Related papers: Waveformer for modelling dynamical systems
With massive advancements in sensor technologies and Internet-of-things, we now have access to terabytes of historical data; however, there is a lack of clarity in how to best exploit the data to predict future events. One possible…
The solution of a partial differential equation can be obtained by computing the inverse operator map between the input and the solution space. Towards this end, we introduce a \textit{multiwavelet-based neural operator learning scheme}…
Deep neural operators are recognized as an effective tool for learning solution operators of complex partial differential equations (PDEs). As compared to laborious analytical and computational tools, a single neural operator can predict…
Data-driven modeling techniques have been explored in the spatial-temporal modeling of complex dynamical systems for many engineering applications. However, a systematic approach is still lacking to leverage the information from different…
Recent years have seen a surge in data-driven surrogates for dynamical systems that can be orders of magnitude faster than numerical solvers. However, many machine learning-based models such as neural operators exhibit spectral bias,…
Seismic waveform modeling is a powerful tool for determining earth structure models and unraveling earthquake rupture processes, but it is usually computationally expensive. We introduce a scheme to vastly accelerate these calculations with…
We present an end-to-end framework to learn partial differential equations that brings together initial data production, selection of boundary conditions, and the use of physics-informed neural operators to solve partial differential…
Numerically solving partial differential equations typically requires fine discretization to resolve necessary spatiotemporal scales, which can be computationally expensive. Recent advances in deep learning have provided a new approach to…
Transformer-based architectures have advanced medical image analysis by effectively modeling long-range dependencies, yet they often struggle in 3D settings due to substantial memory overhead and insufficient capture of fine-grained local…
Neural operator learning models have emerged as very effective surrogates in data-driven methods for partial differential equations (PDEs) across different applications from computational science and engineering. Such operator learning…
We propose a high-order spacetime wavelet method for the solution of nonlinear partial differential equations with a user-prescribed accuracy. The technique utilizes wavelet theory with a priori error estimates to discretize the problem in…
High-frequency features are critical in multiscale phenomena such as turbulent flows and phase transitions, since they encode essential physical information. The recently proposed Wavelet Neural Operator (WNO) utilizes wavelets'…
Seismic wave propagation forms the basis for most aspects of seismological research, yet solving the wave equation is a major computational burden that inhibits the progress of research. This is exacerbated by the fact that new simulations…
Numerical simulations of seismic wave propagation are crucial for investigating velocity structures and improving seismic hazard assessment. However, standard methods such as finite difference or finite element are computationally…
Data-driven learning of partial differential equations' solution operators has recently emerged as a promising paradigm for approximating the underlying solutions. The solution operators are usually parameterized by deep learning models…
In recent years, deep learning for modeling physical phenomena which can be described by partial differential equations (PDEs) have received significant attention. For example, for learning Hamiltonian mechanics, methods based on deep…
Deep learning utilizing transformers has recently achieved a lot of success in many vital areas such as natural language processing, computer vision, anomaly detection, and recommendation systems, among many others. Among several merits of…
This paper focuses on investigating the learning operators for identifying weak solutions to the Navier-Stokes equations. Our objective is to establish a connection between the initial data as input and the weak solution as output. To…
Numerical simulations of seismic wave propagation in heterogeneous 3D media are central to investigating subsurface structures and understanding earthquake processes, yet are computationally expensive for large problems. This is…
This work introduces the Wavelet-Laplace Neural Operator (WLNO), a novel neural operator that fuses Haar wavelet multi-scale spatial decomposition with the Laplace-domain pole-residue formulation of the Laplace Neural Operator (LNO). While…