research applies machine learning to the…

Neural operators extend data-driven models to map between infinite-dimensional functional spaces. These models have successfully solved continuous dynamical systems represented by differential equations, viz weather forecasting, fluid flow,…

Wavelets have proven to be highly successful in several signal and image processing applications. Wavelet design has been an active field of research for over two decades, with the problem often being approached from an analytical…

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…

Simulating nonlinear partial differential equations (PDEs) such as the Navier--Stokes (NS) equations remains computationally intensive, especially when implicit time integration is used to capture multiscale flow dynamics. This work…

The evolution of dynamical systems is generically governed by nonlinear partial differential equations (PDEs), whose solution, in a simulation framework, requires vast amounts of computational resources. In this work, we present a novel…

Neural Operators (NOs) are machine learning models designed to solve partial differential equations (PDEs) by learning to map between function spaces. Neural Operators such as the Deep Operator Network (DeepONet) and the Fourier Neural…

Efficient video action recognition remains a challenging problem. One large model after another takes the place of the state-of-the-art on the Kinetics dataset, but real-world efficiency evaluations are often lacking. In this work, we fill…

Analog machine learning hardware platforms promise to be faster and more energy-efficient than their digital counterparts. Wave physics, as found in acoustics and optics, is a natural candidate for building analog processors for…

Transformer-based models have achieved remarkable results in low-level vision tasks including image super-resolution (SR). However, early Transformer-based approaches that rely on self-attention within non-overlapping windows encounter…

Physics-informed neural networks and operator networks have shown promise for effectively solving equations modeling physical systems. However, these networks can be difficult or impossible to train accurately for some systems of equations.…

In this paper, we propose a novel algorithm for learning the Koopman operator of a dynamical system from a \textit{small} amount of training data. In many applications of data-driven modeling, e.g. biological network modeling,…

Operator learning, which aims to approximate maps between infinite-dimensional function spaces, is an important area in scientific machine learning with applications across various physical domains. Here we introduce the Continuous Vision…

The Transformer and its variants have been proven to be efficient sequence learners in many different domains. Despite their staggering success, a critical issue has been the enormous number of parameters that must be trained (ranging from…

Coupled partial differential equations (PDEs) are key tasks in modeling the complex dynamics of many physical processes. Recently, neural operators have shown the ability to solve PDEs by learning the integral kernel directly in…

A data-driven, model-free approach to modeling the temporal evolution of physical systems mitigates the need for explicit knowledge of the governing equations. Even when physical priors such as partial differential equations are available,…

We present the first neural network model to achieve real-time and streaming target sound extraction. To accomplish this, we propose Waveformer, an encoder-decoder architecture with a stack of dilated causal convolution layers as the…

Finding an embedding space for a linear approximation of a nonlinear dynamical system enables efficient system identification and control synthesis. The Koopman operator theory lays the foundation for identifying the nonlinear-to-linear…