Related papers: Waveformer for modelling dynamical systems

Neural operators have emerged as transformative tools for learning mappings between infinite-dimensional function spaces, offering useful applications in solving complex partial differential equations (PDEs). This paper presents a rigorous…

Transformers have reached remarkable success in sequence modeling. However, these models have efficiency issues as they need to store all the history token-level representations as memory. We present Memformer, an efficient neural network…

This paper explores the efficacy of diffusion-based generative models as neural operators for partial differential equations (PDEs). Neural operators are neural networks that learn a mapping from the parameter space to the solution space of…

A promising approach to preserving model performance in linearized transformers is to employ position-based re-weighting functions. However, state-of-the-art re-weighting functions rely heavily on target sequence lengths, making it…

Exact numerical simulations of dynamics of open quantum systems often require immense computational resources. We demonstrate that a deep artificial neural network comprised of convolutional layers is a powerful tool for predicting…

We present a numerical method which is able to approximate traveling waves (e.g. viscous profiles) in systems with hyperbolic and parabolic parts by a direct long-time forward simulation. A difficulty with long-time simulations of traveling…

Convolution neural networks (CNNs) have succeeded in compressive image sensing. However, due to the inductive bias of locality and weight sharing, the convolution operations demonstrate the intrinsic limitations in modeling the long-range…

Many phenomena in physics, including light, water waves, and sound, are described by wave equations. Given their coefficients, wave equations can be solved to high accuracy, but the presence of the wavelength scale often leads to large…

We investigate the use of deep neural networks to control complex nonlinear dynamical systems, specifically the movement of a rigid body immersed in a fluid. We solve the Navier Stokes equations with two way coupling, which gives rise to…

In the realm of computational science and engineering, constructing models that reflect real-world phenomena requires solving partial differential equations (PDEs) with different conditions. Recent advancements in neural operators, such as…

In recent years there has been a considerable drive towards data-driven analysis, discovery and control of dynamical systems. To this end, operator theoretic methods, namely, Koopman operator methods have gained a lot of interest. In…

Recent advances in machine learning establish the ability of certain neural-network architectures called neural operators to approximate maps between function spaces. Motivated by a prospect of employing them in fundamental physics, we…

Transformer has become ubiquitous due to its dominant performance in various NLP and image processing tasks. However, it lacks understanding of how to generate mathematically grounded uncertainty estimates for transformer architectures.…

Developing fast surrogates for Partial Differential Equations (PDEs) will accelerate design and optimization in almost all scientific and engineering applications. Neural networks have been receiving ever-increasing attention and…

High-order wave-making theories are becoming available but are limited to certain ranges of waves and wavemaker types in their applicability. Alternatively, machine learning can be considered to find nonlinear functional relationships.…

Incorporating the dynamics knowledge into the model is critical for achieving accurate trajectory prediction while considering the spatial and temporal characteristics of the vessel. However, existing methods rarely consider the underlying…

Operator learning has emerged as a promising tool for accelerating the solution of partial differential equations (PDEs). The Deep Operator Networks (DeepONets) represent a pioneering framework in this area: the "vanilla" DeepONet is valued…

Neural operators have emerged as powerful tools for learning solution operators of partial differential equations (PDEs). However, standard spectral methods based on Fourier transforms struggle with problems involving discontinuous…

This work explores the application of deep operator learning principles to a problem in statistical physics. Specifically, we consider the linear kinetic equation, consisting of a differential advection operator and an integral collision…

Master equations are of fundamental importance in modeling stochastic dynamical systems.However, solving master equations is challenging due to the exponential increase in the number of possible states or trajectories with the dimension of…