Related papers: Neural Operators for Accelerating Scientific Simul…
Neural operators have become increasingly popular in solving \textit{partial differential equations} (PDEs) due to their superior capability to capture intricate mappings between function spaces over complex domains. However, the…
Long-term fluid dynamics forecasting is a critically important problem in science and engineering. While neural operators have emerged as a promising paradigm for modeling systems governed by partial differential equations (PDEs), they…
We present a neural-operator-accelerated concurrent multiscale framework that couples atomistic simulations with continuum finite-element analysis for history-dependent materials, thereby making atomistic-continuum multiscale simulations of…
The spatiotemporal resolution of Partial Differential Equations (PDEs) plays important roles in the mathematical description of the world's physical phenomena. In general, scientists and engineers solve PDEs numerically by the use of…
Large-scale numerical simulations are used across many scientific disciplines to facilitate experimental development and provide insights into underlying physical processes, but they come with a significant computational cost. Deep neural…
Scientific machine learning is an emerging field that broadly describes the combination of scientific computing and machine learning to address challenges in science and engineering. Within the context of differential equations, this has…
We examine a variety of numerical methods that arise when considering dynamical systems in the context of physics-based simulations of deformable objects. Such problems arise in various applications, including animation, robotics, control…
Fourier Neural Operators (FNOs) excel on tasks using functional data, such as those originating from partial differential equations. Such characteristics render them an effective approach for simulating the time evolution of quantum…
Particle accelerators are enabling tools for scientific exploration and discovery in various disciplines. Finding optimized operation points for these complex machines is a challenging task, however, due to the large number of parameters…
Neural operators have emerged as powerful surrogates for the solution of partial differential equations (PDEs), yet their ability to handle general, highly variable boundary conditions (BCs) remains limited. Existing approaches often fail…
The precise simulation of turbulent flows is of immense importance in a variety of scientific and engineering fields, including climate science, freshwater science, and the development of energy-efficient manufacturing processes. Within the…
Dynamical systems see widespread use in natural sciences like physics, biology, chemistry, as well as engineering disciplines such as circuit analysis, computational fluid dynamics, and control. For simple systems, the differential…
Exascale computing holds great opportunities for molecular dynamics (MD) simulations. However, to take full advantage of the new possibilities, we must learn how to focus computational power on the discovery of complex molecular mechanisms,…
Partial differential equations (PDEs) are ubiquitous in the world around us, modelling phenomena from heat and sound to quantum systems. Recent advances in deep learning have resulted in the development of powerful neural solvers; however,…
In the design of engineered components, rigorous vibration testing is essential for performance validation and identification of resonant frequencies and amplitudes encountered during operation. Performing this evaluation numerically via…
This work introduces a neural operator based surrogate modeling framework for neutron transport computation. Two architectures, the Deep Operator Network (DeepONet) and the Fourier Neural Operator (FNO), were trained for fixed source…
In many neuromorphic workflows, simulators play a vital role for important tasks such as training spiking neural networks (SNNs), running neuroscience simulations, and designing, implementing and testing neuromorphic algorithms. Currently…
This paper proposes an integrated approach combining computer networks and artificial neural networks to construct an intelligent network operator, functioning as an AI model. State information from computer networks is transformed into…
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…
In this work, we propose a novel framework to enhance the efficiency and accuracy of neural operators through self-composition, offering both theoretical guarantees and practical benefits. Inspired by iterative methods in solving numerical…