The large-scale simulation of dynamical systems is critical in numerous scientific and
engineering disciplines. However, traditional numerical solvers are limited by the choice of …

Ensemble-based large-scale simulation of dynamical systems is essential to a wide range of
science and engineering problems. Conventional numerical solvers used in the simulation …

This paper provides a new avenue for exploiting deep neural networks to improve physics-
based simulation. Specifically, we integrate the classic Lagrangian mechanics with a deep …

Simulating physical systems is a core component of scientific computing, encompassing a
wide range of physical domains and applications. Recently, there has been a surge in data …

Recently, a lot of papers proposed to use neural networks to approximately solve partial
differential equations (PDEs). Yet, there has been a lack of flexible framework for convenient …

Solving partial differential equations (PDE) is an indispensable part of many branches of
science as many processes can be modelled in terms of PDEs. However, recent numerical …

Neural networks have shown promising potential in accelerating the numerical simulation of
systems governed by partial differential equations (PDEs). While many of the existing neural …

Democratization of machine learning requires architectures that automatically adapt to new
problems. Neural Differential Equations (NDEs) have emerged as a popular modeling …

Neural networks have shown promising potential in accelerating the numerical simulation of
systems governed by partial differential equations (PDEs). Different from many existing …

Neural ordinary differential equations (neural ODEs) have emerged as a novel network
architecture that bridges dynamical systems and deep learning. However, the gradient …